Modeling and Estimation of Transient CarrierFrequency Offset in Wireless Transceivers

Abstract

Future remote gadgets need to backing numerous applications (eg remote apply autonomy remote computerization and versatile gaming) with amazingly low dormancy and unwavering quality prerequisites over remote associations Upgrading remote handsets while exchanging between remote associations with diverse circuit attributes obliges tending to numerous fittings disabilities that have been neglected at one time Case in point exchanging between transmission and gathering radio capacities to encourage time division duplexing can change the heap on the force supply As the supply voltage changes in light of the sudden change in load the bearer recurrence floats Such a float brings about transient bearer recurrence counterbalance (CFO) that cant be assessed by ordinary CFO estimators and is normally tended to by embeddings alternately broadening watchman interims In this paper we investigate the displaying also estimation of the transient CFO which is displayed as the reaction of an under damped second request framework To adjust for the transient CFO we propose a low unpredictability parametric estimation calculation which utilizes the invalid space of the Hankel-like network built from stage contrast of the two parts of the tedious preparing grouping Moreover to minimize the mean squared mistake of the evaluated parameters in commotion a weighted subspace fitting calculation is inferred with a slight increment in multifaceted nature The Craacutemerndashrao headed for any unprejudiced estimator of the transient CFO parameters is inferred

CHAPTER-1

INTRODUCTION

In order to satisfy the exponential growing demand of wireless multimedia services a high speed

data access is requiredTherefore various techniques have been proposed in recent years to

achieve high system capacities Among them we interest to the multiple-input multiple- output

(MIMO)The MIMO concept has attracted lot of attention in wireless communications due to its

potential to increase the system capacity without extra bandwidth Multipath propagation usually

causes selective frequency channels To combat the effect of frequency selective fading MIMO

is associated with orthogonal frequency-division multiplexing (OFDM) technique OFDM is a

modulation technique which transforms frequency selective channel into a set of parallel flat

fading channelsA cyclic prefix CP is added at the beginning of each OFDM symbol to eliminate

ICI and ISI The inserted cyclic prefix is equal to or longer than to the channel The 3GPP Long

Term Evolution (LTE) is defining the next generation radio access networkLTE Downlink

systems adopt Orthogonal Frequency Division Multiple Access (OFDMA) and MIMO to

provide up to 100 Mbps (assuming a 2x2 MIMO system with 20MHz bandwidth)

11 OFDM

Orthogonal Frequency Division Multiplex the modulation concept being used for many

wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile

Video

Orthogonal Frequency Division Multiplex or OFDM is a modulation format that is finding

increasing levels of use in todays radio communications scene OFDM has been adopted in the

Wi-Fi arena where the 80211a standard uses it to provide data rates up to 54 Mbps in the 5 GHz

ISM (Industrial Scientific and Medical) band In addition to this the recently ratified 80211g

standard has it in the 24 GHz ISM band In addition to this it is being used for WiMAX and is

also the format of choice for the next generation cellular radio communications systems

including 3G LTE and UMB

If this was not enough it is also being used for digital terrestrial television transmissions as well

as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long

medium and short wave bands is being launched and this has also adopted COFDM Then for the

future it is being proposed as the modulation technique for fourth generation cell phone systems

that are in their early stages of development and OFDM is also being used for many of the

proposed mobile phone video systems

OFDM orthogonal frequency division multiplex is a rather different format for modulation to

that used for more traditional forms of transmission It utilises many carriers together to provide

many advantages over simpler modulation formats

An OFDM signal consists of a number of closely spaced modulated carriers When modulation

of any form - voice data etc is applied to a carrier then sidebands spread out either side It is

necessary for a receiver to be able to receive the whole signal to be able to successfully

demodulate the data As a result when signals are transmitted close to one another they must be

spaced so that the receiver can separate them using a filter and there must be a guard band

between them This is not the case with OFDM Although the sidebands from each carrier

overlap they can still be received without the interference that might be expected because they

are orthogonal to each another This is achieved by having the carrier spacing equal to the

reciprocal of the symbol period

Fig11Traditional view of receiving signals carrying modulation

To see how OFDM works it is necessary to look at the receiver This acts as a bank of

demodulators translating each carrier down to DC The resulting signal is integrated over the

symbol period to regenerate the data from that carrier The same demodulator also demodulates

the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that

they will have a whole number of cycles in the symbol period and their contribution will sum to

zero - in other words there is no interference contribution

Fig12OFDM Spectrum

One requirement of the OFDM transmitting and receiving systems is that they must be linear

Any non-linearity will cause interference between the carriers as a result of inter-modulation

distortion This will introduce unwanted signals that would cause interference and impair the

orthogonality of the transmission

In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such

as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the

peaks whilst the average power is much lower and this leads to inefficiency In some systems the

peaks are limited Although this introduces distortion that results in a higher level of data errors

the system can rely on the error correction to remove them

The data to be transmitted on an OFDM signal is spread across the carriers of the signal each

carrier taking part of the payload This reduces the data rate taken by each carrier The lower data

rate has the advantage that interference from reflections is much less critical This is achieved by

adding a guard band time or guard interval into the system This ensures that the data is only

sampled when the signal is stable and no new delayed signals arrive that would alter the timing

and phase of the signal

The OFDM transmission scheme has the following key advantages __Makes efficient use of the

spectrum by allowing overlap

__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to

frequency selective fading than single carrier systems are

__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and

interleaving one can recover symbols lost due to the frequency selectivity of the channel C

hannel equalization becomes simpler than by using adaptive equalization techniques with single

carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity

as discussed in OFDM is computationally efficient by using FFT techniques to

implement the modulation and demodulation functions

__In conjunction with differential modulation there is no need to implement a channel estimator

__Is less sensitive to sample timing offsets than single carrier systems are

__Provides good protection against cochannel interference and impulsive parasitic noise

In terms of drawbacks OFDM has the following characteristics

__The OFDM signal has a noise like amplitude with a very large dynamic range

therefore it requires RF power amplifiers with a high peak to average power ratio

__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to

leakage of the DFT

12 The Standard IEEE 80211a

The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of

requirements for the physical layer (PHY) and a medium access control (MAC) layer For high

data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE

80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that

require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on

which the 80211 WLANs operate is different from wired media in many ways One of those

differences is the presence of interference in unlicensed frequency bands which can impact

communications between WLAN NICs Interference on the wireless medium can result in packet

loss which causes the network to suffer in terms of throughput performance Current 24-GHz

80211b radios handle interference well because they support a feature in the MAC layer known

as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to

increase the probability of delivering packets without errors induced by the interferer When a

frame is fragmented the sequence control field in the MAC header indicates placement of the

individual fragments and whether the current fragment is the last in the sequence When frames

are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)

control frames are used to manage the data transmission Therefore using fragmentation

esigners can avoid interference problems in their WLAN designs But interference is not the only

problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and

research laboratories all over the

world It has already been accepted for the new wireless local area network standards IEEE

80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access

Communication (MMAC) Systems Also it is expected to be used for wireless broadband

multimedia communications Data rate is really what broadband is about The new standard

specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers

for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-

and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE

80211a following the parameters established for that case OFDM can be seen as either a

modulation technique or a multiplexing technique

One of the main reasons to use OFDM is to increase the robustness against frequency selective

fading or narrowband interference In a single carrier system a single fade or interferer can cause

the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will

be affected Error correction coding can then be used to correct for the few erroneous subcarriers

The concept of using parallel data transmission and frequency division multiplexing was

published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US

patent was filed and issued in January 1970 In a classical parallel data system the total signal

frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is

modulated with a separate symbol and then the N subchannels are frequency-multiplexed It

seems good to avoid spectral overlap of channels to eliminate interchannel interference

However this leads to inefficient use of the available spectrum To cope with the inefficiency

the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping

subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid

the use of high-speed equalization and to combat impulsive noise and multipath distortion as

well as to fully use the available bandwidth

Illustrates the difference between the conventional nonoverlapping multicarrier technique and the

overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation

technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique

however we need to reduce crosstalk between subcarriers which means that we want

orthogonality between the different modulated carriers The word orthogonal indicates that there

is a precise mathematical relationship between the frequencies of the carriers in the system In a

normal frequency-division multiplex system many carriers are spaced apart in such a way that

the signals can be received using conventional filters and demodulators In such receivers guard

bands are introduced between the different carriers and in the frequency domain which results in

a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM

signal so that the sidebands of the individual carriers overlap and the signals are still received

without adjacent carrier interference To do this the carriers must be mathematically orthogonal

The receiver acts as a bank of demodulators translating each carrier down to DC with the

resulting signal integrated over a symbol period to recover the raw data If the other carriers all

beat down the frequencies that in the time domain have a whole number of cycles in the symbol

period T then the integration process results in zero contribution from all these other carriers

Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of

1T

Fig13 Spectra of an OFDM subchannel and and OFDM signal

13 Guard Interval

The distribution of the data across a large number of carriers in the OFDM signal has some

further advantages Nulls caused by multi-path effects or interference on a given frequency only

affect a small number of the carriers the remaining ones being received correctly By using

error-coding techniques which does mean adding further data to the transmitted signal it

enables many or all of the corrupted data to be reconstructed within the receiver This can be

done because the error correction code is transmitted in a different part of the signal

14 OFDM variants

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Abstract

Future remote gadgets need to backing numerous applications (eg remote apply autonomy remote computerization and versatile gaming) with amazingly low dormancy and unwavering quality prerequisites over remote associations Upgrading remote handsets while exchanging between remote associations with diverse circuit attributes obliges tending to numerous fittings disabilities that have been neglected at one time Case in point exchanging between transmission and gathering radio capacities to encourage time division duplexing can change the heap on the force supply As the supply voltage changes in light of the sudden change in load the bearer recurrence floats Such a float brings about transient bearer recurrence counterbalance (CFO) that cant be assessed by ordinary CFO estimators and is normally tended to by embeddings alternately broadening watchman interims In this paper we investigate the displaying also estimation of the transient CFO which is displayed as the reaction of an under damped second request framework To adjust for the transient CFO we propose a low unpredictability parametric estimation calculation which utilizes the invalid space of the Hankel-like network built from stage contrast of the two parts of the tedious preparing grouping Moreover to minimize the mean squared mistake of the evaluated parameters in commotion a weighted subspace fitting calculation is inferred with a slight increment in multifaceted nature The Craacutemerndashrao headed for any unprejudiced estimator of the transient CFO parameters is inferred

CHAPTER-1

INTRODUCTION

In order to satisfy the exponential growing demand of wireless multimedia services a high speed

data access is requiredTherefore various techniques have been proposed in recent years to

achieve high system capacities Among them we interest to the multiple-input multiple- output

(MIMO)The MIMO concept has attracted lot of attention in wireless communications due to its

potential to increase the system capacity without extra bandwidth Multipath propagation usually

causes selective frequency channels To combat the effect of frequency selective fading MIMO

is associated with orthogonal frequency-division multiplexing (OFDM) technique OFDM is a

modulation technique which transforms frequency selective channel into a set of parallel flat

fading channelsA cyclic prefix CP is added at the beginning of each OFDM symbol to eliminate

ICI and ISI The inserted cyclic prefix is equal to or longer than to the channel The 3GPP Long

Term Evolution (LTE) is defining the next generation radio access networkLTE Downlink

systems adopt Orthogonal Frequency Division Multiple Access (OFDMA) and MIMO to

provide up to 100 Mbps (assuming a 2x2 MIMO system with 20MHz bandwidth)

11 OFDM

Orthogonal Frequency Division Multiplex the modulation concept being used for many

wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile

Video

Orthogonal Frequency Division Multiplex or OFDM is a modulation format that is finding

increasing levels of use in todays radio communications scene OFDM has been adopted in the

Wi-Fi arena where the 80211a standard uses it to provide data rates up to 54 Mbps in the 5 GHz

ISM (Industrial Scientific and Medical) band In addition to this the recently ratified 80211g

standard has it in the 24 GHz ISM band In addition to this it is being used for WiMAX and is

also the format of choice for the next generation cellular radio communications systems

including 3G LTE and UMB

If this was not enough it is also being used for digital terrestrial television transmissions as well

as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long

medium and short wave bands is being launched and this has also adopted COFDM Then for the

future it is being proposed as the modulation technique for fourth generation cell phone systems

that are in their early stages of development and OFDM is also being used for many of the

proposed mobile phone video systems

OFDM orthogonal frequency division multiplex is a rather different format for modulation to

that used for more traditional forms of transmission It utilises many carriers together to provide

many advantages over simpler modulation formats

An OFDM signal consists of a number of closely spaced modulated carriers When modulation

of any form - voice data etc is applied to a carrier then sidebands spread out either side It is

necessary for a receiver to be able to receive the whole signal to be able to successfully

demodulate the data As a result when signals are transmitted close to one another they must be

spaced so that the receiver can separate them using a filter and there must be a guard band

between them This is not the case with OFDM Although the sidebands from each carrier

overlap they can still be received without the interference that might be expected because they

are orthogonal to each another This is achieved by having the carrier spacing equal to the

reciprocal of the symbol period

Fig11Traditional view of receiving signals carrying modulation

To see how OFDM works it is necessary to look at the receiver This acts as a bank of

demodulators translating each carrier down to DC The resulting signal is integrated over the

symbol period to regenerate the data from that carrier The same demodulator also demodulates

the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that

they will have a whole number of cycles in the symbol period and their contribution will sum to

zero - in other words there is no interference contribution

Fig12OFDM Spectrum

One requirement of the OFDM transmitting and receiving systems is that they must be linear

Any non-linearity will cause interference between the carriers as a result of inter-modulation

distortion This will introduce unwanted signals that would cause interference and impair the

orthogonality of the transmission

In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such

as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the

peaks whilst the average power is much lower and this leads to inefficiency In some systems the

peaks are limited Although this introduces distortion that results in a higher level of data errors

the system can rely on the error correction to remove them

The data to be transmitted on an OFDM signal is spread across the carriers of the signal each

carrier taking part of the payload This reduces the data rate taken by each carrier The lower data

rate has the advantage that interference from reflections is much less critical This is achieved by

adding a guard band time or guard interval into the system This ensures that the data is only

sampled when the signal is stable and no new delayed signals arrive that would alter the timing

and phase of the signal

The OFDM transmission scheme has the following key advantages __Makes efficient use of the

spectrum by allowing overlap

__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to

frequency selective fading than single carrier systems are

__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and

interleaving one can recover symbols lost due to the frequency selectivity of the channel C

hannel equalization becomes simpler than by using adaptive equalization techniques with single

carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity

as discussed in OFDM is computationally efficient by using FFT techniques to

implement the modulation and demodulation functions

__In conjunction with differential modulation there is no need to implement a channel estimator

__Is less sensitive to sample timing offsets than single carrier systems are

__Provides good protection against cochannel interference and impulsive parasitic noise

In terms of drawbacks OFDM has the following characteristics

__The OFDM signal has a noise like amplitude with a very large dynamic range

therefore it requires RF power amplifiers with a high peak to average power ratio

__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to

leakage of the DFT

12 The Standard IEEE 80211a

The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of

requirements for the physical layer (PHY) and a medium access control (MAC) layer For high

data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE

80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that

require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on

which the 80211 WLANs operate is different from wired media in many ways One of those

differences is the presence of interference in unlicensed frequency bands which can impact

communications between WLAN NICs Interference on the wireless medium can result in packet

loss which causes the network to suffer in terms of throughput performance Current 24-GHz

80211b radios handle interference well because they support a feature in the MAC layer known

as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to

increase the probability of delivering packets without errors induced by the interferer When a

frame is fragmented the sequence control field in the MAC header indicates placement of the

individual fragments and whether the current fragment is the last in the sequence When frames

are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)

control frames are used to manage the data transmission Therefore using fragmentation

esigners can avoid interference problems in their WLAN designs But interference is not the only

problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and

research laboratories all over the

world It has already been accepted for the new wireless local area network standards IEEE

80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access

Communication (MMAC) Systems Also it is expected to be used for wireless broadband

multimedia communications Data rate is really what broadband is about The new standard

specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers

for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-

and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE

80211a following the parameters established for that case OFDM can be seen as either a

modulation technique or a multiplexing technique

One of the main reasons to use OFDM is to increase the robustness against frequency selective

fading or narrowband interference In a single carrier system a single fade or interferer can cause

the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will

be affected Error correction coding can then be used to correct for the few erroneous subcarriers

The concept of using parallel data transmission and frequency division multiplexing was

published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US

patent was filed and issued in January 1970 In a classical parallel data system the total signal

frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is

modulated with a separate symbol and then the N subchannels are frequency-multiplexed It

seems good to avoid spectral overlap of channels to eliminate interchannel interference

However this leads to inefficient use of the available spectrum To cope with the inefficiency

the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping

subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid

the use of high-speed equalization and to combat impulsive noise and multipath distortion as

well as to fully use the available bandwidth

Illustrates the difference between the conventional nonoverlapping multicarrier technique and the

overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation

technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique

however we need to reduce crosstalk between subcarriers which means that we want

orthogonality between the different modulated carriers The word orthogonal indicates that there

is a precise mathematical relationship between the frequencies of the carriers in the system In a

normal frequency-division multiplex system many carriers are spaced apart in such a way that

the signals can be received using conventional filters and demodulators In such receivers guard

bands are introduced between the different carriers and in the frequency domain which results in

a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM

signal so that the sidebands of the individual carriers overlap and the signals are still received

without adjacent carrier interference To do this the carriers must be mathematically orthogonal

The receiver acts as a bank of demodulators translating each carrier down to DC with the

resulting signal integrated over a symbol period to recover the raw data If the other carriers all

beat down the frequencies that in the time domain have a whole number of cycles in the symbol

period T then the integration process results in zero contribution from all these other carriers

Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of

1T

Fig13 Spectra of an OFDM subchannel and and OFDM signal

13 Guard Interval

The distribution of the data across a large number of carriers in the OFDM signal has some

further advantages Nulls caused by multi-path effects or interference on a given frequency only

affect a small number of the carriers the remaining ones being received correctly By using

error-coding techniques which does mean adding further data to the transmitted signal it

enables many or all of the corrupted data to be reconstructed within the receiver This can be

done because the error correction code is transmitted in a different part of the signal

14 OFDM variants

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

CHAPTER-1

INTRODUCTION

In order to satisfy the exponential growing demand of wireless multimedia services a high speed

data access is requiredTherefore various techniques have been proposed in recent years to

achieve high system capacities Among them we interest to the multiple-input multiple- output

(MIMO)The MIMO concept has attracted lot of attention in wireless communications due to its

potential to increase the system capacity without extra bandwidth Multipath propagation usually

causes selective frequency channels To combat the effect of frequency selective fading MIMO

is associated with orthogonal frequency-division multiplexing (OFDM) technique OFDM is a

modulation technique which transforms frequency selective channel into a set of parallel flat

fading channelsA cyclic prefix CP is added at the beginning of each OFDM symbol to eliminate

ICI and ISI The inserted cyclic prefix is equal to or longer than to the channel The 3GPP Long

Term Evolution (LTE) is defining the next generation radio access networkLTE Downlink

systems adopt Orthogonal Frequency Division Multiple Access (OFDMA) and MIMO to

provide up to 100 Mbps (assuming a 2x2 MIMO system with 20MHz bandwidth)

11 OFDM

Orthogonal Frequency Division Multiplex the modulation concept being used for many

wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile

Video

Orthogonal Frequency Division Multiplex or OFDM is a modulation format that is finding

increasing levels of use in todays radio communications scene OFDM has been adopted in the

Wi-Fi arena where the 80211a standard uses it to provide data rates up to 54 Mbps in the 5 GHz

ISM (Industrial Scientific and Medical) band In addition to this the recently ratified 80211g

standard has it in the 24 GHz ISM band In addition to this it is being used for WiMAX and is

also the format of choice for the next generation cellular radio communications systems

including 3G LTE and UMB

If this was not enough it is also being used for digital terrestrial television transmissions as well

as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long

medium and short wave bands is being launched and this has also adopted COFDM Then for the

future it is being proposed as the modulation technique for fourth generation cell phone systems

that are in their early stages of development and OFDM is also being used for many of the

proposed mobile phone video systems

OFDM orthogonal frequency division multiplex is a rather different format for modulation to

that used for more traditional forms of transmission It utilises many carriers together to provide

many advantages over simpler modulation formats

An OFDM signal consists of a number of closely spaced modulated carriers When modulation

of any form - voice data etc is applied to a carrier then sidebands spread out either side It is

necessary for a receiver to be able to receive the whole signal to be able to successfully

demodulate the data As a result when signals are transmitted close to one another they must be

spaced so that the receiver can separate them using a filter and there must be a guard band

between them This is not the case with OFDM Although the sidebands from each carrier

overlap they can still be received without the interference that might be expected because they

are orthogonal to each another This is achieved by having the carrier spacing equal to the

reciprocal of the symbol period

Fig11Traditional view of receiving signals carrying modulation

To see how OFDM works it is necessary to look at the receiver This acts as a bank of

demodulators translating each carrier down to DC The resulting signal is integrated over the

symbol period to regenerate the data from that carrier The same demodulator also demodulates

the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that

they will have a whole number of cycles in the symbol period and their contribution will sum to

zero - in other words there is no interference contribution

Fig12OFDM Spectrum

One requirement of the OFDM transmitting and receiving systems is that they must be linear

Any non-linearity will cause interference between the carriers as a result of inter-modulation

distortion This will introduce unwanted signals that would cause interference and impair the

orthogonality of the transmission

In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such

as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the

peaks whilst the average power is much lower and this leads to inefficiency In some systems the

peaks are limited Although this introduces distortion that results in a higher level of data errors

the system can rely on the error correction to remove them

The data to be transmitted on an OFDM signal is spread across the carriers of the signal each

carrier taking part of the payload This reduces the data rate taken by each carrier The lower data

rate has the advantage that interference from reflections is much less critical This is achieved by

adding a guard band time or guard interval into the system This ensures that the data is only

sampled when the signal is stable and no new delayed signals arrive that would alter the timing

and phase of the signal

The OFDM transmission scheme has the following key advantages __Makes efficient use of the

spectrum by allowing overlap

__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to

frequency selective fading than single carrier systems are

__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and

interleaving one can recover symbols lost due to the frequency selectivity of the channel C

hannel equalization becomes simpler than by using adaptive equalization techniques with single

carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity

as discussed in OFDM is computationally efficient by using FFT techniques to

implement the modulation and demodulation functions

__In conjunction with differential modulation there is no need to implement a channel estimator

__Is less sensitive to sample timing offsets than single carrier systems are

__Provides good protection against cochannel interference and impulsive parasitic noise

In terms of drawbacks OFDM has the following characteristics

__The OFDM signal has a noise like amplitude with a very large dynamic range

therefore it requires RF power amplifiers with a high peak to average power ratio

__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to

leakage of the DFT

12 The Standard IEEE 80211a

The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of

requirements for the physical layer (PHY) and a medium access control (MAC) layer For high

data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE

80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that

require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on

which the 80211 WLANs operate is different from wired media in many ways One of those

differences is the presence of interference in unlicensed frequency bands which can impact

communications between WLAN NICs Interference on the wireless medium can result in packet

loss which causes the network to suffer in terms of throughput performance Current 24-GHz

80211b radios handle interference well because they support a feature in the MAC layer known

as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to

increase the probability of delivering packets without errors induced by the interferer When a

frame is fragmented the sequence control field in the MAC header indicates placement of the

individual fragments and whether the current fragment is the last in the sequence When frames

are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)

control frames are used to manage the data transmission Therefore using fragmentation

esigners can avoid interference problems in their WLAN designs But interference is not the only

problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and

research laboratories all over the

world It has already been accepted for the new wireless local area network standards IEEE

80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access

Communication (MMAC) Systems Also it is expected to be used for wireless broadband

multimedia communications Data rate is really what broadband is about The new standard

specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers

for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-

and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE

80211a following the parameters established for that case OFDM can be seen as either a

modulation technique or a multiplexing technique

One of the main reasons to use OFDM is to increase the robustness against frequency selective

fading or narrowband interference In a single carrier system a single fade or interferer can cause

the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will

be affected Error correction coding can then be used to correct for the few erroneous subcarriers

The concept of using parallel data transmission and frequency division multiplexing was

published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US

patent was filed and issued in January 1970 In a classical parallel data system the total signal

frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is

modulated with a separate symbol and then the N subchannels are frequency-multiplexed It

seems good to avoid spectral overlap of channels to eliminate interchannel interference

However this leads to inefficient use of the available spectrum To cope with the inefficiency

the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping

subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid

the use of high-speed equalization and to combat impulsive noise and multipath distortion as

well as to fully use the available bandwidth

Illustrates the difference between the conventional nonoverlapping multicarrier technique and the

overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation

technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique

however we need to reduce crosstalk between subcarriers which means that we want

orthogonality between the different modulated carriers The word orthogonal indicates that there

is a precise mathematical relationship between the frequencies of the carriers in the system In a

normal frequency-division multiplex system many carriers are spaced apart in such a way that

the signals can be received using conventional filters and demodulators In such receivers guard

bands are introduced between the different carriers and in the frequency domain which results in

a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM

signal so that the sidebands of the individual carriers overlap and the signals are still received

without adjacent carrier interference To do this the carriers must be mathematically orthogonal

The receiver acts as a bank of demodulators translating each carrier down to DC with the

resulting signal integrated over a symbol period to recover the raw data If the other carriers all

beat down the frequencies that in the time domain have a whole number of cycles in the symbol

period T then the integration process results in zero contribution from all these other carriers

Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of

1T

Fig13 Spectra of an OFDM subchannel and and OFDM signal

13 Guard Interval

The distribution of the data across a large number of carriers in the OFDM signal has some

further advantages Nulls caused by multi-path effects or interference on a given frequency only

affect a small number of the carriers the remaining ones being received correctly By using

error-coding techniques which does mean adding further data to the transmitted signal it

enables many or all of the corrupted data to be reconstructed within the receiver This can be

done because the error correction code is transmitted in a different part of the signal

14 OFDM variants

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

In order to satisfy the exponential growing demand of wireless multimedia services a high speed

data access is requiredTherefore various techniques have been proposed in recent years to

achieve high system capacities Among them we interest to the multiple-input multiple- output

(MIMO)The MIMO concept has attracted lot of attention in wireless communications due to its

potential to increase the system capacity without extra bandwidth Multipath propagation usually

causes selective frequency channels To combat the effect of frequency selective fading MIMO

is associated with orthogonal frequency-division multiplexing (OFDM) technique OFDM is a

modulation technique which transforms frequency selective channel into a set of parallel flat

fading channelsA cyclic prefix CP is added at the beginning of each OFDM symbol to eliminate

ICI and ISI The inserted cyclic prefix is equal to or longer than to the channel The 3GPP Long

Term Evolution (LTE) is defining the next generation radio access networkLTE Downlink

systems adopt Orthogonal Frequency Division Multiple Access (OFDMA) and MIMO to

provide up to 100 Mbps (assuming a 2x2 MIMO system with 20MHz bandwidth)

11 OFDM

Orthogonal Frequency Division Multiplex the modulation concept being used for many

wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile

Video

Orthogonal Frequency Division Multiplex or OFDM is a modulation format that is finding

increasing levels of use in todays radio communications scene OFDM has been adopted in the

Wi-Fi arena where the 80211a standard uses it to provide data rates up to 54 Mbps in the 5 GHz

ISM (Industrial Scientific and Medical) band In addition to this the recently ratified 80211g

standard has it in the 24 GHz ISM band In addition to this it is being used for WiMAX and is

also the format of choice for the next generation cellular radio communications systems

including 3G LTE and UMB

If this was not enough it is also being used for digital terrestrial television transmissions as well

as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long

medium and short wave bands is being launched and this has also adopted COFDM Then for the

future it is being proposed as the modulation technique for fourth generation cell phone systems

that are in their early stages of development and OFDM is also being used for many of the

proposed mobile phone video systems

OFDM orthogonal frequency division multiplex is a rather different format for modulation to

that used for more traditional forms of transmission It utilises many carriers together to provide

many advantages over simpler modulation formats

An OFDM signal consists of a number of closely spaced modulated carriers When modulation

of any form - voice data etc is applied to a carrier then sidebands spread out either side It is

necessary for a receiver to be able to receive the whole signal to be able to successfully

demodulate the data As a result when signals are transmitted close to one another they must be

spaced so that the receiver can separate them using a filter and there must be a guard band

between them This is not the case with OFDM Although the sidebands from each carrier

overlap they can still be received without the interference that might be expected because they

are orthogonal to each another This is achieved by having the carrier spacing equal to the

reciprocal of the symbol period

Fig11Traditional view of receiving signals carrying modulation

To see how OFDM works it is necessary to look at the receiver This acts as a bank of

demodulators translating each carrier down to DC The resulting signal is integrated over the

symbol period to regenerate the data from that carrier The same demodulator also demodulates

the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that

they will have a whole number of cycles in the symbol period and their contribution will sum to

zero - in other words there is no interference contribution

Fig12OFDM Spectrum

One requirement of the OFDM transmitting and receiving systems is that they must be linear

Any non-linearity will cause interference between the carriers as a result of inter-modulation

distortion This will introduce unwanted signals that would cause interference and impair the

orthogonality of the transmission

In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such

as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the

peaks whilst the average power is much lower and this leads to inefficiency In some systems the

peaks are limited Although this introduces distortion that results in a higher level of data errors

the system can rely on the error correction to remove them

The data to be transmitted on an OFDM signal is spread across the carriers of the signal each

carrier taking part of the payload This reduces the data rate taken by each carrier The lower data

rate has the advantage that interference from reflections is much less critical This is achieved by

adding a guard band time or guard interval into the system This ensures that the data is only

sampled when the signal is stable and no new delayed signals arrive that would alter the timing

and phase of the signal

The OFDM transmission scheme has the following key advantages __Makes efficient use of the

spectrum by allowing overlap

__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to

frequency selective fading than single carrier systems are

__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and

interleaving one can recover symbols lost due to the frequency selectivity of the channel C

hannel equalization becomes simpler than by using adaptive equalization techniques with single

carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity

as discussed in OFDM is computationally efficient by using FFT techniques to

implement the modulation and demodulation functions

__In conjunction with differential modulation there is no need to implement a channel estimator

__Is less sensitive to sample timing offsets than single carrier systems are

__Provides good protection against cochannel interference and impulsive parasitic noise

In terms of drawbacks OFDM has the following characteristics

__The OFDM signal has a noise like amplitude with a very large dynamic range

therefore it requires RF power amplifiers with a high peak to average power ratio

__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to

leakage of the DFT

12 The Standard IEEE 80211a

The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of

requirements for the physical layer (PHY) and a medium access control (MAC) layer For high

data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE

80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that

require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on

which the 80211 WLANs operate is different from wired media in many ways One of those

differences is the presence of interference in unlicensed frequency bands which can impact

communications between WLAN NICs Interference on the wireless medium can result in packet

loss which causes the network to suffer in terms of throughput performance Current 24-GHz

80211b radios handle interference well because they support a feature in the MAC layer known

as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to

increase the probability of delivering packets without errors induced by the interferer When a

frame is fragmented the sequence control field in the MAC header indicates placement of the

individual fragments and whether the current fragment is the last in the sequence When frames

are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)

control frames are used to manage the data transmission Therefore using fragmentation

esigners can avoid interference problems in their WLAN designs But interference is not the only

problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and

research laboratories all over the

world It has already been accepted for the new wireless local area network standards IEEE

80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access

Communication (MMAC) Systems Also it is expected to be used for wireless broadband

multimedia communications Data rate is really what broadband is about The new standard

specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers

for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-

and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE

80211a following the parameters established for that case OFDM can be seen as either a

modulation technique or a multiplexing technique

One of the main reasons to use OFDM is to increase the robustness against frequency selective

fading or narrowband interference In a single carrier system a single fade or interferer can cause

the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will

be affected Error correction coding can then be used to correct for the few erroneous subcarriers

The concept of using parallel data transmission and frequency division multiplexing was

published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US

patent was filed and issued in January 1970 In a classical parallel data system the total signal

frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is

modulated with a separate symbol and then the N subchannels are frequency-multiplexed It

seems good to avoid spectral overlap of channels to eliminate interchannel interference

However this leads to inefficient use of the available spectrum To cope with the inefficiency

the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping

subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid

the use of high-speed equalization and to combat impulsive noise and multipath distortion as

well as to fully use the available bandwidth

Illustrates the difference between the conventional nonoverlapping multicarrier technique and the

overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation

technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique

however we need to reduce crosstalk between subcarriers which means that we want

orthogonality between the different modulated carriers The word orthogonal indicates that there

is a precise mathematical relationship between the frequencies of the carriers in the system In a

normal frequency-division multiplex system many carriers are spaced apart in such a way that

the signals can be received using conventional filters and demodulators In such receivers guard

bands are introduced between the different carriers and in the frequency domain which results in

a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM

signal so that the sidebands of the individual carriers overlap and the signals are still received

without adjacent carrier interference To do this the carriers must be mathematically orthogonal

The receiver acts as a bank of demodulators translating each carrier down to DC with the

resulting signal integrated over a symbol period to recover the raw data If the other carriers all

beat down the frequencies that in the time domain have a whole number of cycles in the symbol

period T then the integration process results in zero contribution from all these other carriers

Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of

1T

Fig13 Spectra of an OFDM subchannel and and OFDM signal

13 Guard Interval

The distribution of the data across a large number of carriers in the OFDM signal has some

further advantages Nulls caused by multi-path effects or interference on a given frequency only

affect a small number of the carriers the remaining ones being received correctly By using

error-coding techniques which does mean adding further data to the transmitted signal it

enables many or all of the corrupted data to be reconstructed within the receiver This can be

done because the error correction code is transmitted in a different part of the signal

14 OFDM variants

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

If this was not enough it is also being used for digital terrestrial television transmissions as well

as DAB digital radio A new form of broadcasting called Digital Radio Mondiale for the long

medium and short wave bands is being launched and this has also adopted COFDM Then for the

future it is being proposed as the modulation technique for fourth generation cell phone systems

that are in their early stages of development and OFDM is also being used for many of the

proposed mobile phone video systems

OFDM orthogonal frequency division multiplex is a rather different format for modulation to

that used for more traditional forms of transmission It utilises many carriers together to provide

many advantages over simpler modulation formats

An OFDM signal consists of a number of closely spaced modulated carriers When modulation

of any form - voice data etc is applied to a carrier then sidebands spread out either side It is

necessary for a receiver to be able to receive the whole signal to be able to successfully

demodulate the data As a result when signals are transmitted close to one another they must be

spaced so that the receiver can separate them using a filter and there must be a guard band

between them This is not the case with OFDM Although the sidebands from each carrier

overlap they can still be received without the interference that might be expected because they

are orthogonal to each another This is achieved by having the carrier spacing equal to the

reciprocal of the symbol period

Fig11Traditional view of receiving signals carrying modulation

To see how OFDM works it is necessary to look at the receiver This acts as a bank of

demodulators translating each carrier down to DC The resulting signal is integrated over the

symbol period to regenerate the data from that carrier The same demodulator also demodulates

the other carriers As the carrier spacing equal to the reciprocal of the symbol period means that

they will have a whole number of cycles in the symbol period and their contribution will sum to

zero - in other words there is no interference contribution

Fig12OFDM Spectrum

One requirement of the OFDM transmitting and receiving systems is that they must be linear

Any non-linearity will cause interference between the carriers as a result of inter-modulation

distortion This will introduce unwanted signals that would cause interference and impair the

orthogonality of the transmission

In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such

as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the

peaks whilst the average power is much lower and this leads to inefficiency In some systems the

peaks are limited Although this introduces distortion that results in a higher level of data errors

the system can rely on the error correction to remove them

The data to be transmitted on an OFDM signal is spread across the carriers of the signal each

carrier taking part of the payload This reduces the data rate taken by each carrier The lower data

rate has the advantage that interference from reflections is much less critical This is achieved by

adding a guard band time or guard interval into the system This ensures that the data is only

sampled when the signal is stable and no new delayed signals arrive that would alter the timing

and phase of the signal

The OFDM transmission scheme has the following key advantages __Makes efficient use of the

spectrum by allowing overlap

__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to

frequency selective fading than single carrier systems are

__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and

interleaving one can recover symbols lost due to the frequency selectivity of the channel C

hannel equalization becomes simpler than by using adaptive equalization techniques with single

carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity

as discussed in OFDM is computationally efficient by using FFT techniques to

implement the modulation and demodulation functions

__In conjunction with differential modulation there is no need to implement a channel estimator

__Is less sensitive to sample timing offsets than single carrier systems are

__Provides good protection against cochannel interference and impulsive parasitic noise

In terms of drawbacks OFDM has the following characteristics

__The OFDM signal has a noise like amplitude with a very large dynamic range

therefore it requires RF power amplifiers with a high peak to average power ratio

__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to

leakage of the DFT

12 The Standard IEEE 80211a

The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of

requirements for the physical layer (PHY) and a medium access control (MAC) layer For high

data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE

80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that

require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on

which the 80211 WLANs operate is different from wired media in many ways One of those

differences is the presence of interference in unlicensed frequency bands which can impact

communications between WLAN NICs Interference on the wireless medium can result in packet

loss which causes the network to suffer in terms of throughput performance Current 24-GHz

80211b radios handle interference well because they support a feature in the MAC layer known

as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to

increase the probability of delivering packets without errors induced by the interferer When a

frame is fragmented the sequence control field in the MAC header indicates placement of the

individual fragments and whether the current fragment is the last in the sequence When frames

are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)

control frames are used to manage the data transmission Therefore using fragmentation

esigners can avoid interference problems in their WLAN designs But interference is not the only

problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and

research laboratories all over the

world It has already been accepted for the new wireless local area network standards IEEE

80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access

Communication (MMAC) Systems Also it is expected to be used for wireless broadband

multimedia communications Data rate is really what broadband is about The new standard

specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers

for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-

and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE

80211a following the parameters established for that case OFDM can be seen as either a

modulation technique or a multiplexing technique

One of the main reasons to use OFDM is to increase the robustness against frequency selective

fading or narrowband interference In a single carrier system a single fade or interferer can cause

the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will

be affected Error correction coding can then be used to correct for the few erroneous subcarriers

The concept of using parallel data transmission and frequency division multiplexing was

published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US

patent was filed and issued in January 1970 In a classical parallel data system the total signal

frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is

modulated with a separate symbol and then the N subchannels are frequency-multiplexed It

seems good to avoid spectral overlap of channels to eliminate interchannel interference

However this leads to inefficient use of the available spectrum To cope with the inefficiency

the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping

subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid

the use of high-speed equalization and to combat impulsive noise and multipath distortion as

well as to fully use the available bandwidth

Illustrates the difference between the conventional nonoverlapping multicarrier technique and the

overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation

technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique

however we need to reduce crosstalk between subcarriers which means that we want

orthogonality between the different modulated carriers The word orthogonal indicates that there

is a precise mathematical relationship between the frequencies of the carriers in the system In a

normal frequency-division multiplex system many carriers are spaced apart in such a way that

the signals can be received using conventional filters and demodulators In such receivers guard

bands are introduced between the different carriers and in the frequency domain which results in

a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM

signal so that the sidebands of the individual carriers overlap and the signals are still received

without adjacent carrier interference To do this the carriers must be mathematically orthogonal

The receiver acts as a bank of demodulators translating each carrier down to DC with the

resulting signal integrated over a symbol period to recover the raw data If the other carriers all

beat down the frequencies that in the time domain have a whole number of cycles in the symbol

period T then the integration process results in zero contribution from all these other carriers

Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of

1T

Fig13 Spectra of an OFDM subchannel and and OFDM signal

13 Guard Interval

The distribution of the data across a large number of carriers in the OFDM signal has some

further advantages Nulls caused by multi-path effects or interference on a given frequency only

affect a small number of the carriers the remaining ones being received correctly By using

error-coding techniques which does mean adding further data to the transmitted signal it

enables many or all of the corrupted data to be reconstructed within the receiver This can be

done because the error correction code is transmitted in a different part of the signal

14 OFDM variants

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Fig12OFDM Spectrum

One requirement of the OFDM transmitting and receiving systems is that they must be linear

Any non-linearity will cause interference between the carriers as a result of inter-modulation

distortion This will introduce unwanted signals that would cause interference and impair the

orthogonality of the transmission

In terms of the equipment to be used the high peak to average ratio of multi-carrier systems such

as OFDM requires the RF final amplifier on the output of the transmitter to be able to handle the

peaks whilst the average power is much lower and this leads to inefficiency In some systems the

peaks are limited Although this introduces distortion that results in a higher level of data errors

the system can rely on the error correction to remove them

The data to be transmitted on an OFDM signal is spread across the carriers of the signal each

carrier taking part of the payload This reduces the data rate taken by each carrier The lower data

rate has the advantage that interference from reflections is much less critical This is achieved by

adding a guard band time or guard interval into the system This ensures that the data is only

sampled when the signal is stable and no new delayed signals arrive that would alter the timing

and phase of the signal

The OFDM transmission scheme has the following key advantages __Makes efficient use of the

spectrum by allowing overlap

__By dividing the channel into narrowband flat fading sub channels OFDM is more resistant to

frequency selective fading than single carrier systems are

__Eliminates ISI and IFI through use of a cyclic prefixUsing adequate channel coding and

interleaving one can recover symbols lost due to the frequency selectivity of the channel C

hannel equalization becomes simpler than by using adaptive equalization techniques with single

carrier systems _It is possible to use maximum likelihood decoding with reasonable complexity

as discussed in OFDM is computationally efficient by using FFT techniques to

implement the modulation and demodulation functions

__In conjunction with differential modulation there is no need to implement a channel estimator

__Is less sensitive to sample timing offsets than single carrier systems are

__Provides good protection against cochannel interference and impulsive parasitic noise

In terms of drawbacks OFDM has the following characteristics

__The OFDM signal has a noise like amplitude with a very large dynamic range

therefore it requires RF power amplifiers with a high peak to average power ratio

__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to

leakage of the DFT

12 The Standard IEEE 80211a

The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of

requirements for the physical layer (PHY) and a medium access control (MAC) layer For high

data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE

80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that

require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on

which the 80211 WLANs operate is different from wired media in many ways One of those

differences is the presence of interference in unlicensed frequency bands which can impact

communications between WLAN NICs Interference on the wireless medium can result in packet

loss which causes the network to suffer in terms of throughput performance Current 24-GHz

80211b radios handle interference well because they support a feature in the MAC layer known

as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to

increase the probability of delivering packets without errors induced by the interferer When a

frame is fragmented the sequence control field in the MAC header indicates placement of the

individual fragments and whether the current fragment is the last in the sequence When frames

are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)

control frames are used to manage the data transmission Therefore using fragmentation

esigners can avoid interference problems in their WLAN designs But interference is not the only

problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and

research laboratories all over the

world It has already been accepted for the new wireless local area network standards IEEE

80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access

Communication (MMAC) Systems Also it is expected to be used for wireless broadband

multimedia communications Data rate is really what broadband is about The new standard

specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers

for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-

and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE

80211a following the parameters established for that case OFDM can be seen as either a

modulation technique or a multiplexing technique

One of the main reasons to use OFDM is to increase the robustness against frequency selective

fading or narrowband interference In a single carrier system a single fade or interferer can cause

the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will

be affected Error correction coding can then be used to correct for the few erroneous subcarriers

The concept of using parallel data transmission and frequency division multiplexing was

published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US

patent was filed and issued in January 1970 In a classical parallel data system the total signal

frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is

modulated with a separate symbol and then the N subchannels are frequency-multiplexed It

seems good to avoid spectral overlap of channels to eliminate interchannel interference

However this leads to inefficient use of the available spectrum To cope with the inefficiency

the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping

subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid

the use of high-speed equalization and to combat impulsive noise and multipath distortion as

well as to fully use the available bandwidth

Illustrates the difference between the conventional nonoverlapping multicarrier technique and the

overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation

technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique

however we need to reduce crosstalk between subcarriers which means that we want

orthogonality between the different modulated carriers The word orthogonal indicates that there

is a precise mathematical relationship between the frequencies of the carriers in the system In a

normal frequency-division multiplex system many carriers are spaced apart in such a way that

the signals can be received using conventional filters and demodulators In such receivers guard

bands are introduced between the different carriers and in the frequency domain which results in

a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM

signal so that the sidebands of the individual carriers overlap and the signals are still received

without adjacent carrier interference To do this the carriers must be mathematically orthogonal

The receiver acts as a bank of demodulators translating each carrier down to DC with the

resulting signal integrated over a symbol period to recover the raw data If the other carriers all

beat down the frequencies that in the time domain have a whole number of cycles in the symbol

period T then the integration process results in zero contribution from all these other carriers

Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of

1T

Fig13 Spectra of an OFDM subchannel and and OFDM signal

13 Guard Interval

The distribution of the data across a large number of carriers in the OFDM signal has some

further advantages Nulls caused by multi-path effects or interference on a given frequency only

affect a small number of the carriers the remaining ones being received correctly By using

error-coding techniques which does mean adding further data to the transmitted signal it

enables many or all of the corrupted data to be reconstructed within the receiver This can be

done because the error correction code is transmitted in a different part of the signal

14 OFDM variants

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

__In conjunction with differential modulation there is no need to implement a channel estimator

__Is less sensitive to sample timing offsets than single carrier systems are

__Provides good protection against cochannel interference and impulsive parasitic noise

In terms of drawbacks OFDM has the following characteristics

__The OFDM signal has a noise like amplitude with a very large dynamic range

therefore it requires RF power amplifiers with a high peak to average power ratio

__It is more sensitive to carrier frequency offset and drift than single carrier systems are due to

leakage of the DFT

12 The Standard IEEE 80211a

The IEEE 80211 specification is a wireless LAN (WLAN) standard that defines a set of

requirements for the physical layer (PHY) and a medium access control (MAC) layer For high

data rates the standard provides two PHYs - IEEE 80211b for 24-GHz operation and IEEE

80211a for 5-GHz operation The IEEE 80211a standard is designed to serve applications that

require data rates higher than 11 Mbps in the 5-GHz frequency band The wireless medium on

which the 80211 WLANs operate is different from wired media in many ways One of those

differences is the presence of interference in unlicensed frequency bands which can impact

communications between WLAN NICs Interference on the wireless medium can result in packet

loss which causes the network to suffer in terms of throughput performance Current 24-GHz

80211b radios handle interference well because they support a feature in the MAC layer known

as fragmentation In fragmentation data frames are broken into smaller frames in an attempt to

increase the probability of delivering packets without errors induced by the interferer When a

frame is fragmented the sequence control field in the MAC header indicates placement of the

individual fragments and whether the current fragment is the last in the sequence When frames

are fragmented into request-to-send (RTS) clear-to-send (CTS) and acknowledge (ACK)

control frames are used to manage the data transmission Therefore using fragmentation

esigners can avoid interference problems in their WLAN designs But interference is not the only

problem for todayrsquos WLAN designers Security OFDM is of great interest by researchers and

research laboratories all over the

world It has already been accepted for the new wireless local area network standards IEEE

80211a High Performance LAN type 2 (HIPERLAN2) and Mobile Multimedia Access

Communication (MMAC) Systems Also it is expected to be used for wireless broadband

multimedia communications Data rate is really what broadband is about The new standard

specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers

for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-

and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE

80211a following the parameters established for that case OFDM can be seen as either a

modulation technique or a multiplexing technique

One of the main reasons to use OFDM is to increase the robustness against frequency selective

fading or narrowband interference In a single carrier system a single fade or interferer can cause

the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will

be affected Error correction coding can then be used to correct for the few erroneous subcarriers

The concept of using parallel data transmission and frequency division multiplexing was

published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US

patent was filed and issued in January 1970 In a classical parallel data system the total signal

frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is

modulated with a separate symbol and then the N subchannels are frequency-multiplexed It

seems good to avoid spectral overlap of channels to eliminate interchannel interference

However this leads to inefficient use of the available spectrum To cope with the inefficiency

the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping

subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid

the use of high-speed equalization and to combat impulsive noise and multipath distortion as

well as to fully use the available bandwidth

Illustrates the difference between the conventional nonoverlapping multicarrier technique and the

overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation

technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique

however we need to reduce crosstalk between subcarriers which means that we want

orthogonality between the different modulated carriers The word orthogonal indicates that there

is a precise mathematical relationship between the frequencies of the carriers in the system In a

normal frequency-division multiplex system many carriers are spaced apart in such a way that

the signals can be received using conventional filters and demodulators In such receivers guard

bands are introduced between the different carriers and in the frequency domain which results in

a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM

signal so that the sidebands of the individual carriers overlap and the signals are still received

without adjacent carrier interference To do this the carriers must be mathematically orthogonal

The receiver acts as a bank of demodulators translating each carrier down to DC with the

resulting signal integrated over a symbol period to recover the raw data If the other carriers all

beat down the frequencies that in the time domain have a whole number of cycles in the symbol

period T then the integration process results in zero contribution from all these other carriers

Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of

1T

Fig13 Spectra of an OFDM subchannel and and OFDM signal

13 Guard Interval

The distribution of the data across a large number of carriers in the OFDM signal has some

further advantages Nulls caused by multi-path effects or interference on a given frequency only

affect a small number of the carriers the remaining ones being received correctly By using

error-coding techniques which does mean adding further data to the transmitted signal it

enables many or all of the corrupted data to be reconstructed within the receiver This can be

done because the error correction code is transmitted in a different part of the signal

14 OFDM variants

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Communication (MMAC) Systems Also it is expected to be used for wireless broadband

multimedia communications Data rate is really what broadband is about The new standard

specify bit rates of up to 54 Mbps Such high rate imposes large bandwidth thus pushing carriers

for values higher than UHF band For instance IEEE80211a has frequencies allocated in the 5-

and 17- GHz bands This project is oriented to the application of OFDM to the standard IEEE

80211a following the parameters established for that case OFDM can be seen as either a

modulation technique or a multiplexing technique

One of the main reasons to use OFDM is to increase the robustness against frequency selective

fading or narrowband interference In a single carrier system a single fade or interferer can cause

the entire link to fail but in a multicarrier system only a small percentage of the subcarriers will

be affected Error correction coding can then be used to correct for the few erroneous subcarriers

The concept of using parallel data transmission and frequency division multiplexing was

published in the mid-1960s [1 2] Some early development is traced back to the 1950s A US

patent was filed and issued in January 1970 In a classical parallel data system the total signal

frequency band is divided into N nonoverlapping frequency subchannels Each subchannel is

modulated with a separate symbol and then the N subchannels are frequency-multiplexed It

seems good to avoid spectral overlap of channels to eliminate interchannel interference

However this leads to inefficient use of the available spectrum To cope with the inefficiency

the ideas proposed from the mid-1960s were to use parallel data and FDM with overlapping

subchannels in which each carrying a signaling rate b is spaced b apart in frequency to avoid

the use of high-speed equalization and to combat impulsive noise and multipath distortion as

well as to fully use the available bandwidth

Illustrates the difference between the conventional nonoverlapping multicarrier technique and the

overlapping multicarrier modulation techniqueBy using the overlapping multicarrier modulation

technique we save almost 50 of bandwidth To realize the overlapping multicarrier technique

however we need to reduce crosstalk between subcarriers which means that we want

orthogonality between the different modulated carriers The word orthogonal indicates that there

is a precise mathematical relationship between the frequencies of the carriers in the system In a

normal frequency-division multiplex system many carriers are spaced apart in such a way that

the signals can be received using conventional filters and demodulators In such receivers guard

bands are introduced between the different carriers and in the frequency domain which results in

a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM

signal so that the sidebands of the individual carriers overlap and the signals are still received

without adjacent carrier interference To do this the carriers must be mathematically orthogonal

The receiver acts as a bank of demodulators translating each carrier down to DC with the

resulting signal integrated over a symbol period to recover the raw data If the other carriers all

beat down the frequencies that in the time domain have a whole number of cycles in the symbol

period T then the integration process results in zero contribution from all these other carriers

Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of

1T

Fig13 Spectra of an OFDM subchannel and and OFDM signal

13 Guard Interval

The distribution of the data across a large number of carriers in the OFDM signal has some

further advantages Nulls caused by multi-path effects or interference on a given frequency only

affect a small number of the carriers the remaining ones being received correctly By using

error-coding techniques which does mean adding further data to the transmitted signal it

enables many or all of the corrupted data to be reconstructed within the receiver This can be

done because the error correction code is transmitted in a different part of the signal

14 OFDM variants

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

the signals can be received using conventional filters and demodulators In such receivers guard

bands are introduced between the different carriers and in the frequency domain which results in

a lowering of spectrum efficiency It is possible however to arrange the carriers in an OFDM

signal so that the sidebands of the individual carriers overlap and the signals are still received

without adjacent carrier interference To do this the carriers must be mathematically orthogonal

The receiver acts as a bank of demodulators translating each carrier down to DC with the

resulting signal integrated over a symbol period to recover the raw data If the other carriers all

beat down the frequencies that in the time domain have a whole number of cycles in the symbol

period T then the integration process results in zero contribution from all these other carriers

Thus the carriers are linearly independent (ie orthogonal) if the carrier spacing is a multiple of

1T

Fig13 Spectra of an OFDM subchannel and and OFDM signal

13 Guard Interval

The distribution of the data across a large number of carriers in the OFDM signal has some

further advantages Nulls caused by multi-path effects or interference on a given frequency only

affect a small number of the carriers the remaining ones being received correctly By using

error-coding techniques which does mean adding further data to the transmitted signal it

enables many or all of the corrupted data to be reconstructed within the receiver This can be

done because the error correction code is transmitted in a different part of the signal

14 OFDM variants

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

There are several other variants of OFDM for which the initials are seen in the technical

literature These follow the basic format for OFDM but have additional attributes or variations

141 COFDM Coded Orthogonal frequency division multiplex A form of OFDM where error

correction coding is incorporated into the signal

142 Flash OFDM This is a variant of OFDM that was developed by Flarion and it is a fast

hopped form of OFDM It uses multiple tones and fast hopping to spread signals over a given

spectrum band

143 OFDMA Orthogonal frequency division multiple access A scheme used to provide a

multiple access capability for applications such as cellular telecommunications when using

OFDM technologies

144 VOFDM Vector OFDM This form of OFDM uses the concept of MIMO technology It

is being developed by CISCO Systems MIMO stands for Multiple Input Multiple output and it

uses multiple antennas to transmit and receive the signals so that multi-path effects can be

utilised to enhance the signal reception and improve the transmission speeds that can be

supported

145 WOFDM Wideband OFDM The concept of this form of OFDM is that it uses a degree

of spacing between the channels that is large enough that any frequency errors between

transmitter and receiver do not affect the performance It is particularly applicable to Wi-Fi

systems

Each of these forms of OFDM utilise the same basic concept of using close spaced orthogonal

carriers each carrying low data rate signals During the demodulation phase the data is then

combined to provide the complete signal

OFDM and COFDM have gained a significant presence in the wireless market place The

combination of high data capacity high spectral efficiency and its resilience to interference as a

result of multi-path effects means that it is ideal for the high data applications that are becoming

a common factor in todays communications scene

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

15 OVERVIEW OF LTE DOWNLINK SYSTEM

According to the duration of one frame in LTE Downlink system is 10 msEach LTE radio frame

is divided into 10 sub-frames of 1 ms As described in Figure 1 each sub-frame is divided into

two time slots each with duration of 05 ms Each time slot consists of either 7 or 6 OFDM

symbols depending on the length of the CP (normal or extended) In LTE Downlink physical

layer 12 consecutive subcarriers are grouped into one Physical Resource Block (PRB) A PRB

has the duration of 1 time slot

Figure 14 LTE radio Frame structure

LTE provides scalable bandwidth from 14 MHz to 20 MHz and supports both frequency

division duplexing (FDD) and time-division duplexing (TDD) Table 1 shows the different

transmission parameters for LTE Downlink systems

16 DOWNLINKLTE SYSTEM MODELThe system model is given in Figure2 A MIMO-OFDM system with receive antennas is assumed transmit and

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Figure 15 MIMO-OFDM system

OFDMA is employed as the multiplexing scheme in the LTE Downlink systems OFDMA is a

multiple users radio access technique based on OFDM technique OFDM consists in dividing the

transmission bandwidth into several orthogonal sub-carriers The entire set of subcarriers is

shared between different users Figure 3 illustrates a baseband OFDM system model The N

complex constellation symbols are modulated on the orthogonal sub-carriers by mean of the

Inverse Discrete Fourier

Each OFDM symbol is transmitted over frequency-selective fading MIMO channels assumed

independents of each other Each channel is modeled as a Finite Impulse Response (FIR) filter

With L tapsTherefore we consider in our system model only a single transmit and a single

receive antenna After removing the CP and performing the DFT the received OFDM symbol at

one receive antenna can be written as

Y represents the received signal vector X is a matrix which contains the transmitted elements on

its diagonal H is a channel frequency response and micro is the noise vector whose entries have the

iid complex Gaussian distribution with zero mean and variance amp We assume that the

noise micro is uncorrelated with the channel H

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Recent works have shown that multiple input multiple output (MIMO) systems can achieve an

increased capacity without the need of increasing the operational bandwidth Also for the fixed

transmission rate they are able to improve the signal transmission quality (Bit Error Rate) by

using spatial diversity In order to obtain these advantages MIMO systems require accurate

channel state information (CSI) at least at the receiver side This information is in the form of

complex channel matrixThe method employing training sequences is a popular and efficient

channel estimation method A number of training- based channel estimation methods for MIMO

systems havebeen proposed However in most of the presented works independent identically

distributed (iid)Rayleigh channels are assumed This assumption is rarely fulfilled in practice

as spatial channel correlation occurs in most of propagation environments In an MMSE channel

estimator for MIMO-OFDM was developed and its performance was tested under spatial

correlated channelHowever a very simple correlated channel model was used These

investigations neglected the issue of antenna array used at the receiver sideIn practical cases

there is a demand for small spacing of array antenna elements at least at the mobile side of

MIMO system This is required to make the transceiver of compact size However the resulting

tight spacing is responsible for channel correlation Also the received signals are affected by

mutual coupling effects of the array elements

17 Wavelet Based MIMO-OFDM

Wavelet Transform is an important mathematical function because as a tool for multi resolution

disintegration of continuous time signal by different frequencies also different times Now

wavelet transform upper frequencies are superior decided in time as well as lesser frequencies

are better decided in frequency Happening this intellect the signal remains reproduced through

an orthogonal wavelet purpose in addition the transform is calculated independently changed

parts of the time domain signal The wavelet transform can be classified as two categories

continuous ripple transform and discrete ripple transform

The Discrete Ripple Transform could be observed by way of sub-band coding The signal is

analysed and it accepted over a succession of filter banks The splitting the full-band source

signal into altered frequency bands as well as encrypt every band separately established on their

spectrumvitalities is called sub-band coding method

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

The learning of sub-band coding fright starting the digital filter bank scheme it is represented as

a set of filters with has altered centre frequencies Double channel filter bank is mostly used in

addition the effective way to tool the discrete ripple transform (DRT) Naturally the filter bank

proposal has double steps which are used in signal transmission scheme

The first step is named as analysis stage which agrees toward the decomposition procedure in

which the signal samples remain condensed by double (downsampling) Another step is called

synthesis period which agrees to the exclamation procedure in which the signal samples are

improved by two (up sampling)

The analysis period involves of sub-band filter surveyed by down sampler while the synthesis

period involves of sub-band filter situated next up sampler The sub-band filter period used

through the channel filter exists perfect restoration Quadrature Mirror Filter (QMF)

Subsequently there are low pass filter as well as high pass filters at each level the analysis period

takes double output coefficients also they are named as estimate coefficients which contain the

small frequency information of the signal then detail coefficients which comprise the high

frequency data of the signal The analysis period of the multi-level double channels impeccable

restoration filter bank scheme is charity for formative the DWT coefficients The procedure of

restoration the basis signal as of the DWT coefficients is so-called the inverse discrete Ripple

transform (IDRT) Aimed at each level of restoration filter bank the calculation then details

coefficients are up sampled in addition to passed over low pass filter and high pass synthesis

filter

The possessions of wavelets in addition to varieties it by way of a moral excellent for

countless applications identical image synthesis nuclear engineering biomedical engineering

magnetic resonance imaging music fractals turbulence pure mathematics data compression

computer graphics also animation human vision radar optics astronomy acoustics and

seismology

This paper investigates the case of a MIMO wireless system in which the signal is transmitted

from a fixed transmitter to a mobile terminal receiver equipped with a uniform circular array

(UCA) antenna The investigations make use of the assumption that the signals arriving at this

array have an angle of arrival (AoA) that follows a Laplacian distribution

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

18 OFDM MODEL

181 Orthogonal frequency-division multiplexing

Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on

multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital

communication whether wireless or over copper wires used in applications such as digital

television and audio broadcasting DSL Internet access wireless networks powerline networks

and 4G mobile communications

OFDM is essentially identical to coded OFDM (COFDM) and discrete multi-tone modulation

(DMT) and is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier

modulation method The word coded comes from the use of forward error correction (FEC)[1]

A large number of closely spaced orthogonal sub-carrier signals are used to carry data[1] on

several parallel data streams or channels Each sub-carrier is modulated with a conventional

modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low

symbol rate maintaining total data rates similar to conventional single-carrier modulation

schemes in the same bandwidth

The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe

channel conditions (for example attenuation of high frequencies in a long copper wire

narrowband interference and frequency-selective fading due to multipath) without complex

equalization filters Channel equalization is simplified because OFDM may be viewed as using

many slowly modulated narrowband signals rather than one rapidly modulated wideband signal

The low symbol rate makes the use of a guard interval between symbols affordable making it

possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on

analogue TV these are visible as ghosting and blurring respectively) to achieve a diversity gain

ie a signal-to-noise ratio improvement This mechanism also facilitates the design of single

frequency networks (SFNs) where several adjacent transmitters send the same signal

simultaneously at the same frequency as the signals from multiple distant transmitters may be

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

combined constructively rather than interfering as would typically occur in a traditional single-

carrier system

182 Example of applications

The following list is a summary of existing OFDM based standards and products For further

details see the Usage section at the end of the article

1821Cable

ADSL and VDSL broadband access via POTS copper wiring

DVB-C2 an enhanced version of the DVB-C digital cable TV standard

Power line communication (PLC)

ITU-T Ghn a standard which provides high-speed local area networking of existing

home wiring (power lines phone lines and coaxial cables)

TrailBlazer telephone line modems

Multimedia over Coax Alliance (MoCA) home networking

1822 Wireless

The wireless LAN (WLAN) radio interfaces IEEE 80211a g n ac and HIPERLAN2

The digital radio systems DABEUREKA 147 DAB+ Digital Radio Mondiale HD

Radio T-DMB and ISDB-TSB

The terrestrial digital TV systems DVB-T and ISDB-T

The terrestrial mobile TV systems DVB-H T-DMB ISDB-T and MediaFLO forward

link

The wireless personal area network (PAN) ultra-wideband (UWB) IEEE 802153a

implementation suggested by WiMedia Alliance

The OFDM based multiple access technology OFDMA is also used in several 4G and pre-4G

cellular networks and mobile broadband standards

The mobility mode of the wireless MANbroadband wireless access (BWA) standard

IEEE 80216e (or Mobile-WiMAX)

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

The mobile broadband wireless access (MBWA) standard IEEE 80220

the downlink of the 3GPP Long Term Evolution (LTE) fourth generation mobile

broadband standard The radio interface was formerly named High Speed OFDM Packet

Access (HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

Key features

The advantages and disadvantages listed below are further discussed in the Characteristics and

principles of operation section below

Summary of advantages

High spectral efficiency as compared to other double sideband modulation schemes

spread spectrum etc

Can easily adapt to severe channel conditions without complex time-domain equalization

Robust against narrow-band co-channel interference

Robust against intersymbol interference (ISI) and fading caused by multipath

propagation

Efficient implementation using Fast Fourier Transform (FFT)

Low sensitivity to time synchronization errors

Tuned sub-channel receiver filters are not required (unlike conventional FDM)

Facilitates single frequency networks (SFNs) ie transmitter macrodiversity

Summary of disadvantages

Sensitive to Doppler shift

Sensitive to frequency synchronization problems

High peak-to-average-power ratio (PAPR) requiring linear transmitter circuitry which

suffers from poor power efficiency

Loss of efficiency caused by cyclic prefixguard interval

19 Characteristics and principles of operation

191 Orthogonality

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Conceptually OFDM is a specialized FDM the additional constraint being all the carrier signals

are orthogonal to each other

In OFDM the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each

other meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard

bands are not required This greatly simplifies the design of both the transmitter and the receiver

unlike conventional FDM a separate filter for each sub-channel is not required

The orthogonality requires that the sub-carrier spacing is Hertz where TU seconds is the

useful symbol duration (the receiver side window size) and k is a positive integer typically

equal to 1 Therefore with N sub-carriers the total passband bandwidth will be B asymp NmiddotΔf (Hz)

The orthogonality also allows high spectral efficiency with a total symbol rate near the Nyquist

rate for the equivalent baseband signal (ie near half the Nyquist rate for the double-side band

physical passband signal) Almost the whole available frequency band can be utilized OFDM

generally has a nearly white spectrum giving it benign electromagnetic interference properties

with respect to other co-channel users

A simple example A useful symbol duration TU = 1 ms would require a sub-carrier

spacing of (or an integer multiple of that) for orthogonality N = 1000

sub-carriers would result in a total passband bandwidth of NΔf = 1 MHz For this symbol

time the required bandwidth in theory according to Nyquist is N2TU = 05 MHz (ie

half of the achieved bandwidth required by our scheme) If a guard interval is applied

(see below) Nyquist bandwidth requirement would be even lower The FFT would result

in N = 1000 samples per symbol If no guard interval was applied this would result in a

base band complex valued signal with a sample rate of 1 MHz which would require a

baseband bandwidth of 05 MHz according to Nyquist However the passband RF signal

is produced by multiplying the baseband signal with a carrier waveform (ie double-

sideband quadrature amplitude-modulation) resulting in a passband bandwidth of 1 MHz

A single-side band (SSB) or vestigial sideband (VSB) modulation scheme would achieve

almost half that bandwidth for the same symbol rate (ie twice as high spectral

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

efficiency for the same symbol alphabet length) It is however more sensitive to multipath

interference

OFDM requires very accurate frequency synchronization between the receiver and the

transmitter with frequency deviation the sub-carriers will no longer be orthogonal causing inter-

carrier interference (ICI) (ie cross-talk between the sub-carriers) Frequency offsets are

typically caused by mismatched transmitter and receiver oscillators or by Doppler shift due to

movement While Doppler shift alone may be compensated for by the receiver the situation is

worsened when combined with multipath as reflections will appear at various frequency offsets

which is much harder to correct This effect typically worsens as speed increases [2] and is an

important factor limiting the use of OFDM in high-speed vehicles In order to mitigate ICI in

such scenarios one can shape each sub-carrier in order to minimize the interference resulting in a

non-orthogonal subcarriers overlapping[3] For example a low-complexity scheme referred to as

WCP-OFDM (Weighted Cyclic Prefix Orthogonal Frequency-Division Multiplexing) consists in

using short filters at the transmitter output in order to perform a potentially non-rectangular pulse

shaping and a near perfect reconstruction using a single-tap per subcarrier equalization[4] Other

ICI suppression techniques usually increase drastically the receiver complexity[5]

192 Implementation using the FFT algorithm

The orthogonality allows for efficient modulator and demodulator implementation using the FFT

algorithm on the receiver side and inverse FFT on the sender side Although the principles and

some of the benefits have been known since the 1960s OFDM is popular for wideband

communications today by way of low-cost digital signal processing components that can

efficiently calculate the FFT

The time to compute the inverse-FFT or FFT transform has to take less than the time for each

symbol[6] Which for example for DVB-T (FFT 8k) means the computation has to be done in 896

micros or less

For an 8192-point FFT this may be approximated to[6][clarification needed]

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

[6]

MIPS = Million instructions per second

The computational demand approximately scales linearly with FFT size so a double size FFT

needs double the amount of time and vice versa[6] As a comparison an Intel Pentium III CPU at

1266 GHz is able to calculate a 8 192 point FFT in 576 micros using FFTW[7] Intel Pentium M at

16 GHz does it in 387 micros[8] Intel Core Duo at 30 GHz does it in 968 micros[9]

193 Guard interval for elimination of intersymbol interference

One key principle of OFDM is that since low symbol rate modulation schemes (ie where the

symbols are relatively long compared to the channel time characteristics) suffer less from

intersymbol interference caused by multipath propagation it is advantageous to transmit a

number of low-rate streams in parallel instead of a single high-rate stream Since the duration of

each symbol is long it is feasible to insert a guard interval between the OFDM symbols thus

eliminating the intersymbol interference

The guard interval also eliminates the need for a pulse-shaping filter and it reduces the

sensitivity to time synchronization problems

A simple example If one sends a million symbols per second using conventional single-

carrier modulation over a wireless channel then the duration of each symbol would be

one microsecond or less This imposes severe constraints on synchronization and

necessitates the removal of multipath interference If the same million symbols per

second are spread among one thousand sub-channels the duration of each symbol can be

longer by a factor of a thousand (ie one millisecond) for orthogonality with

approximately the same bandwidth Assume that a guard interval of 18 of the symbol

length is inserted between each symbol Intersymbol interference can be avoided if the

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

multipath time-spreading (the time between the reception of the first and the last echo) is

shorter than the guard interval (ie 125 microseconds) This corresponds to a maximum

difference of 375 kilometers between the lengths of the paths

The cyclic prefix which is transmitted during the guard interval consists of the end of the

OFDM symbol copied into the guard interval and the guard interval is transmitted followed by

the OFDM symbol The reason that the guard interval consists of a copy of the end of the OFDM

symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of

the multipaths when it performs OFDM demodulation with the FFT In some standards such as

Ultrawideband in the interest of transmitted power cyclic prefix is skipped and nothing is sent

during the guard interval The receiver will then have to mimic the cyclic prefix functionality by

copying the end part of the OFDM symbol and adding it to the beginning portion

194 Simplified equalization

The effects of frequency-selective channel conditions for example fading caused by multipath

propagation can be considered as constant (flat) over an OFDM sub-channel if the sub-channel

is sufficiently narrow-banded (ie if the number of sub-channels is sufficiently large) This

makes frequency domain equalization possible at the receiver which is far simpler than the time-

domain equalization used in conventional single-carrier modulation In OFDM the equalizer

only has to multiply each detected sub-carrier (each Fourier coefficient) in each OFDM symbol

by a constant complex number or a rarely changed value

Our example The OFDM equalization in the above numerical example would require

one complex valued multiplication per subcarrier and symbol (ie complex

multiplications per OFDM symbol ie one million multiplications per second at the

receiver) The FFT algorithm requires [this is imprecise over half of

these complex multiplications are trivial ie = to 1 and are not implemented in software

or HW] complex-valued multiplications per OFDM symbol (ie 10 million

multiplications per second) at both the receiver and transmitter side This should be

compared with the corresponding one million symbolssecond single-carrier modulation

case mentioned in the example where the equalization of 125 microseconds time-

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

spreading using a FIR filter would require in a naive implementation 125 multiplications

per symbol (ie 125 million multiplications per second) FFT techniques can be used to

reduce the number of multiplications for an FIR filter based time-domain equalizer to a

number comparable with OFDM at the cost of delay between reception and decoding

which also becomes comparable with OFDM

If differential modulation such as DPSK or DQPSK is applied to each sub-carrier equalization

can be completely omitted since these non-coherent schemes are insensitive to slowly changing

amplitude and phase distortion

In a sense improvements in FIR equalization using FFTs or partial FFTs leads mathematically

closer to OFDM[citation needed] but the OFDM technique is easier to understand and implement and

the sub-channels can be independently adapted in other ways than varying equalization

coefficients such as switching between different QAM constellation patterns and error-

correction schemes to match individual sub-channel noise and interference characteristics[clarification needed]

Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement

of the channel conditions[10][11] (ie the equalizer gain and phase shift for each sub-carrier) Pilot

signals and training symbols (preambles) may also be used for time synchronization (to avoid

intersymbol interference ISI) and frequency synchronization (to avoid inter-carrier interference

ICI caused by Doppler shift)

OFDM was initially used for wired and stationary wireless communications However with an

increasing number of applications operating in highly mobile environments the effect of

dispersive fading caused by a combination of multi-path propagation and doppler shift is more

significant Over the last decade research has been done on how to equalize OFDM transmission

over doubly selective channels[12][13][14]

195 Channel coding and interleaving

OFDM is invariably used in conjunction with channel coding (forward error correction) and

almost always uses frequency andor time interleaving

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Frequency (subcarrier) interleaving increases resistance to frequency-selective channel

conditions such as fading For example when a part of the channel bandwidth fades frequency

interleaving ensures that the bit errors that would result from those subcarriers in the faded part

of the bandwidth are spread out in the bit-stream rather than being concentrated Similarly time

interleaving ensures that bits that are originally close together in the bit-stream are transmitted

far apart in time thus mitigating against severe fading as would happen when travelling at high

speed

However time interleaving is of little benefit in slowly fading channels such as for stationary

reception and frequency interleaving offers little to no benefit for narrowband channels that

suffer from flat-fading (where the whole channel bandwidth fades at the same time)

The reason why interleaving is used on OFDM is to attempt to spread the errors out in the bit-

stream that is presented to the error correction decoder because when such decoders are

presented with a high concentration of errors the decoder is unable to correct all the bit errors

and a burst of uncorrected errors occurs A similar design of audio data encoding makes compact

disc (CD) playback robust

A classical type of error correction coding used with OFDM-based systems is convolutional

coding often concatenated with Reed-Solomon coding Usually additional interleaving (on top

of the time and frequency interleaving mentioned above) in between the two layers of coding is

implemented The choice for Reed-Solomon coding as the outer error correction code is based on

the observation that the Viterbi decoder used for inner convolutional decoding produces short

errors bursts when there is a high concentration of errors and Reed-Solomon codes are

inherently well-suited to correcting bursts of errors

Newer systems however usually now adopt near-optimal types of error correction codes that

use the turbo decoding principle where the decoder iterates towards the desired solution

Examples of such error correction coding types include turbo codes and LDPC codes which

perform close to the Shannon limit for the Additive White Gaussian Noise (AWGN) channel

Some systems that have implemented these codes have concatenated them with either Reed-

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Solomon (for example on the MediaFLO system) or BCH codes (on the DVB-S2 system) to

improve upon an error floor inherent to these codes at high signal-to-noise ratios

196 Adaptive transmission

The resilience to severe channel conditions can be further enhanced if information about the

channel is sent over a return-channel Based on this feedback information adaptive modulation

channel coding and power allocation may be applied across all sub-carriers or individually to

each sub-carrier In the latter case if a particular range of frequencies suffers from interference

or attenuation the carriers within that range can be disabled or made to run slower by applying

more robust modulation or error coding to those sub-carriers

The term discrete multitone modulation (DMT) denotes OFDM based communication systems

that adapt the transmission to the channel conditions individually for each sub-carrier by means

of so-called bit-loading Examples are ADSL and VDSL

The upstream and downstream speeds can be varied by allocating either more or fewer carriers

for each purpose Some forms of rate-adaptive DSL use this feature in real time so that the

bitrate is adapted to the co-channel interference and bandwidth is allocated to whichever

subscriber needs it most

197 OFDM extended with multiple access

OFDM in its primary form is considered as a digital modulation technique and not a multi-user

channel access method since it is utilized for transferring one bit stream over one

communication channel using one sequence of OFDM symbols However OFDM can be

combined with multiple access using time frequency or coding separation of the users

In orthogonal frequency-division multiple access (OFDMA) frequency-division multiple access

is achieved by assigning different OFDM sub-channels to different users OFDMA supports

differentiated quality of service by assigning different number of sub-carriers to different users in

a similar fashion as in CDMA and thus complex packet scheduling or Media Access Control

schemes can be avoided OFDMA is used in

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

the mobility mode of the IEEE 80216 Wireless MAN standard commonly referred to as

WiMAX

the IEEE 80220 mobile Wireless MAN standard commonly referred to as MBWA

the 3GPP Long Term Evolution (LTE) fourth generation mobile broadband standard

downlink The radio interface was formerly named High Speed OFDM Packet Access

(HSOPA) now named Evolved UMTS Terrestrial Radio Access (E-UTRA)

the now defunct Qualcomm3GPP2 Ultra Mobile Broadband (UMB) project intended as

a successor of CDMA2000 but replaced by LTE

OFDMA is also a candidate access method for the IEEE 80222 Wireless Regional Area

Networks (WRAN) The project aims at designing the first cognitive radio based standard

operating in the VHF-low UHF spectrum (TV spectrum)

In Multi-carrier code division multiple access (MC-CDMA) also known as OFDM-CDMA

OFDM is combined with CDMA spread spectrum communication for coding separation of the

users Co-channel interference can be mitigated meaning that manual fixed channel allocation

(FCA) frequency planning is simplified or complex dynamic channel allocation (DCA) schemes

are avoided

198 Space diversity

In OFDM based wide area broadcasting receivers can benefit from receiving signals from

several spatially dispersed transmitters simultaneously since transmitters will only destructively

interfere with each other on a limited number of sub-carriers whereas in general they will

actually reinforce coverage over a wide area This is very beneficial in many countries as it

permits the operation of national single-frequency networks (SFN) where many transmitters

send the same signal simultaneously over the same channel frequency SFNs utilise the available

spectrum more effectively than conventional multi-frequency broadcast networks (MFN) where

program content is replicated on different carrier frequencies SFNs also result in a diversity gain

in receivers situated midway between the transmitters The coverage area is increased and the

outage probability decreased in comparison to an MFN due to increased received signal strength

averaged over all sub-carriers

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Although the guard interval only contains redundant data which means that it reduces the

capacity some OFDM-based systems such as some of the broadcasting systems deliberately

use a long guard interval in order to allow the transmitters to be spaced farther apart in an SFN

and longer guard intervals allow larger SFN cell-sizes A rule of thumb for the maximum

distance between transmitters in an SFN is equal to the distance a signal travels during the guard

interval mdash for instance a guard interval of 200 microseconds would allow transmitters to be

spaced 60 km apart

A single frequency network is a form of transmitter macrodiversity The concept can be further

utilized in dynamic single-frequency networks (DSFN) where the SFN grouping is changed from

timeslot to timeslot

OFDM may be combined with other forms of space diversity for example antenna arrays and

MIMO channels This is done in the IEEE80211 Wireless LAN standard

199 Linear transmitter power amplifier

An OFDM signal exhibits a high peak-to-average power ratio (PAPR) because the independent

phases of the sub-carriers mean that they will often combine constructively Handling this high

PAPR requires

a high-resolution digital-to-analogue converter (DAC) in the transmitter

a high-resolution analogue-to-digital converter (ADC) in the receiver

a linear signal chain

Any non-linearity in the signal chain will cause intermodulation distortion that

raises the noise floor

may cause inter-carrier interference

generates out-of-band spurious radiation

The linearity requirement is demanding especially for transmitter RF output circuitry where

amplifiers are often designed to be non-linear in order to minimise power consumption In

practical OFDM systems a small amount of peak clipping is allowed to limit the PAPR in a

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

judicious trade-off against the above consequences However the transmitter output filter which

is required to reduce out-of-band spurs to legal levels has the effect of restoring peak levels that

were clipped so clipping is not an effective way to reduce PAPR

Although the spectral efficiency of OFDM is attractive for both terrestrial and space

communications the high PAPR requirements have so far limited OFDM applications to

terrestrial systems

The crest factor CF (in dB) for an OFDM system with n uncorrelated sub-carriers is[15]

CF = 10 log( n ) + CFc

where CFc is the crest factor (in dB) for each sub-carrier (CFc is 301 dB for the sine waves

used for BPSK and QPSK modulation)

For example the DVB-T signal in 2K mode is composed of 1705 sub-carriers that are each

QPSK-modulated giving a crest factor of 3532 dB[15]

Many crest factor reduction techniques have been developed

The dynamic range required for an FM receiver is 120 dB while DAB only require about 90 dB[16] As a comparison each extra bit per sample increases the dynamic range with 6 dB

1991 Efficiency comparison between single carrier and multicarrier

The performance of any communication system can be measured in terms of its power efficiency

and bandwidth efficiency The power efficiency describes the ability of communication system

to preserve bit error rate (BER) of the transmitted signal at low power levels Bandwidth

efficiency reflects how efficiently the allocated bandwidth is utilized and is defined as the

throughput data rate per Hertz in a given bandwidth If the large number of subcarriers are used

the bandwidth efficiency of multicarrier system such as OFDM with using optical fiber channel

is defined as

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

Factor 2 is because of two polarization states in the fiber

where is the symbol rate in giga symbol per second (Gsps) and is the bandwidth of

OFDM signal

There is saving of bandwidth by using Multicarrier modulation with orthogonal frequency

division multiplexing So the bandwidth for multicarrier system is less in comparison with

single carrier system and hence bandwidth efficiency of multicarrier system is larger than single

carrier system

SNoTransmission

Type

M in

M-

QAM

No of

Subcarriers

Bit

rate

Fiber

length

Power at the

receiver(at BER

of 10minus9)

Bandwidth

efficiency

1 single carrier 64 110

Gbits20 km -373 dBm 60000

2 multicarrier 64 12810

Gbits20 km -363 dBm 106022

There is only 1 dB reduction in receiver power but we get 767 improvement in bandwidth

efficiency with using multicarrier transmission technique

1992 Idealized system model

This section describes a simple idealized OFDM system model suitable for a time-invariant

AWGN channel

Transmitter

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

An OFDM carrier signal is the sum of a number of orthogonal sub-carriers with baseband data

on each sub-carrier being independently modulated commonly using some type of quadrature

amplitude modulation (QAM) or phase-shift keying (PSK) This composite baseband signal is

typically used to modulate a main RF carrier

is a serial stream of binary digits By inverse multiplexing these are first demultiplexed into

parallel streams and each one mapped to a (possibly complex) symbol stream using some

modulation constellation (QAM PSK etc) Note that the constellations may be different so

some streams may carry a higher bit-rate than others

An inverse FFT is computed on each set of symbols giving a set of complex time-domain

samples These samples are then quadrature-mixed to passband in the standard way The real and

imaginary components are first converted to the analogue domain using digital-to-analogue

converters (DACs) the analogue signals are then used to modulate cosine and sine waves at the

carrier frequency respectively These signals are then summed to give the transmission

signal

Receiver

The receiver picks up the signal which is then quadrature-mixed down to baseband using

cosine and sine waves at the carrier frequency This also creates signals centered on so low-

pass filters are used to reject these The baseband signals are then sampled and digitised using

analog-to-digital converters (ADCs) and a forward FFT is used to convert back to the frequency

domain

This returns parallel streams each of which is converted to a binary stream using an

appropriate symbol detector These streams are then re-combined into a serial stream which

is an estimate of the original binary stream at the transmitter

1993 Mathematical description

If sub-carriers are used and each sub-carrier is modulated using alternative symbols the

OFDM symbol alphabet consists of combined symbols

The low-pass equivalent OFDM signal is expressed as

where are the data symbols is the number of sub-carriers and is the OFDM symbol

time The sub-carrier spacing of makes them orthogonal over each symbol period this property

is expressed as

where denotes the complex conjugate operator and is the Kronecker delta

To avoid intersymbol interference in multipath fading channels a guard interval of length is

inserted prior to the OFDM block During this interval a cyclic prefix is transmitted such that the

signal in the interval equals the signal in the interval The OFDM signal

with cyclic prefix is thus

The low-pass signal above can be either real or complex-valued Real-valued low-pass

equivalent signals are typically transmitted at basebandmdashwireline applications such as DSL use

this approach For wireless applications the low-pass signal is typically complex-valued in

which case the transmitted signal is up-converted to a carrier frequency In general the

transmitted signal can be represented as

Usage

OFDM is used in Digital Audio Broadcasting (DAB) Digital television DVB-TT2 (terrestrial)

DVB-H (handheld) DMB-TH DVB-C2 (cable) Wireless LAN IEEE 80211a ADSL

(GdmtITU G9921) Mobile phone 4G

It is assumed that the cyclic prefix is longer than the maximum propagation delay So the

orthogonality between subcarriers and non intersymbol interference can be preserved

The number ofsubcarriers and multipaths is K and L in the system respectively The received

signal is obtained as

where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y

is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a

vector of independent identically distributed complex Gaussian noise with zero-mean and

variance The noise N is assumed to be uncorrelated with the channel H

CHAPTER-2

PROPOSED METHOD

21 Impact of Frequency Offset

The spacing between adjacent subcarriers in an OFDM system is typically very small and hence

accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is

introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of

receiver motion Due to the the residual frequency offset the orthogonality between transmit and

receive pulses will be lost and the received symbols will have a time- variant phase rotation We

see the effect of normalized residual frequency

Fig 21Frequency division multiplexing system

This chapter discusses the development of an algorithm to estimate CFO in an OFDM system

and forms the crux of this thesis The first section of the chapter derives the equations for the

received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a

function that provides a measure of the impact of CFO on the average probability of error in the

received symbols The nature of such an error function provides the means to identify the

magnitude of CFO based on observed symbols In the subsequent sections observations are

made about the analytical nature of such an error function and how it improves the performance

of the estimation algorithmWhile that diagram illustrates the components that would make up

the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be

reasonable to eliminate the components that do not necessarily affect the estimation of the CFO

The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the

system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the

impact of CFO on the demodulation of the received bits it may be safely assumed that the

received bits are time-synchronised with the receiver clock It is interesting to couple the

performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block

turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond

the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are

separated in frequency space and constellation space While these are practicalconsiderations in

the implementation of the OFDM tranceiver they may be omitted fromthis discussion without

loss of relevance For the purposes of this section and throughoutthis work we will assume that

the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are

ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the

digital domain

22 Expressions for Transmitted and Received Symbols

Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2

aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT

block Using the matrix notation W to denote the inverse Fourier Transform we have

t = Ws

The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft

This operation can be denoted using the vector notation as

u = Ftt

= FtWs

Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation

Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM

transmitter

where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the

transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit

DDS In the presence of channel noise the received symbol vector r can be represented as

r = u + z

= FtWs + z

where z denotes the complex circular white Gaussian noise added by the channel At the

receiver demodulation consists of translating the received signal to baseband frequency followed

by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency

The equalizer output y can thus be represented as

y = FFTfFHrrg

= WHFHr(FtWs + z)

= WHFHrFtWs +WHFHrz

where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the

receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer

ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random

vector z denotes a complex circular white Gaussian random vector hence multiplication by the

unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the

uncompensated CFO matrix Thus

y = WHFHrFtWs +WHFHrz

Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector

Let f2I be the covariance matrix of fDenoting WHPW as H

y = Hs + f

The demodulated symbol yi at the ith subcarrier is given by

yi = hTi

s + fi

where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D

C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus

en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error

inmapping the decoded symbol ^yn under operating conditions defined by the noise variance

f2 and the frequency offset

23 Carrier Frequency Offset

As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS

frequencies The following relations apply between the digital frequencies in 11

t = t fTs

r = r fTs

f= 1

2_ (t 1048576 r) (211)

= 1

2_(t 1048576 r) _ Ts (212)

As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N

2Ts

24 Time-Domain Estimation Techniques for CFO

For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused

cyclic prefix (CP) based Estimation

Blind CFO Estimation

Training-based CFO Estimation

241 Cyclic Prefix (CP)

The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)

that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol

(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last

samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a

multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of

channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not

constitute any information hence the effect of addition of long CP is loss in throughput of

system

Fig24 Inter-carrier interference (ICI) subject to CFO

25 Effect of CFO and STO

The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then

converted down to the baseband by using a local carrier signal of(hopefully) the same carrier

frequency at the receiver In general there are two types of distortion associated with the carrier

signal One is the phase noise due to the instability of carrier signal generators used at the

transmitter and receiver which can be modeled as a zero-mean Wiener random process The

other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the

orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency

domain with shifting of and time domain multiplying with the exponential term and the Doppler

frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX

of the transmitted signal for the OFDM symbol duration In other words a symbol-timing

synchronization must be performed to detect the starting point of each OFDM symbol (with the

CP removed) which facilitates obtaining the exact samples STO of samples affects the received

symbols in the time and frequency domain where the effects of channel and noise are neglected

for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO

All these foure cases

Case I This is the case when the estimated starting point of OFDM symbol coincides with the

exact timing preserving the orthogonality among subcar- rier frequency components In this

case the OFDM symbol can be perfectly recovered without any type of interference

Case II This is the case when the estimated starting point of OFDM symbol is before the exact

point yet after the end of the (lagged) channel response to the previous OFDM symbol In this

case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring

any ISI by the previous symbol in this case

Case III This is the case when the starting point of the OFDM symbol is estimated to exist

prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the

symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier

components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-

Channel Interference) occurs

26 Frequency-Domain Estimation Techniques for CFO

If two identical training symbols are transmitted consecutively the corresponding signals with

CFO of are related with each other which is a well-known approach by Moose Similar to

SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM

there exists multi-antenna interference (MAI) in the received antennas between the received

signals from different transmit antennas The MAI makes CFO estimation more difficult as

compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for

training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a

few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind

kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they

introduced a random-hopping scheme which robusties the CFO estimator against channel nulls

For training-based CFO estimators the overviews concerning the necessary changes to the

training sequences and thecorresponding CFO estimators when extending SISO-OFDM to

MIMO-OFDM were provided However with the provided training sequences satisfactory CFO

estimation performance cannot be achieved With the training sequences the training period

grows linearly with the number of transmit antennas which results in an increased overhead In

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

It is assumed that the cyclic prefix is longer than the maximum propagation delay So the

orthogonality between subcarriers and non intersymbol interference can be preserved

The number ofsubcarriers and multipaths is K and L in the system respectively The received

signal is obtained as

where X is a matrix of size K x K with the elements of the transmitted signals on its diagonal Y

is the received vector of size K xl H is a channel frequency response of size K x 1 and N is a

vector of independent identically distributed complex Gaussian noise with zero-mean and

variance The noise N is assumed to be uncorrelated with the channel H

CHAPTER-2

PROPOSED METHOD

21 Impact of Frequency Offset

The spacing between adjacent subcarriers in an OFDM system is typically very small and hence

accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is

introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of

receiver motion Due to the the residual frequency offset the orthogonality between transmit and

receive pulses will be lost and the received symbols will have a time- variant phase rotation We

see the effect of normalized residual frequency

Fig 21Frequency division multiplexing system

This chapter discusses the development of an algorithm to estimate CFO in an OFDM system

and forms the crux of this thesis The first section of the chapter derives the equations for the

received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a

function that provides a measure of the impact of CFO on the average probability of error in the

received symbols The nature of such an error function provides the means to identify the

magnitude of CFO based on observed symbols In the subsequent sections observations are

made about the analytical nature of such an error function and how it improves the performance

of the estimation algorithmWhile that diagram illustrates the components that would make up

the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be

reasonable to eliminate the components that do not necessarily affect the estimation of the CFO

The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the

system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the

impact of CFO on the demodulation of the received bits it may be safely assumed that the

received bits are time-synchronised with the receiver clock It is interesting to couple the

performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block

turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond

the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are

separated in frequency space and constellation space While these are practicalconsiderations in

the implementation of the OFDM tranceiver they may be omitted fromthis discussion without

loss of relevance For the purposes of this section and throughoutthis work we will assume that

the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are

ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the

digital domain

22 Expressions for Transmitted and Received Symbols

Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2

aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT

block Using the matrix notation W to denote the inverse Fourier Transform we have

t = Ws

The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft

This operation can be denoted using the vector notation as

u = Ftt

= FtWs

Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation

Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM

transmitter

where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the

transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit

DDS In the presence of channel noise the received symbol vector r can be represented as

r = u + z

= FtWs + z

where z denotes the complex circular white Gaussian noise added by the channel At the

receiver demodulation consists of translating the received signal to baseband frequency followed

by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency

The equalizer output y can thus be represented as

y = FFTfFHrrg

= WHFHr(FtWs + z)

= WHFHrFtWs +WHFHrz

where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the

receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer

ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random

vector z denotes a complex circular white Gaussian random vector hence multiplication by the

unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the

uncompensated CFO matrix Thus

y = WHFHrFtWs +WHFHrz

Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector

Let f2I be the covariance matrix of fDenoting WHPW as H

y = Hs + f

The demodulated symbol yi at the ith subcarrier is given by

yi = hTi

s + fi

where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D

C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus

en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error

inmapping the decoded symbol ^yn under operating conditions defined by the noise variance

f2 and the frequency offset

23 Carrier Frequency Offset

As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS

frequencies The following relations apply between the digital frequencies in 11

t = t fTs

r = r fTs

f= 1

2_ (t 1048576 r) (211)

= 1

2_(t 1048576 r) _ Ts (212)

As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N

2Ts

24 Time-Domain Estimation Techniques for CFO

For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused

cyclic prefix (CP) based Estimation

Blind CFO Estimation

Training-based CFO Estimation

241 Cyclic Prefix (CP)

The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)

that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol

(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last

samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a

multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of

channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not

constitute any information hence the effect of addition of long CP is loss in throughput of

system

Fig24 Inter-carrier interference (ICI) subject to CFO

25 Effect of CFO and STO

The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then

converted down to the baseband by using a local carrier signal of(hopefully) the same carrier

frequency at the receiver In general there are two types of distortion associated with the carrier

signal One is the phase noise due to the instability of carrier signal generators used at the

transmitter and receiver which can be modeled as a zero-mean Wiener random process The

other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the

orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency

domain with shifting of and time domain multiplying with the exponential term and the Doppler

frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX

of the transmitted signal for the OFDM symbol duration In other words a symbol-timing

synchronization must be performed to detect the starting point of each OFDM symbol (with the

CP removed) which facilitates obtaining the exact samples STO of samples affects the received

symbols in the time and frequency domain where the effects of channel and noise are neglected

for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO

All these foure cases

Case I This is the case when the estimated starting point of OFDM symbol coincides with the

exact timing preserving the orthogonality among subcar- rier frequency components In this

case the OFDM symbol can be perfectly recovered without any type of interference

Case II This is the case when the estimated starting point of OFDM symbol is before the exact

point yet after the end of the (lagged) channel response to the previous OFDM symbol In this

case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring

any ISI by the previous symbol in this case

Case III This is the case when the starting point of the OFDM symbol is estimated to exist

prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the

symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier

components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-

Channel Interference) occurs

26 Frequency-Domain Estimation Techniques for CFO

If two identical training symbols are transmitted consecutively the corresponding signals with

CFO of are related with each other which is a well-known approach by Moose Similar to

SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM

there exists multi-antenna interference (MAI) in the received antennas between the received

signals from different transmit antennas The MAI makes CFO estimation more difficult as

compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for

training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a

few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind

kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they

introduced a random-hopping scheme which robusties the CFO estimator against channel nulls

For training-based CFO estimators the overviews concerning the necessary changes to the

training sequences and thecorresponding CFO estimators when extending SISO-OFDM to

MIMO-OFDM were provided However with the provided training sequences satisfactory CFO

estimation performance cannot be achieved With the training sequences the training period

grows linearly with the number of transmit antennas which results in an increased overhead In

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

CHAPTER-2

PROPOSED METHOD

21 Impact of Frequency Offset

The spacing between adjacent subcarriers in an OFDM system is typically very small and hence

accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is

introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of

receiver motion Due to the the residual frequency offset the orthogonality between transmit and

receive pulses will be lost and the received symbols will have a time- variant phase rotation We

see the effect of normalized residual frequency

Fig 21Frequency division multiplexing system

This chapter discusses the development of an algorithm to estimate CFO in an OFDM system

and forms the crux of this thesis The first section of the chapter derives the equations for the

received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a

function that provides a measure of the impact of CFO on the average probability of error in the

received symbols The nature of such an error function provides the means to identify the

magnitude of CFO based on observed symbols In the subsequent sections observations are

made about the analytical nature of such an error function and how it improves the performance

of the estimation algorithmWhile that diagram illustrates the components that would make up

the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be

reasonable to eliminate the components that do not necessarily affect the estimation of the CFO

The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the

system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the

impact of CFO on the demodulation of the received bits it may be safely assumed that the

received bits are time-synchronised with the receiver clock It is interesting to couple the

performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block

turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond

the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are

separated in frequency space and constellation space While these are practicalconsiderations in

the implementation of the OFDM tranceiver they may be omitted fromthis discussion without

loss of relevance For the purposes of this section and throughoutthis work we will assume that

the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are

ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the

digital domain

22 Expressions for Transmitted and Received Symbols

Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2

aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT

block Using the matrix notation W to denote the inverse Fourier Transform we have

t = Ws

The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft

This operation can be denoted using the vector notation as

u = Ftt

= FtWs

Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation

Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM

transmitter

where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the

transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit

DDS In the presence of channel noise the received symbol vector r can be represented as

r = u + z

= FtWs + z

where z denotes the complex circular white Gaussian noise added by the channel At the

receiver demodulation consists of translating the received signal to baseband frequency followed

by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency

The equalizer output y can thus be represented as

y = FFTfFHrrg

= WHFHr(FtWs + z)

= WHFHrFtWs +WHFHrz

where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the

receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer

ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random

vector z denotes a complex circular white Gaussian random vector hence multiplication by the

unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the

uncompensated CFO matrix Thus

y = WHFHrFtWs +WHFHrz

Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector

Let f2I be the covariance matrix of fDenoting WHPW as H

y = Hs + f

The demodulated symbol yi at the ith subcarrier is given by

yi = hTi

s + fi

where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D

C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus

en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error

inmapping the decoded symbol ^yn under operating conditions defined by the noise variance

f2 and the frequency offset

23 Carrier Frequency Offset

As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS

frequencies The following relations apply between the digital frequencies in 11

t = t fTs

r = r fTs

f= 1

2_ (t 1048576 r) (211)

= 1

2_(t 1048576 r) _ Ts (212)

As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N

2Ts

24 Time-Domain Estimation Techniques for CFO

For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused

cyclic prefix (CP) based Estimation

Blind CFO Estimation

Training-based CFO Estimation

241 Cyclic Prefix (CP)

The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)

that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol

(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last

samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a

multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of

channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not

constitute any information hence the effect of addition of long CP is loss in throughput of

system

Fig24 Inter-carrier interference (ICI) subject to CFO

25 Effect of CFO and STO

The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then

converted down to the baseband by using a local carrier signal of(hopefully) the same carrier

frequency at the receiver In general there are two types of distortion associated with the carrier

signal One is the phase noise due to the instability of carrier signal generators used at the

transmitter and receiver which can be modeled as a zero-mean Wiener random process The

other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the

orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency

domain with shifting of and time domain multiplying with the exponential term and the Doppler

frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX

of the transmitted signal for the OFDM symbol duration In other words a symbol-timing

synchronization must be performed to detect the starting point of each OFDM symbol (with the

CP removed) which facilitates obtaining the exact samples STO of samples affects the received

symbols in the time and frequency domain where the effects of channel and noise are neglected

for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO

All these foure cases

Case I This is the case when the estimated starting point of OFDM symbol coincides with the

exact timing preserving the orthogonality among subcar- rier frequency components In this

case the OFDM symbol can be perfectly recovered without any type of interference

Case II This is the case when the estimated starting point of OFDM symbol is before the exact

point yet after the end of the (lagged) channel response to the previous OFDM symbol In this

case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring

any ISI by the previous symbol in this case

Case III This is the case when the starting point of the OFDM symbol is estimated to exist

prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the

symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier

components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-

Channel Interference) occurs

26 Frequency-Domain Estimation Techniques for CFO

If two identical training symbols are transmitted consecutively the corresponding signals with

CFO of are related with each other which is a well-known approach by Moose Similar to

SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM

there exists multi-antenna interference (MAI) in the received antennas between the received

signals from different transmit antennas The MAI makes CFO estimation more difficult as

compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for

training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a

few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind

kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they

introduced a random-hopping scheme which robusties the CFO estimator against channel nulls

For training-based CFO estimators the overviews concerning the necessary changes to the

training sequences and thecorresponding CFO estimators when extending SISO-OFDM to

MIMO-OFDM were provided However with the provided training sequences satisfactory CFO

estimation performance cannot be achieved With the training sequences the training period

grows linearly with the number of transmit antennas which results in an increased overhead In

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

21 Impact of Frequency Offset

The spacing between adjacent subcarriers in an OFDM system is typically very small and hence

accurate frequency synchronization is very important Carrier Frequency Offset (CFO) is

introduced in the system due to local oscillator inaccuracies and Doppler Shift in the case of

receiver motion Due to the the residual frequency offset the orthogonality between transmit and

receive pulses will be lost and the received symbols will have a time- variant phase rotation We

see the effect of normalized residual frequency

Fig 21Frequency division multiplexing system

This chapter discusses the development of an algorithm to estimate CFO in an OFDM system

and forms the crux of this thesis The first section of the chapter derives the equations for the

received symbol vector in the presence of noise and Carrier Frequency Offset (CFO) Defines a

function that provides a measure of the impact of CFO on the average probability of error in the

received symbols The nature of such an error function provides the means to identify the

magnitude of CFO based on observed symbols In the subsequent sections observations are

made about the analytical nature of such an error function and how it improves the performance

of the estimation algorithmWhile that diagram illustrates the components that would make up

the OFDM transmitter in formulating a model to reduce Carrier Frequency Offset it would be

reasonable to eliminate the components that do not necessarily affect the estimation of the CFO

The randomizer eliminates long runs of 0s and 1s in addition to adding to the security of the

system by making the coded bit stream unintelligible to eavesdroppers In an analysis of the

impact of CFO on the demodulation of the received bits it may be safely assumed that the

received bits are time-synchronised with the receiver clock It is interesting to couple the

performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block

turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond

the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are

separated in frequency space and constellation space While these are practicalconsiderations in

the implementation of the OFDM tranceiver they may be omitted fromthis discussion without

loss of relevance For the purposes of this section and throughoutthis work we will assume that

the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are

ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the

digital domain

22 Expressions for Transmitted and Received Symbols

Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2

aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT

block Using the matrix notation W to denote the inverse Fourier Transform we have

t = Ws

The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft

This operation can be denoted using the vector notation as

u = Ftt

= FtWs

Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation

Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM

transmitter

where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the

transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit

DDS In the presence of channel noise the received symbol vector r can be represented as

r = u + z

= FtWs + z

where z denotes the complex circular white Gaussian noise added by the channel At the

receiver demodulation consists of translating the received signal to baseband frequency followed

by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency

The equalizer output y can thus be represented as

y = FFTfFHrrg

= WHFHr(FtWs + z)

= WHFHrFtWs +WHFHrz

where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the

receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer

ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random

vector z denotes a complex circular white Gaussian random vector hence multiplication by the

unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the

uncompensated CFO matrix Thus

y = WHFHrFtWs +WHFHrz

Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector

Let f2I be the covariance matrix of fDenoting WHPW as H

y = Hs + f

The demodulated symbol yi at the ith subcarrier is given by

yi = hTi

s + fi

where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D

C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus

en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error

inmapping the decoded symbol ^yn under operating conditions defined by the noise variance

f2 and the frequency offset

23 Carrier Frequency Offset

As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS

frequencies The following relations apply between the digital frequencies in 11

t = t fTs

r = r fTs

f= 1

2_ (t 1048576 r) (211)

= 1

2_(t 1048576 r) _ Ts (212)

As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N

2Ts

24 Time-Domain Estimation Techniques for CFO

For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused

cyclic prefix (CP) based Estimation

Blind CFO Estimation

Training-based CFO Estimation

241 Cyclic Prefix (CP)

The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)

that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol

(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last

samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a

multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of

channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not

constitute any information hence the effect of addition of long CP is loss in throughput of

system

Fig24 Inter-carrier interference (ICI) subject to CFO

25 Effect of CFO and STO

The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then

converted down to the baseband by using a local carrier signal of(hopefully) the same carrier

frequency at the receiver In general there are two types of distortion associated with the carrier

signal One is the phase noise due to the instability of carrier signal generators used at the

transmitter and receiver which can be modeled as a zero-mean Wiener random process The

other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the

orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency

domain with shifting of and time domain multiplying with the exponential term and the Doppler

frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX

of the transmitted signal for the OFDM symbol duration In other words a symbol-timing

synchronization must be performed to detect the starting point of each OFDM symbol (with the

CP removed) which facilitates obtaining the exact samples STO of samples affects the received

symbols in the time and frequency domain where the effects of channel and noise are neglected

for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO

All these foure cases

Case I This is the case when the estimated starting point of OFDM symbol coincides with the

exact timing preserving the orthogonality among subcar- rier frequency components In this

case the OFDM symbol can be perfectly recovered without any type of interference

Case II This is the case when the estimated starting point of OFDM symbol is before the exact

point yet after the end of the (lagged) channel response to the previous OFDM symbol In this

case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring

any ISI by the previous symbol in this case

Case III This is the case when the starting point of the OFDM symbol is estimated to exist

prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the

symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier

components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-

Channel Interference) occurs

26 Frequency-Domain Estimation Techniques for CFO

If two identical training symbols are transmitted consecutively the corresponding signals with

CFO of are related with each other which is a well-known approach by Moose Similar to

SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM

there exists multi-antenna interference (MAI) in the received antennas between the received

signals from different transmit antennas The MAI makes CFO estimation more difficult as

compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for

training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a

few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind

kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they

introduced a random-hopping scheme which robusties the CFO estimator against channel nulls

For training-based CFO estimators the overviews concerning the necessary changes to the

training sequences and thecorresponding CFO estimators when extending SISO-OFDM to

MIMO-OFDM were provided However with the provided training sequences satisfactory CFO

estimation performance cannot be achieved With the training sequences the training period

grows linearly with the number of transmit antennas which results in an increased overhead In

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

received bits are time-synchronised with the receiver clock It is interesting to couple the

performance of an MSER-based CFO Estimator that utilises the noise immunity o_ered by block

turbo codes but the analysis of the MSER algorithm coupled with convolutional codes is beyond

the 8 scope of this thesis The interleaver and subcarrier mapper ensure that the encodedbits are

separated in frequency space and constellation space While these are practicalconsiderations in

the implementation of the OFDM tranceiver they may be omitted fromthis discussion without

loss of relevance For the purposes of this section and throughoutthis work we will assume that

the conversion between Analog and Digital formats is lossless(ie the ADCs and DACs are

ideal)Under these assumptions the reference OFDM tranceiver can operate entirely in the

digital domain

22 Expressions for Transmitted and Received Symbols

Let s = [s1 s2 sN]T be the vector of symbols from the complex alphabet A = fa1 a2

aMg that have been mapped from the input bit vector b Let t denote the output of the IFFT

block Using the matrix notation W to denote the inverse Fourier Transform we have

t = Ws

The subcarrier modulated symbol vector t is used to modulate the carrier signal at frequency ft

This operation can be denoted using the vector notation as

u = Ftt

= FtWs

Fig 22OFDM transmitter - Modified to suit discussion about CFO estimation

Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM

transmitter

where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the

transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit

DDS In the presence of channel noise the received symbol vector r can be represented as

r = u + z

= FtWs + z

where z denotes the complex circular white Gaussian noise added by the channel At the

receiver demodulation consists of translating the received signal to baseband frequency followed

by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency

The equalizer output y can thus be represented as

y = FFTfFHrrg

= WHFHr(FtWs + z)

= WHFHrFtWs +WHFHrz

where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the

receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer

ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random

vector z denotes a complex circular white Gaussian random vector hence multiplication by the

unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the

uncompensated CFO matrix Thus

y = WHFHrFtWs +WHFHrz

Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector

Let f2I be the covariance matrix of fDenoting WHPW as H

y = Hs + f

The demodulated symbol yi at the ith subcarrier is given by

yi = hTi

s + fi

where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D

C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus

en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error

inmapping the decoded symbol ^yn under operating conditions defined by the noise variance

f2 and the frequency offset

23 Carrier Frequency Offset

As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS

frequencies The following relations apply between the digital frequencies in 11

t = t fTs

r = r fTs

f= 1

2_ (t 1048576 r) (211)

= 1

2_(t 1048576 r) _ Ts (212)

As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N

2Ts

24 Time-Domain Estimation Techniques for CFO

For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused

cyclic prefix (CP) based Estimation

Blind CFO Estimation

Training-based CFO Estimation

241 Cyclic Prefix (CP)

The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)

that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol

(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last

samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a

multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of

channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not

constitute any information hence the effect of addition of long CP is loss in throughput of

system

Fig24 Inter-carrier interference (ICI) subject to CFO

25 Effect of CFO and STO

The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then

converted down to the baseband by using a local carrier signal of(hopefully) the same carrier

frequency at the receiver In general there are two types of distortion associated with the carrier

signal One is the phase noise due to the instability of carrier signal generators used at the

transmitter and receiver which can be modeled as a zero-mean Wiener random process The

other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the

orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency

domain with shifting of and time domain multiplying with the exponential term and the Doppler

frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX

of the transmitted signal for the OFDM symbol duration In other words a symbol-timing

synchronization must be performed to detect the starting point of each OFDM symbol (with the

CP removed) which facilitates obtaining the exact samples STO of samples affects the received

symbols in the time and frequency domain where the effects of channel and noise are neglected

for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO

All these foure cases

Case I This is the case when the estimated starting point of OFDM symbol coincides with the

exact timing preserving the orthogonality among subcar- rier frequency components In this

case the OFDM symbol can be perfectly recovered without any type of interference

Case II This is the case when the estimated starting point of OFDM symbol is before the exact

point yet after the end of the (lagged) channel response to the previous OFDM symbol In this

case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring

any ISI by the previous symbol in this case

Case III This is the case when the starting point of the OFDM symbol is estimated to exist

prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the

symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier

components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-

Channel Interference) occurs

26 Frequency-Domain Estimation Techniques for CFO

If two identical training symbols are transmitted consecutively the corresponding signals with

CFO of are related with each other which is a well-known approach by Moose Similar to

SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM

there exists multi-antenna interference (MAI) in the received antennas between the received

signals from different transmit antennas The MAI makes CFO estimation more difficult as

compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for

training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a

few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind

kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they

introduced a random-hopping scheme which robusties the CFO estimator against channel nulls

For training-based CFO estimators the overviews concerning the necessary changes to the

training sequences and thecorresponding CFO estimators when extending SISO-OFDM to

MIMO-OFDM were provided However with the provided training sequences satisfactory CFO

estimation performance cannot be achieved With the training sequences the training period

grows linearly with the number of transmit antennas which results in an increased overhead In

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Fig 23 Simplified OFDM receiver designed to complement functionality of the OFDM

transmitter

where Ft = diag(1 exp(it=N) exp(i2t=N) exp(i(N1)t=N)) denotes the modulation by the

transmitter-side Direct Digital Synthesizer (DDS) and t = 2fft is the frequency of the transmit

DDS In the presence of channel noise the received symbol vector r can be represented as

r = u + z

= FtWs + z

where z denotes the complex circular white Gaussian noise added by the channel At the

receiver demodulation consists of translating the received signal to baseband frequency followed

by taking the DFT of the resultant signal Let r = 2ffr be the receiver DDS frequency

The equalizer output y can thus be represented as

y = FFTfFHrrg

= WHFHr(FtWs + z)

= WHFHrFtWs +WHFHrz

where Fr = diag(1 exp(ir=N) exp(i2r=N) exp(i(N1)r=N)) denotes the modulation by the

receiver DDS In the absence of CFO the receiver DDS frequency r = t and the equalizer

ouputs are the transmitted constellation symbols in the presence of Gaussian noise The random

vector z denotes a complex circular white Gaussian random vector hence multiplication by the

unitary matrices WH and FR does not alter this property Also let P = FHrFt denote the

uncompensated CFO matrix Thus

y = WHFHrFtWs +WHFHrz

Since W and P are unitary matrices f 2 CN is a circular complex Gaussian random vector

Let f2I be the covariance matrix of fDenoting WHPW as H

y = Hs + f

The demodulated symbol yi at the ith subcarrier is given by

yi = hTi

s + fi

where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D

C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus

en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error

inmapping the decoded symbol ^yn under operating conditions defined by the noise variance

f2 and the frequency offset

23 Carrier Frequency Offset

As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS

frequencies The following relations apply between the digital frequencies in 11

t = t fTs

r = r fTs

f= 1

2_ (t 1048576 r) (211)

= 1

2_(t 1048576 r) _ Ts (212)

As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N

2Ts

24 Time-Domain Estimation Techniques for CFO

For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused

cyclic prefix (CP) based Estimation

Blind CFO Estimation

Training-based CFO Estimation

241 Cyclic Prefix (CP)

The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)

that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol

(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last

samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a

multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of

channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not

constitute any information hence the effect of addition of long CP is loss in throughput of

system

Fig24 Inter-carrier interference (ICI) subject to CFO

25 Effect of CFO and STO

The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then

converted down to the baseband by using a local carrier signal of(hopefully) the same carrier

frequency at the receiver In general there are two types of distortion associated with the carrier

signal One is the phase noise due to the instability of carrier signal generators used at the

transmitter and receiver which can be modeled as a zero-mean Wiener random process The

other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the

orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency

domain with shifting of and time domain multiplying with the exponential term and the Doppler

frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX

of the transmitted signal for the OFDM symbol duration In other words a symbol-timing

synchronization must be performed to detect the starting point of each OFDM symbol (with the

CP removed) which facilitates obtaining the exact samples STO of samples affects the received

symbols in the time and frequency domain where the effects of channel and noise are neglected

for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO

All these foure cases

Case I This is the case when the estimated starting point of OFDM symbol coincides with the

exact timing preserving the orthogonality among subcar- rier frequency components In this

case the OFDM symbol can be perfectly recovered without any type of interference

Case II This is the case when the estimated starting point of OFDM symbol is before the exact

point yet after the end of the (lagged) channel response to the previous OFDM symbol In this

case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring

any ISI by the previous symbol in this case

Case III This is the case when the starting point of the OFDM symbol is estimated to exist

prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the

symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier

components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-

Channel Interference) occurs

26 Frequency-Domain Estimation Techniques for CFO

If two identical training symbols are transmitted consecutively the corresponding signals with

CFO of are related with each other which is a well-known approach by Moose Similar to

SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM

there exists multi-antenna interference (MAI) in the received antennas between the received

signals from different transmit antennas The MAI makes CFO estimation more difficult as

compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for

training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a

few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind

kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they

introduced a random-hopping scheme which robusties the CFO estimator against channel nulls

For training-based CFO estimators the overviews concerning the necessary changes to the

training sequences and thecorresponding CFO estimators when extending SISO-OFDM to

MIMO-OFDM were provided However with the provided training sequences satisfactory CFO

estimation performance cannot be achieved With the training sequences the training period

grows linearly with the number of transmit antennas which results in an increased overhead In

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

The demodulated symbol yi at the ith subcarrier is given by

yi = hTi

s + fi

where hiT denotes the ith row of the matrix HFurther y 2 CN Let us de_ne a mapping rule D

C 7 A and ^yn = D(yn) be thedecision on yn The error event for the nth symbol is thus

en = f^yn 6= sng The objective of the carrier frequency offset estimator is to minimize the error

inmapping the decoded symbol ^yn under operating conditions defined by the noise variance

f2 and the frequency offset

23 Carrier Frequency Offset

As mentioned earlier the digital frequencies t and r denote the transmitter and receiver DDS

frequencies The following relations apply between the digital frequencies in 11

t = t fTs

r = r fTs

f= 1

2_ (t 1048576 r) (211)

= 1

2_(t 1048576 r) _ Ts (212)

As per the Nyquist criterion the bandwidth required for N orthogonal pulses is B = N

2Ts

24 Time-Domain Estimation Techniques for CFO

For CFO estimation in the time domain cyclic prefix (CP) or training symbol isused

cyclic prefix (CP) based Estimation

Blind CFO Estimation

Training-based CFO Estimation

241 Cyclic Prefix (CP)

The OFDM guard interval can be inserted in two different ways One is the zeropadding (ZP)

that pads the guard interval with zeros The other is the cyclic extension of the OFDM symbol

(for some continuity) with CP or CSCP is to extend the OFDM symbol by copying the last

samples of the OFDM symbol into its front OFDM symbols with CP and ISI effect of a

multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of

channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not

constitute any information hence the effect of addition of long CP is loss in throughput of

system

Fig24 Inter-carrier interference (ICI) subject to CFO

25 Effect of CFO and STO

The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then

converted down to the baseband by using a local carrier signal of(hopefully) the same carrier

frequency at the receiver In general there are two types of distortion associated with the carrier

signal One is the phase noise due to the instability of carrier signal generators used at the

transmitter and receiver which can be modeled as a zero-mean Wiener random process The

other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the

orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency

domain with shifting of and time domain multiplying with the exponential term and the Doppler

frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX

of the transmitted signal for the OFDM symbol duration In other words a symbol-timing

synchronization must be performed to detect the starting point of each OFDM symbol (with the

CP removed) which facilitates obtaining the exact samples STO of samples affects the received

symbols in the time and frequency domain where the effects of channel and noise are neglected

for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO

All these foure cases

Case I This is the case when the estimated starting point of OFDM symbol coincides with the

exact timing preserving the orthogonality among subcar- rier frequency components In this

case the OFDM symbol can be perfectly recovered without any type of interference

Case II This is the case when the estimated starting point of OFDM symbol is before the exact

point yet after the end of the (lagged) channel response to the previous OFDM symbol In this

case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring

any ISI by the previous symbol in this case

Case III This is the case when the starting point of the OFDM symbol is estimated to exist

prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the

symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier

components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-

Channel Interference) occurs

26 Frequency-Domain Estimation Techniques for CFO

If two identical training symbols are transmitted consecutively the corresponding signals with

CFO of are related with each other which is a well-known approach by Moose Similar to

SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM

there exists multi-antenna interference (MAI) in the received antennas between the received

signals from different transmit antennas The MAI makes CFO estimation more difficult as

compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for

training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a

few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind

kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they

introduced a random-hopping scheme which robusties the CFO estimator against channel nulls

For training-based CFO estimators the overviews concerning the necessary changes to the

training sequences and thecorresponding CFO estimators when extending SISO-OFDM to

MIMO-OFDM were provided However with the provided training sequences satisfactory CFO

estimation performance cannot be achieved With the training sequences the training period

grows linearly with the number of transmit antennas which results in an increased overhead In

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

multipath channel for each sub carrier Cyclic prefix should be greater than delay spread of

channel to avoid inter OFDM symbol interference CP is simply repeating symbols dost not

constitute any information hence the effect of addition of long CP is loss in throughput of

system

Fig24 Inter-carrier interference (ICI) subject to CFO

25 Effect of CFO and STO

The baseband transmit signal is converted up to the pass band by a carrier modu-lation and then

converted down to the baseband by using a local carrier signal of(hopefully) the same carrier

frequency at the receiver In general there are two types of distortion associated with the carrier

signal One is the phase noise due to the instability of carrier signal generators used at the

transmitter and receiver which can be modeled as a zero-mean Wiener random process The

other is the carrier frequency offset (CFO) caused by Doppler frequency CFO destroys the

orthogonality between the sub-carriers the effect of the CFO in receiving signal in frequency

domain with shifting of and time domain multiplying with the exponential term and the Doppler

frequency and normalized CFO for some standard systems like DMB3GPP and mobile WiMAX

of the transmitted signal for the OFDM symbol duration In other words a symbol-timing

synchronization must be performed to detect the starting point of each OFDM symbol (with the

CP removed) which facilitates obtaining the exact samples STO of samples affects the received

symbols in the time and frequency domain where the effects of channel and noise are neglected

for simplicity of exposition Four different cases of OFDM symbolstarting point subject to STO

All these foure cases

Case I This is the case when the estimated starting point of OFDM symbol coincides with the

exact timing preserving the orthogonality among subcar- rier frequency components In this

case the OFDM symbol can be perfectly recovered without any type of interference

Case II This is the case when the estimated starting point of OFDM symbol is before the exact

point yet after the end of the (lagged) channel response to the previous OFDM symbol In this

case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring

any ISI by the previous symbol in this case

Case III This is the case when the starting point of the OFDM symbol is estimated to exist

prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the

symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier

components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-

Channel Interference) occurs

26 Frequency-Domain Estimation Techniques for CFO

If two identical training symbols are transmitted consecutively the corresponding signals with

CFO of are related with each other which is a well-known approach by Moose Similar to

SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM

there exists multi-antenna interference (MAI) in the received antennas between the received

signals from different transmit antennas The MAI makes CFO estimation more difficult as

compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for

training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a

few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind

kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they

introduced a random-hopping scheme which robusties the CFO estimator against channel nulls

For training-based CFO estimators the overviews concerning the necessary changes to the

training sequences and thecorresponding CFO estimators when extending SISO-OFDM to

MIMO-OFDM were provided However with the provided training sequences satisfactory CFO

estimation performance cannot be achieved With the training sequences the training period

grows linearly with the number of transmit antennas which results in an increased overhead In

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Case I This is the case when the estimated starting point of OFDM symbol coincides with the

exact timing preserving the orthogonality among subcar- rier frequency components In this

case the OFDM symbol can be perfectly recovered without any type of interference

Case II This is the case when the estimated starting point of OFDM symbol is before the exact

point yet after the end of the (lagged) channel response to the previous OFDM symbol In this

case the lth symbol is not overlapped with the previous OFDM symbol that is without incurring

any ISI by the previous symbol in this case

Case III This is the case when the starting point of the OFDM symbol is estimated to exist

prior to the end of the (lagged) channel response to the previous OFDM symbol and thus the

symbol timing is too early to avoid the ISI In this case the orthogonality among subcarrier

components is destroyed by the ISI (from the previous symbol) and furthermore ICI (Inter-

Channel Interference) occurs

26 Frequency-Domain Estimation Techniques for CFO

If two identical training symbols are transmitted consecutively the corresponding signals with

CFO of are related with each other which is a well-known approach by Moose Similar to

SISO-OFDM MIMO-OFDM is also very sensitive to CFO More- over for MIMO-OFDM

there exists multi-antenna interference (MAI) in the received antennas between the received

signals from different transmit antennas The MAI makes CFO estimation more difficult as

compare to SISO-OFDM sys- tems and a optimum size training sequence design is required for

training-based CFO estimation in high range of CFOs However unlike SISO- OFDM only a

few CFO estimation in MIMO-OFDM system works have appeared in the literature In a blind

kurtosis-based CFO estimator for MIMO-OFDM was developed In that estimation they

introduced a random-hopping scheme which robusties the CFO estimator against channel nulls

For training-based CFO estimators the overviews concerning the necessary changes to the

training sequences and thecorresponding CFO estimators when extending SISO-OFDM to

MIMO-OFDM were provided However with the provided training sequences satisfactory CFO

estimation performance cannot be achieved With the training sequences the training period

grows linearly with the number of transmit antennas which results in an increased overhead In

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

[22] a white sequence based maximum likelihood (ML) CFO estimator was addressed for

MIMO while a hop- ping pilot based CFO estimator was proposed for MIMO-OFDM Require

a large point discrete Fourier transform (DFT) operation for CFO Estimation In CFO estimator

only applied to at-fading MIMO channels

OFDM system carries the message data on orthogonal sub-carriers for parallel transmission

combating the distortion caused by the frequency-selective channel or equivalently the inter-

symbol-interference in the multi-path fading channel However the advantage of the OFDM can

be useful only when the orthogonality

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

CHAPTER-3

RESULTS

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

CHAPTER-4

MATLAB

INTRODUCTION TO MATLAB

What Is MATLAB

MATLABreg is a high-performance language for technical computing It integrates

computation visualization and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation Typical uses include

Math and computation

Algorithm development

Data acquisition

Modeling simulation and prototyping

Data analysis exploration and visualization

Scientific and engineering graphics

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Application development including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning This allows you to solve many technical computing problems especially

those with matrix and vector formulations in a fraction of the time it would take to write a

program in a scalar non interactive language such as C or FORTRAN

The name MATLAB stands for matrix laboratory MATLAB was originally written to

provide easy access to matrix software developed by the LINPACK and EISPACK projects

Today MATLAB engines incorporate the LAPACK and BLAS libraries embedding the state of

the art in software for matrix computation

MATLAB has evolved over a period of years with input from many users In university

environments it is the standard instructional tool for introductory and advanced courses in

mathematics engineering and science In industry MATLAB is the tool of choice for high-

productivity research development and analysis

MATLAB features a family of add-on application-specific solutions called toolboxes

Very important to most users of MATLAB toolboxes allow you to learn and apply specialized

technology Toolboxes are comprehensive collections of MATLAB functions (M-files) that

extend the MATLAB environment to solve particular classes of problems Areas in which

toolboxes are available include signal processing control systems neural networks fuzzy logic

wavelets simulation and many others

The MATLAB System

The MATLAB system consists of five main parts

Development Environment

This is the set of tools and facilities that help you use MATLAB functions and files Many

of these tools are graphical user interfaces It includes the MATLAB desktop and Command

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Window a command history an editor and debugger and browsers for viewing help the

workspace files and the search path

The MATLAB Mathematical Function

This is a vast collection of computational algorithms ranging from elementary functions

like sum sine cosine and complex arithmetic to more sophisticated functions like matrix

inverse matrix eigen values Bessel functions and fast Fourier transforms

The MATLAB Language

This is a high-level matrixarray language with control flow statements functions data

structures inputoutput and object-oriented programming features It allows both programming

in the small to rapidly create quick and dirty throw-away programs and programming in the

large to create complete large and complex application programs

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs as well as

annotating and printing these graphs It includes high-level functions for two-dimensional and

three-dimensional data visualization image processing animation and presentation graphics It

also includes low-level functions that allow you to fully customize the appearance of graphics as

well as to build complete graphical user interfaces on your MATLAB applications

The MATLAB Application Program Interface (API)

This is a library that allows you to write C and Fortran programs that interact with

MATLAB It includes facilities for calling routines from MATLAB (dynamic linking) calling

MATLAB as a computational engine and for reading and writing MAT-files

MATLAB WORKING ENVIRONMENT

MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Matlab Desktop is the main Matlab application window The desktop contains five sub

windows the command window the workspace browser the current directory window the

command history window and one or more figure windows which are shown only when the

user displays a graphic

The command window is where the user types MATLAB commands and expressions at the

prompt (gtgt) and where the output of those commands is displayed MATLAB defines the

workspace as the set of variables that the user creates in a work session The workspace browser

shows these variables and some information about them Double clicking on a variable in the

workspace browser launches the Array Editor which can be used to obtain information and

income instances edit certain properties of the variable

The current Directory tab above the workspace tab shows the contents of the current

directory whose path is shown in the current directory window For example in the windows

operating system the path might be as follows CMATLABWork indicating that directory

ldquoworkrdquo is a subdirectory of the main directory ldquoMATLABrdquo WHICH IS INSTALLED IN

DRIVE C clicking on the arrow in the current directory window shows a list of recently used

paths Clicking on the button to the right of the window allows the user to change the current

directory

MATLAB uses a search path to find M-files and other MATLAB related files which are

organize in directories in the computer file system Any file run in MATLAB must reside in the

current directory or in a directory that is on search path By default the files supplied with

MATLAB and math works toolboxes are included in the search path The easiest way to see

which directories are on the search path

The easiest way to see which directories are soon the search path or to add or modify a search

path is to select set path from the File menu the desktop and then use the set path dialog box It

is good practice to add any commonly used directories to the search path to avoid repeatedly

having the change the current directory

The Command History Window contains a record of the commands a user has entered in

the command window including both current and previous MATLAB sessions Previously

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

entered MATLAB commands can be selected and re-executed from the command history

window by right clicking on a command or sequence of commands

This action launches a menu from which to select various options in addition to executing the

commands This is useful to select various options in addition to executing the commands This

is a useful feature when experimenting with various commands in a work session

Using the MATLAB Editor to create M-Files

The MATLAB editor is both a text editor specialized for creating M-files and a graphical

MATLAB debugger The editor can appear in a window by itself or it can be a sub window in

the desktop M-files are denoted by the extension m as in pixelupm The MATLAB editor

window has numerous pull-down menus for tasks such as saving viewing and debugging files

Because it performs some simple checks and also uses color to differentiate between various

elements of code this text editor is recommended as the tool of choice for writing and editing M-

functions To open the editor type edit at the prompt opens the M-file filenamem in an editor

window ready for editing As noted earlier the file must be in the current directory or in a

directory in the search path

Getting Help

The principal way to get help online is to use the MATLAB help browser opened as a

separate window either by clicking on the question mark symbol () on the desktop toolbar or by

typing help browser at the prompt in the command window The help Browser is a web browser

integrated into the MATLAB desktop that displays a Hypertext Markup Language(HTML)

documents The Help Browser consists of two panes the help navigator pane used to find

information and the display pane used to view the information Self-explanatory tabs other than

navigator pane are used to perform a search

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

CHAPTER-5

COMMUNICATION

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Communications System Toolboxtrade provides algorithms and tools for the design simulation

and analysis of communications systems These capabilities are provided as MATLAB reg

functions MATLAB System objectstrade and Simulink reg blocks The system toolbox includes

algorithms for source coding channel coding interleaving modulation equalization

synchronization and channel modeling Tools are provided for bit error rate analysis generating

eye and constellation diagrams and visualizing channel characteristics The system toolbox also

provides adaptive algorithms that let you model dynamic communications systems that use

OFDM OFDMA and MIMO techniques Algorithms support fixed-point data arithmetic and C

or HDL code generation

Key Features

Algorithms for designing the physical layer of communications systems including source

coding channel

coding interleaving modulation channel models MIMO equalization and synchronization

GPU-enabled System objects for computationally intensive algorithms such as Turbo LDPC

and Viterbi

decoders

Interactive visualization tools including eye diagrams constellations and channel scattering

functions

Graphical tool for comparing the simulated bit error rate of a system with analytical results

Channel models including AWGN Multipath Rayleigh Fading Rician Fading MIMO

Multipath Fading and

LTE MIMO Multipath Fading

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Basic RF impairments including nonlinearity phase noise thermal noise and phase and

frequency offsets

Algorithms available as MATLAB functions MATLAB System objects and Simulink blocks

Support for fixed-point modeling and C and HDL code generation

System Design Characterization and Visualization

The design and simulation of a communications system requires analyzing its response to the

noise and interference inherent in real-world environments studying its behavior using graphical

and quantitative means and determining whether the resulting performance meets standards of

acceptability Communications System Toolbox implements a variety of tasks for

communications system design and simulation Many of the functions System objectstrade and

blocks in the system toolbox perform computations associated with a particular component of a

communications system such as a demodulator or equalizer Other capabilities are designed for

visualization or analysis

System Characterization

The system toolbox offers several standard methods for quantitatively characterizing system

performance

Bit error rate (BER) computations

Adjacent channel power ratio (ACPR) measurements

Error vector magnitude (EVM) measurements

Modulation error ratio (MER) measurements

Because BER computations are fundamental to the characterization of any communications

system the system

toolbox provides the following tools and capabilities for configuring BER test scenarios and

accelerating BER simulations

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

BER tool mdash A graphical user interface that enables you to analyze BER performance of

communications systems You can analyze performance via a simulation-based semianalytic or

theoretical approach

Error Rate Test Console mdash A MATLAB object that runs simulations for communications

systems to measure error rate performance It supports user-specified test points and generation

of parametric performance plots and surfaces Accelerated performance can be realized when

running on a multicore computing platform

Multicore and GPU acceleration mdash A capability provided by Parallel Computing Toolboxtrade

that enables you to accelerate simulation performance using multicore and GPU hardware within

your computer

Distributed computing and cloud computing support mdash Capabilities provided by Parallel

Computing Toolbox and MATLAB Distributed Computing Servertrade that enable you to leverage

the computing power of your server farms and the Amazon EC2 Web service Performance

Visualization The system toolbox provides the following capabilities for visualizing system

performance

Channel visualization tool mdash For visualizing the characteristics of a fading channel

Eye diagrams and signal constellation scatter plots mdash For a qualitative visual understanding

of system behavior that enables you to make initial design decisions

Signal trajectory plots mdash For a continuous picture of the signalrsquos trajectory between decision

points

BER plots mdash For visualizing quantitative BER performance of a design candidate

parameterized by metrics such as SNR and fixed-point word size

Analog and Digital Modulation

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Analog and digital modulation techniques encode the information stream into a signal that is

suitable for transmission Communications System Toolbox provides a number of modulation

and corresponding demodulation capabilities These capabilities are available as MATLAB

functions and objects MATLAB System Modulation types provided by the toolbox are

Analog including AM FM PM SSB and DSBSC

Digital including FSK PSK BPSK DPSK OQPSK MSK PAM QAM and TCM

Source and Channel Coding

Communications System Toolbox provides source and channel coding capabilities that let you

develop and evaluate communications architectures quickly enabling you to explore what-if

scenarios and avoid the need to create coding capabilities from scratch

Source Coding

Source coding also known as quantization or signal formatting is a way of processing data in

order to reduce redundancy or prepare it for later processing The system toolbox provides a

variety of types of algorithms for implementing source coding and decoding including

Quantizing

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Companding (micro-law and A-law)

Differential pulse code modulation (DPCM)

Huffman coding

Arithmetic coding

Channel Coding

Orthogonal space-time block code (OSTBC) (encoder and decoder for MIMO channels)

Turbo encoder and decoder examples

The system toolbox provides utility functions for creating your own channel coding You can

create generator polynomials and coefficients and syndrome decoding tables as well as product

parity-check and generator matrices

The system toolbox also provides block and convolutional interleaving and deinterleaving

functions to reduce data errors caused by burst errors in a communication system

Block including General block interleaver algebraic interleaver helical scan interleaver matrix

interleaver and random interleaver

Convolutional including General multiplexed interleaver convolutional interleaver and helical

interleaver

Channel Modeling and RF Impairments

Channel Modeling

Communications System Toolbox provides algorithms and tools for modeling noise fading

interference and other distortions that are typically found in communications channels The

system toolbox supports the following types of channels

Additive white Gaussian noise (AWGN)

Multiple-input multiple-output (MIMO) fading

Single-input single-output (SISO) Rayleigh and Rician fading

Binary symmetric

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

A MATLAB channel object provides a concise configurable implementation of channel models

enabling you to

specify parameters such as

Path delays

Average path gains

Maximum Doppler shifts

K-Factor for Rician fading channels

Doppler spectrum parameters

For MIMO systems the MATLAB MIMO channel object expands these parameters to also

include

Number of transmit antennas (up to 8)

Number of receive antennas (up to 8)

Transmit correlation matrix

Receive correlation matrix

To combat the effects noise and channel corruption the system toolbox provides block and

convolutional coding and decoding techniques to implement error detection and correction For

simple error detection with no inherent correction a cyclic redundancy check capability is also

available Channel coding capabilities provided by the system toolbox include

BCH encoder and decoder

Reed-Solomon encoder and decoder

LDPC encoder and decoder

Convolutional encoder and Viterbi decoder

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

RF Impairments

To model the effects of a nonideal RF front end you can introduce the following impairments

into your communications system enabling you to explore and characterize performance with

real-world effects

Memoryless nonlinearity

Phase and frequency offset

Phase noise

Thermal noise

You can include more complex RF impairments and RF circuit models in your design using

SimRFtrade

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Equalization and Synchronization

Communications System Toolbox lets you explore equalization and synchronization techniques

These techniques are generally adaptive in nature and challenging to design and characterize

The system toolbox provides algorithms and tools that let you rapidly select the appropriate

technique in your communications system Equalization To evaluate different approaches to

equalization the system toolbox provides you with adaptive algorithms such as

LMS

Normalized LMS

Variable step LMS

Signed LMS

MLSE (Viterbi)

RLS

CMA

These adaptive equalizers are available as nonlinear decision feedback equalizer (DFE)

implementations and as

linear (symbol or fractionally spaced) equalizer implementations

Synchronization

The system toolbox provides algorithms for both carrier phase synchronization and timing phase

synchronization For timing phase synchronization the system toolbox provides a MATLAB

Timing Phase Synchronizer object that offers the following implementation methods

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Early-late gate timing method

Gardnerrsquos method

Fourth-order nonlinearity method

Stream Processing in MATLAB and Simulink

Most communication systems handle streaming and frame-based data using a combination of

temporal processing and simultaneous multi frequency and multichannel processing This type of

streaming multidimensional processing can be seen in advanced communication architectures

such as OFDM and MIMO Communications System Toolbox enables the simulation of

advanced communications systems by supporting stream processing and frame-based simulation

in MATLAB and Simulink In MATLAB stream processing is enabled by System objectstrade

which use MATLAB objects to represent time-based and data-driven algorithms sources and

sinks System objects implicitly manage many details of stream processing such as data

indexing buffering and management of algorithm state You can mix System objects with

standard MATLAB functions and operators Most System objects have a corresponding

Simulink block with the same capabilities Simulink handles stream processing implicitly by

managing the flow of data through the blocks that make up a Simulink model Simulink is an

interactive graphical environment for modeling and simulating dynamic systems that uses

hierarchical diagrams to represent a system model It includes a library of general-purpose

predefined blocks to represent algorithms sources sinks and system hierarchy

Implementing a Communications System

Fixed-Point Modeling Many communications systems use hardware that requires a fixed-point

representation of your design

Communications System Toolbox supports fixed-point modeling in all relevant blocks and

System objectstrade with tools that help you configure fixed-point attributes

Fixed-point support in the system toolbox includes

Word sizes from 1 to 128 bits

Arbitrary binary-point placement

Overflow handling methods (wrap or saturation)

Rounding methods ceiling convergent floor nearest round simplest and zero

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

Fixed-Point Tool in Simulink Fixed Pointtrade facilitates the conversion of floating-point data

types to fixed point For configuration of fixed-point properties the tool tracks overflows and

maxima and minima

Code Generation

Once you have developed your algorithm or communications system you can automatically

generate C code from it for verification rapid prototyping and implementation Most System

objects functions and blocks in Communications System Toolbox can generate ANSIISO C

code using MATLAB Codertrade Simulink Codertrade or Embedded Codertrade A subset of System

objects and Simulink blocks can also generate HDL code To leverage existing intellectual

property you can select optimizations for specific processor architectures and integrate legacy C

code with the generated code

You can also generate C code for both floating-point andfixed-point data types

DSP Prototyping DSPs are used in communication system implementation for verification rapid

prototyping or final hardware implementation Using the processor-in-the-loop (PIL) simulation

capability found in Embedded Coder you can verify generated source code and compiled code

by running your algorithmrsquos implementation code on a target processor FPGA Prototyping

FPGAs are used in communication systems for implementing high-speed signal processing

algorithms Using the FPGA-in-the-loop (FIL) capability found in HDL Verifiertrade you can test

RTL code in real hardware for any

existing HDL code either manually written or automatically generated HDL code

CHAPTER-6

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

CONCLUSION

In this paper we examine an one of a kind issue in minimal remote handsets transient bearer

recurrence balance (CFO) The transient CFO is seen under TXRX exchanging in frameworks

that oblige time division duplex (TDD) operation We showed that the transient CFO can be

demonstrated as the step reaction of an under damped second request framework To digitally

adjust for the transient CFO we propose calculations based on the subspace decay of the Hankel-

like grid A weighted subspace fitting calculation is additionally proposed to progress the

estimation precision The execution examination is confirmed in light of both numerical

recreations and exploratory results from the test bed gathered specimens The transient

hindrances emerge in gadgets that need to switch between different radio works and debase the

framework execution through the bended sign

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

CHAPTER-7

REFERENCES

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

[1] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAn overview ofMIMO

communicationsmdash A key to gigabit wirelessrdquo Proc IEEE vol 92no 2 pp 198ndash218 Feb

2004

[2]B Muquet Z Wang G B Giannakis M de Courville andP Duhamel ldquoCyclic prefixing or

zero padding for wireless multicarrier transmissionsrdquo IEEE Trans Commun vol 50 no 12

pp 2136ndash2148 Dec2002

[3] Y Li N Seshadri and S Ariyavisitakul ldquoChannel estimation for OFDM systems with

transmitter diversity in mobile wireless channelsrdquo IEEE J Sel Areas Commun vol17 no3

pp461ndash471March 1999

[4] D Wan B Han J Zhao X Gao and X You ldquoChannel estimation algorithms for

broadband MIMO-OFDM sparse channelrdquo Proc14th IEEE Int Symp on Personal Indoor and

Mobile Radio Communications pp1929ndash1933 Beijing China Sept 2003

[5] 3GPP ldquoEvolved Universal Terrestrial Radio Access (E-UTRA) Physical channels and

modulationrdquo TS 36211 3rd Generation Partnership Project (3GPP) Sept 2008

[6] J-J van de Beek O Edfors M Sandell S K Wilson and P O Borjesson ldquoOn channel

estimation in OFDM systemsrdquo in Proc IEEE45th Vehicular Technology Conf Chicago IL Jul

1995 pp 815-819

[7]O Edfors M Sandell J-J van de Beek S K Wilson and P O Borjesson ldquoOFDM channel

estimation by singular value decompositionrdquoin Proc IEEE 46th Vehicular Technology

Conference Atlanta GA USAApr 1996 pp 923-927

[8] S D Ma and T S Ng ldquoTime domain signal detection based on second-order statistics for

MIMOOFDM systemsrdquo IEEE TransSignal Process vol55 no3pp1150ndash1158Mar2007

[9] SD Ma and TS Ng ldquoSemi-blind time-domain equalization for MIMO-OFDM systemsrdquo

IEEE Transactions on Vehicular Technology 57(4) 2219-2227 July 2008

[10] MM RanaldquoChannel estimation techniques and LTE Terminal implementation challengesrdquo in

Proc International Conference on Computer and Information Technology pp 545-549 December

2010

[11] M Simko D Wu C Mehlfuumlhrer J Eilert D Liu ldquoImplementation Aspects of Channel

Estimationfor 3GPP LTE Terminalsrdquo in Proc Proc European Wireless 2011 Vienna April

2011

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

[12] M T Zhang M M Jovanovic and F C Lee ldquoDesign considerationsfor low-voltage on-

board dcdc modules for next generations of dataprocessing circuitsrdquo IEEE Trans Power

Electron vol 11 no 2 pp 328ndash337 Mar 1996

[13] C Gezgin ldquoPredicting load transient response of output voltage indcndashdc convertersrdquo in

Proc IEEE Appl Power Electron Conf 2004pp 1339ndash1344

[14] P H Moose ldquoA technique for orthogonal frequency division multiplexingfrequency offset

correctionrdquo IEEE Trans Communications vol 42no 10 pp 2908ndash2914 Oct 1994

[15] J J van de BeekM Sandell and P O Borjesson ldquoML estimation of timeand frequency

offset in OFDM systemsrdquo IEEE Trans Signal Processvol 45 no 7 pp 1800ndash1805 Jul 1997

[16] T P Zielinski and K Duda ldquoFrequency and damping estimation methodsmdashAn overviewrdquo

Metrology Meas Syst vol 18 no 4 pp 505ndash 528 Dec 2011

[17] R Kumaresan and R W Tufts ldquoEstimation the parameters of exponentially damped

sinusoids and pole-zero modeling in noiserdquo IEEE Trans Acoust Speech Signal Process vol

ASSP-30 no 6 pp 833ndash840 Dec 1982

[18] Y Li K Liu and J Razavilar ldquoA parameter estimation scheme for damped sinusoidal

signals based on low-rank Hankel approximationrdquo IEEE Trans Signal Processing vol 45 no

2 pp 481ndash486 Feb 1997

[19] Y Hua and T K Sarkar ldquoMatrix pencil method for estimating parameters of exponentially

dampedundamped sinusoids in noiserdquo IEEE Trans Acoust Speech Signal Process vol 38 no

5 pp 814ndash824 May 1990

[20] K Steiglitz and L EMcBride ldquoA technique for the identification of linear systemsrdquo IEEE

Trans Autom Control vol AC-10 no 4 pp 461ndash464 Oct 1965

[21] R Pintelon and J Schoukens System Identification A Frequency Domain Approach 2nd

ed Hoboken NJ USA Wiley-IEEE Press 2012

[22] Y-X Yao and S M Pandit ldquoCraacutemerndashRao lower bounds for a damped sinusoidal processrdquo

IEEE Trans Signal Process vol 43 no 4 pp 878ndash 885 Apr 1995

[23] A C Kot S Parthasarathy DW Tufts and R J Vaccaro ldquoThe statistical performance of

state-variable balancing and Pronyrsquos method in parameter estimationrdquo in Proc IEEE Int Conf

Acoust Speech Signal Process Dallas TX USA Apr 1987 vol 12 pp 1549ndash1552

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-

• 11 OFDM
• Orthogonal Frequency Division Multiplex the modulation concept being used for many wireless and radio communications radio applications from DAB DVB Wi-Fi and Mobile Video
• 181 Orthogonal frequency-division multiplexing
• Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies OFDM has developed into a popular scheme for wideband digital communication whether wireless or over copper wires used in applications such as digital television and audio broadcasting DSL Internet access wireless networks powerline networks and 4G mobile communications
• • 182 Example of applications
  • • 1821Cable
    • 1822 Wireless
    • • Key features
      • • Summary of advantages
        • Summary of disadvantages
        • • 19 Characteristics and principles of operation
          • • 191 Orthogonality
            • 192 Implementation using the FFT algorithm
            • 193 Guard interval for elimination of intersymbol interference
            • 194 Simplified equalization
            • 195 Channel coding and interleaving
            • 196 Adaptive transmission
            • 197 OFDM extended with multiple access
            • 198 Space diversity
            • 199 Linear transmitter power amplifier
            • • 1991 Efficiency comparison between single carrier and multicarrier
              • 1992 Idealized system model
              • • Transmitter
                • Receiver
                • • 1993 Mathematical description
                  • Usage
                  • MATLAB DESKTOP-