eee-752 emerging wireless networks ofdm

EEE-752EEE-752Emerging Wireless NetworksEmerging Wireless Networks

OFDMOFDMRiaz Hussain

FA08-PCE-003

[email protected]

Ph.D. Student

Department of Electrical Engineering

COMSATS Institute of Information Technology

Islamabad, Pakistan

Riaz Hussain [email protected] EEE752-EWN: OFDM 1

OFDMOFDMFDM– Division on the basis of frequency– But a very special case

Orthogonal– Carefully selecting the frequencies that are orthogonal

In FDM– Divided bands must be separate– In fact should have some guard band

To prevent cross-talk among modulated signals To prevent adjacent channel interference (ACI)

In OFDM– Bands can overlap– Still signals can be separated– No fear of ACI


Orthogonality & Vector SpaceOrthogonality & Vector Space Two vectors are orthogonal if their inner product

(dot product) is zero– e.g.: A = 4 B = 3i

A . B = |A| |B| Cosθ

= 0

In 2- or 3-dimensionl Euclidean space, two vectors are orthogonal if their dot product is zero, i.e. they make an angle of 90° or π/2 radians.– e.g.: The vectors (1, 3, 2), (3, −1, 0), (1/3, 1, −5/3) are

orthogonal to each other

Since (1)(3) + (3)(−1) + (2)(0) = 0,

(3)(1/3) + (−1)(1) + (0)(−5/3) = 0,

(1)(1/3) + (3)(1) − (2)(5/3) = 0Riaz Hussain [email protected] EEE752-EWN: OFDM 3

Orthogonality in OFDMOrthogonality in OFDMIn geometry orthogonal is synonym to

perpendicular, but here orthogonality has no geometric significance

When you trough a ball in a projectile does its horizontal velocity change? --- assuming no friction.– NO– Why Not? when gravitation force is acting on it?

Example: Orthogonal CDMA Codes

So in OFDM orthogonality signifies that no component of one signal contributes to the

other signalRiaz Hussain [email protected] EEE752-EWN: OFDM 4

00000001001000110100010101100111

Orthogonal FunctionsOrthogonal Functions In mathematics, two functions f and g are called

orthogonal if their inner product is zero.

∫ f*(x) g(x) dx = 0Here, the star is the complex conjugate.

f(x) = sin(ωx); g(x) = sin (2 ωx) f(x) = sin(ωx); g(x) = sin (3 ωx)

f(x) = sin(ωx); g(x) = cos (ωx)

Integration over a complete period


OFDMOFDM

OFDM is the combination of modulation and multiplexing

Frequency Spectrum– Use many carriers that are equally spaced:

Mapping of information changes in the carrier phase,

frequency, amplitude or combination

Method of sharing bandwidth with other

independent data channels

sk T

kff1

0

k = 0, 1, … , N-1Ts = Symbol Time

sTf

1


OFDM SystemOFDM SystemMultiplexing is applied to independent

signals, but these independent signals are a sub-set of one main signal

Signal is split into independent channelsEach modulated by the dataRemultiplexed to create OFDM carrier


AdvantagesAdvantagesCarriers are orthogonal

– No ACI

Many carriers with small spacing– Long symbol time– Useful to reduce ISI

ISI

Symbol n-1 Symbol n Symbol n+1Direct Path

Delayed Path

ISI = Inter Symbol Interference

ISI

Symbol n-1 Symbol n Symbol n+1


Pulse ShapingPulse Shaping

In FDM – sinc-shaped pulse is applied in time domain to

each individual symbol to reduce the ACI– as a byproduct it also results in reduced ISI

In OFDM – sinc-shaped pulse is applied in frequency

domain of each channel that maintains the orthogonality of the sub-carriers --- conquering ISI


ExampleExample

Ofdm2.pdf p:5


Issues With MultiCarrier Issues With MultiCarrier ModulationModulation

1. Large bandwidth penalty since the subcarriers can’t have perfectly rectangular pulse shapes and still be time-limited.

2. Very high quality (expensive) low pass filters will be required to maintain the orthogonality of the subcarriers at the receiver.

3. This scheme requires L independent RF units and demodulation paths.

OFDM overcomes these shortcomings by using DFT– FFT/IFFT an highly efficient computational technique– Can create large number of orthogonal subcarriers using single radio


Courtesy of: Shivkumar Kalyanaramand: RPI

Google: “Shiv RPI”

OFDM SymbolsOFDM Symbols Group L data symbols into a block known as an OFDM

symbol. – An OFDM symbol lasts for a duration of T seconds,

where T = LTs.– Guard period > delay spread– OFDM transmissions allow ISI within an OFDM

symbol, but by including a sufficiently large guard band, it is possible to guarantee that there is no interference between subsequent OFDM symbols.

The next task is to attempt to remove the ISI within each OFDM symbol --- Circular Convolution




Circular Convolution & DFT/IDFTCircular Convolution & DFT/IDFT

Circular convolution:

Detection of X (knowing H):

(note: ISI free! Just a scaling by H)

Circular convolution allows DFT!




Cyclic Prefix: Eliminate Cyclic Prefix: Eliminate intraintra-symbol interference!-symbol interference!

In order for the IFFT/FFT to create an ISI-free channel, the channel must appear to provide a circular convolution

If a cyclic prefix is added to the transmitted signal, then this creates a signal that appears to be x[n]L, and so y[n] = x[n] * h[n].

The first v samples of ycp interference from preceding OFDM symbol => discarded. The last v samples disperse into the subsequent OFDM symbol => discarded. This leaves exactly L samples for the desired output y, which is precisely what is required to recover the L data symbols embedded in x.




Cyclic Prefix (Contd)Cyclic Prefix (Contd) These L residual samples of y will be equivalent to

By mimicking a circular convolution, a cyclic prefix that is at least as long as the channel duration (v+1)…… allows the channel output y to be decomposed into a simple multiplication of the channel frequency response H = DFT{h} and the channel frequency domain input, X = DFT{x}.




OFDM ImplementationOFDM Implementation

1. Break a wideband signal of bandwidth B into L narrowband signals (subcarriers) each of bandwidth B/L. The L subcarriers for a given OFDM symbol are represented by a vector X, which contains the L current symbols.

2. In order to use a single wideband radio instead of L independent narrow band radios, the subcarriers are modulated using an IFFT operation.

3. In order for the IFFT/FFT to decompose the ISI channel into orthogonal subcarriers, a cyclic prefix of length v must be appended after the IFFT operation. The resulting L + v symbols are then sent in serial through the wideband channel.




P/S

QAM demod

decoder

invert channel

=frequency

domainequalizer

S/P(QAM) encoder

N-IFFTadd

cyclic prefix

P/SD/A +

transmit filter

N-FFT S/Premove

cyclic prefix

TRANSMITTER

RECEIVER

N subchannels 2N real samples

2N real samplesN subchannels

Receive filter

+A/D

multipath channel

An OFDM Modem An OFDM Modem

Bits

00110



OFDM ApplicationsOFDM ApplicationsWiFi

– 802.11a (54 Mbps; 5 GHz ISM)– 802.11g(54 Mbps; 2.4 GHz ISM)

WIMAX3G-LTE (UMB)DABDVB4G (Proposed Modulation Technique)

Riaz Hussain [email protected] EEE752-ETWN: OFDM 18

OFDM in WiMAXOFDM in WiMAX




OFDM in Wimax (Contd)OFDM in Wimax (Contd)

Pilot, Guard, DC subcarriers: overhead Data subcarriers are used to create “subchannels”


OFDM Block DiagramOFDM Block Diagram

OFDM modulation

(IFFT)

Channel coding /

interleaving

Guard interval

I/Q I/QSymbol mapping

(modulation)

Transmitter

OFDM demod. (FFT)

Decoding / deinter-leaving

Guard interval removal

Time sync.

I/Q I/Q

symbol de-mapping

(detection)

Channel est.

Receiver

0101010010110




Other Versions of OFDMOther Versions of OFDMVOFDM (Vector OFDM = MIMO-OFDM)WOFDM(Wideband)

– develops spacing between channels large enough so that any frequency errors between transmitter and receiver have no effect on performance

Flash OFDM– uses multiple tones and fast hopping to spread

signals over a given spectrum band

COFDM (Coded)

Riaz Hussain [email protected] EEE752-ETWN: OFDM 22

MIMO-OFDMMIMO-OFDM Multiple Input, Multiple Output Orthogonal Frequency Division Multiplexing is a

technology developed by Iospan Wireless that uses multiple antennas to transmit and receive radio signals. MIMO-OFDM will allow service providers to deploy a Broadband Wireless Access (BWA) system that has Non-Line-of-Sight (NLOS) functionality. Specifically, MIMO-OFDM takes advantage of the multipath properties of environments using base station antennas that do not have LOS. According to Iospan,

"In this environment, radio signals bounce off buildings, trees and other objects as they travel between the two antennas. This bouncing effect produces multiple "echoes" or "images" of the signal. As a result, the original signal and the individual echoes each arrive at the receiver antenna at slightly different times causing the echoes to interfere with one another thus degrading signal quality.

The MIMO system uses multiple antennas to simultaneously transmit data, in small pieces to the receiver, which can process the data flows and put them back together. This process, called spatial multiplexing, proportionally boosts the data-transmission speed by a factor equal to the number of transmitting antennas. In addition, since all data is transmitted both in the same frequency band and with separate spatial signatures, this technique utilizes spectrum very efficiently.


Summary (1)Summary (1)MulticarrierOrthogonalityReduced

– ISI– ACI– Multipath fading

Requirements– L-independent RF units and demodulation

paths– Maintenance of orthogonality among

subcarriers

Summary (2)Summary (2)Fulfills Requirements:

– In order to use a single wideband radio instead of L independent narrow band radios, the subcarriers are modulated using an IFFT operation.

– In order for the IFFT/FFT to decompose the ISI channel into orthogonal subcarriers, a cyclic prefix of length v (channel duration) must be appended after the IFFT operation. The resulting L + v symbols are then sent in serial through the wideband channel. -------------------- the alternative to this was to design a very high quality low pass filter --- not practically implementable

OFDM transmissions allow ISI within an OFDM symbol, to ensure no interference between subsequent OFDM symbols a guardband is introduced

Summary (3)Summary (3)Design Issues:

– Subcarrier Bandwidth:Bsc = B/L ::: B = Nominal BW;

L = Number of subcarriers determines size of FFT/IFFT

– OFDM Symbol Time:T = Ts(L + Ng) ::: Sampling Time (Ts) = 1/B;

Guard Symbols (Ng) = GL

Guard Fraction (G) = % of L for CP determines v

Guard Time (Tg) = TsNg To eliminate intra symbol interference among/within

OFDM subcarriers

– Data Subcarriers:

Ld = L – pilot subcarriers – null subcarriers– Guard-time: (To eliminate interference between OFDM symbols)

Depends on the channel conditions --- delay spread of an OFDM symbol

GT = % of T ::: usualy 10% – 15%– Data Rate:

R = (B/L)(Ld log2(M)/(1 + G)) M = No. of discrete symbol level used in modulation

ReferencesReferences

Shivkumar Kalyanaraman: RPI lectures


eee-752 emerging wireless networks ofdm

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