2014 - channel estimation and equalization for 5g wireless communication systems (ufmc)

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ChannelEstimationandEqualizationfor5GWirelessCommunicationSystemsTHESISOCTOBER2014

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XiaojieWangUniversittStuttgart5PUBLICATIONS7CITATIONS

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Institut fur NachrichtenubertragungProfessor Dr.-Ing. Stephan ten Brink

Master Thesis

Channel Estimation and Equalizationfor 5G Wireless Communication

Systems

Xiaojie Wang

Date of hand out: April 01, 2014Date of hand in: September 30, 2014

Supervisor: Thorsten WildFrank SchaichProf. Stephan ten Brink

Abstract

In this thesis, channel estimation techniques are studied and investigated for a novel multi-carrier modulation scheme, Universal Filtered Multi-Carrier (UFMC). UFMC (a.k.a. UF-OFDM) is considered as a candidate for the 5th Generation of wireless communication sys-tems, which aims at replacing OFDM and enhances system robustness and performance inrelaxed synchronization condition e.g. time-frequency misalignment. Thus, it may more ef-ficiently support Machine Type Communication (MTC) and Internet of Things (IoT), whichare considered as challenging applications for next generation of wireless communication sys-tems. There exist many methods of channel estimation, time-frequency synchronization andequalization for classical CP-OFDM systems. Pilot-aided methods known from CP-OFDMare adopted and applied to UFMC systems. The performance of UFMC is then comparedwith CP-OFDM.

Index terms: OFDM, 5G, UFMC, Channel estimation, Channel equalization, timing offset,carrier frequency offset, synchronization

Kurzfassung

In dieser Arbeit werden Kanalschatzverfahren fur eine neuartige Mehrtrager-Modulationsschema,Universal Filtered Multi-Carrier (UFMC), untersucht. UFMC (auch bekannt als UF-OFDM)wird als Kandidat fur die 5-te Generation von drahtlosen Kommunikationssysteme bezeich-net, das auf OFDM ersetzen soll und steigert System-Stabilitat und Leistungsfahigkeit in ent-spannter Synchronisationsbedingung z.B. Zeit- und Frequenzversatz. Deshalb kann es effizi-enter Maschinentyp Kommunikation (MTC) und das Internet der Dinge (IoT) unterstutzen,die als anspruchsvolle Anwendungen fur die nachste Generation von drahtlosen Kommuni-kationssystemen berucksichtigt werden. Es existieren viele Verfahren zur Kanalschatzung,Zeit- und Frequenzsynchronisation und Entzerrung fur klassische CP-OFDM Systeme. Derhaufigste Ansatz unter Verwendung von Pilotfolgen, bekannt fur OFDM Systeme wird stu-diert in UFMC Systeme und die Leistungsfahigkeiten wird dann mit CP-OFDM verglichen.

Title page image: Spectrum of Universal Filtered Multi-Carrier with 6 Physical ResourceBlocks, which are filtered by Dolph-Chebyshev filter.

Contents

Acronyms V

Symbols VII

1. Introduction 1

2. Fundamentals 32.1. Wireless Channel Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1. Tapped-delay line channel model . . . . . . . . . . . . . . . . . . . 42.1.2. Statistical description of the wireless channel . . . . . . . . . . . . . 52.1.3. Various wireless channel models . . . . . . . . . . . . . . . . . . . . 9

2.2. Multi-Carrier Modulation Techniques . . . . . . . . . . . . . . . . . . . . . 112.2.1. OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2. UFMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3. Pilot sequences and LTE frame structure . . . . . . . . . . . . . . . . . . . . 202.3.1. LTE frame structure . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3.2. Pilot sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3. Time-Frequency Synchronization 233.1. The effect of timing and frequency offset . . . . . . . . . . . . . . . . . . . . 243.2. Approaches of synchronization . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.1. Timing offset estimation . . . . . . . . . . . . . . . . . . . . . . . . 253.2.2. Joint timing- and carrier-frequency-offset estimation . . . . . . . . . 27

3.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.1. Timing offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.2. Joint timing- and frequency offset . . . . . . . . . . . . . . . . . . . 35

4. Channel Estimation 404.1. The effect of channel-assisted ISI . . . . . . . . . . . . . . . . . . . . . . . . 404.2. Single user channel estimation . . . . . . . . . . . . . . . . . . . . . . . . . 424.3. Multi-user channel estimation . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3.1. LS sliding window estimator . . . . . . . . . . . . . . . . . . . . . . 524.3.2. MMSE sliding window estimator . . . . . . . . . . . . . . . . . . . 58

5. Conclusion 61

A. Appendix 62A.1. Derivation of noise variance in UFMC . . . . . . . . . . . . . . . . . . . . . 62A.2. Covariance of noise in UFMC . . . . . . . . . . . . . . . . . . . . . . . . . 63A.3. Derivation of symbol estimates in UFMC . . . . . . . . . . . . . . . . . . . 64

Bibliography 67

Acronyms

QAM Quadrature Amplitude Modulation

IFFT Inverse Fast Fourier Transformation

IDFT Inverse Discrete Fourier Transformation

FFT Fast Fourier Transformation

OFDM Orthogonal Frequency Division Multiplexing

FDM Frequency Division Multiplexing

FBMC Filter Bank Multi-Carrier

UFMC Universal Filtered Multi-Carrier

ICI Inter Carrier Interference

ISI Inter Symbol Interference

AWGN Additive White Gaussian Noise

CFO Carrier Frequency Offset

CP Cyclic Prefix

rCFO relative CFO

MIMO Multiple Input Multiple Output

FIR Finite Impulse Response

PRB Physical Resource Block

LTE Long Term Evolution

MTC Machine Type Communication

MUI Multi-User Interference

UoI User of Interest

LOS Line Of Sight

NLOS Non-Line Of Sight

MS Mobile Station

PDF Probability Density Function

CIR Channel Impulse Response

ACF Auto-Correlation Function

i.i.d independent identical distributed

CTF Channel Transfer Function

WSSUS Wide Sense Stationary Uncorrelated Scatters

PDP Power Delay Profile

rms root mean square

ITU International Telecommunication Union

PAPR Peak to Average Power Ratio

FMT Filtered Multi Tone

CSI Channel State Information

EUTRAN Evolved Universal Terrestrial Radio Access

CAZAC Constant Amplitude Zero Auto Correlation

3GPP 3rd Generation Partnership Project

MU Multi User

SNR Signal to Noise Ratio

MSE Mean Square Error

XCF Cross Correlation Function

TTI Transmission Time Interval

SER Symbol Error Rate

MUI Multi User Interference

LS Least Squares

MMSE Minimum Mean Square Error

Symbols

h(, t) time-varying CIR in time domain

an attenuation factor of nth path

n propagation delay at the nth path

fc carrier frequency

[] the Dirac Delta function

H( f , t) time-varying channel transfer function

hi complex valued channel gain of i-th path

Lch length of CIR

fRician PDF of Rician distribution

fRayleigh PDF of Rayleigh distribution

I0() the modified Bessel function of the first kind with order zero

R( f , f , t, t ) time frequency correlation function of CTF

t time difference

f frequency difference

R(t) spaced-time correlation function

R( f ) spaced-frequency correlation function

Bcoh coherence bandwidth of channel

BS signal bandwidth

Tcoh coherence time of channel

TS symbol time duration

J0() the zero-th order Bessel Function of the first kind

the wavelength of the signal carrier frequency

fDoppler Doppler frequency due to motion of user

v speed of user

c speed of light

s() Doppler spectral density function

F{} Fourier transformation

F1{} inverse Fourier transformation

Ph() Power delay profile

Pi power of signal at path i

decaying factor exponentially decaying impulse response channel model

m mean delay of channel

rms rms delay spread of channel

N number of total subcarriers

LCP length of cyclic prefix in OFDM

X(k) frequency domain signal

x(k) time domain signal after IFFT

yO transmitted signal of OFDM

rO received signal of OFDM

w(n) time domain zero mean AWGN

2n variance of noise

WO(n) frequency domain noise of OFDM

YO unequalized symbol estimates

X(k) symbol estimates at subcarrier k

B total number of subbands

NB number of allocated subcarriers for subband i

L FIR filter length in UFMC

xi IDFT output of subband i

Xi frequency domain signal of subband i

Xi 2N-point FFT of xi

fi FIR filter response for subband i

Fi frequency response of FIR filter for subband i

yi filtered subband signal i

yU transmitted signal of UFMC

rU received signal of UFMC

wm raised-cosine window

YU frequency domain signal of received signal in UFMC

Si a set contains the subcarrier indexes within the subband i

WU frequency domain noise in UFMC

S(k) signal amplitude reduction factor in UFMC

IICI ICI within and between subbands in UFMC

IISI ISI in UFMC

xZC,u u-th root Zadoff-Chu sequence

NZC length of Zadoff-Chu sequence

A(k) cross-correlation function between received signal and pilot

ld sample distance between two pilots in a sub-frame

n timing offset

normalized carrier frequency offset

Npilot number of pilots within a TTI

q quantized rCFO

lq quantization levels of rCFO

SqCFO set, that contains all quantized rCFO

(n,) the log-likelihood function of OFDM systems under timing- and frequency offset

(m) energy term in CP-based synchronization

weighting factor of energy term in CP-based synchronization

LSW size of sliding window

NMC number of samples within a complete multi carrier symbol

nML ML stimated timing offset using CP

ML ML stimated CFO using CP

H(k) channel estimate at subcarrier k

lp1, lp2 indexes of pilots

(l) weighting factor for interpolation

HSW(k, l) channel estimate at subcarrier k at time l after sliding window

y received time domain signal

h CIR vector

w AWGN vector

convolution operator

() conjugate complex

E{} expectation operator

argument of a complex number

()+ pseudo inverse

1. Introduction

The fourth generation of wireless communication systems, Long Term Evolution (LTE), beganto roll out around 2010. LTE and LTE-Advanced have been optimized to deliver high-rate dataservices to wireless users employing strict synchronism and orthogonality [1]. It is reasonablein todays networks typically delivering high-rate traffic to high-end devices like smart phonesand tablets. However, such an approach is unfeasible for new types of wireless services suchas Internet of Things and the tactile Internet. With the fast growing machine-type communica-tions and the advent of Internet of Things, a fundamental system redesign is required for future5G wireless communication systems. Furthermore, the strict paradigm of synchronism and or-thogonality as applied in LTE is not suitable to achieve efficiency and scalability [2]. A verydiverse variety of traffic types ranging from regular high-rate traffic, sporadic small packet andurgent low latency transmission have to be dealt with in future 5G wireless communicationsystems.

In order to reduce the signaling overhead and the battery consumption for low-end devices(e.g. simple sensor element) in 5G, they should be allowed to transmit with relaxed syn-chronization conditions regarding time-frequency misalignments. However, todays mostprominent multi-carrier modulation technique Orthogonal Frequency Division Multiplexing(OFDM) is very sensitive to time-frequency misalignments due to its comparatively high spec-tral side-lobe level. Filter-bank based multi-carrier (FBMC) [3] is considered to be a future 5Gcandidate technology for replacing OFDM. Each subcarrier is individually filtered in FBMCto enhance robustness against inter-carrier interference (ICI) effects. However, typical FBMCsystems utilize filters, whose length is multiple times of samples per multi-carrier symbol.Hence, its drawback is its long filter length. This fact makes it disadvantageous for communi-cation in short uplink bursts, as required in potential application scenarios of 5G systems [1],like low latency communication or energy-efficient Machine-Type Communication (MTC).Universal Filtered Multi-Carrier (UFMC) is a novel multi-carrier modulation technique [4],which can be seen as a generalization of filtered OFDM and FBMC (in its filtered multi-tone(FMT) variant). While the entire band is filtered in filtered OFDM and each subcarrier isfiltered individually in FBMC, groups of subcarriers (subband-blocks) are filtered in UFMC.By filtering a group of subcarriers, the filter length can be reduced considerably, compared toFBMC. Another advantage of UFMC systems is that quadrature amplitude modulation (QAM)is still applicable in UFMC (in contrast to the FBMC case [3]), making UFMC compatible toall kinds of Multiple Input Multiple Output (MIMO). FFT-based receive processing can be alsoapplied in UFMC systems, thus per-subcarrier equalization is still applicable like in OFDMsystems. As the nature of UFMC is very close to OFDM, it is also known as Universal Fil-tered OFDM (UF-OFDM) [5]. A detailed comparison among OFDM, FBMC and UFMC is

1. Introduction 2

available in [6]. Several advantages of UFMC are shown in [5, 7, 8].

UFMC is very attractive for future 5G communication systems with its properties of reducedout-of-band radiation, compared to OFDM. However, several very important issues such astime-frequency synchronization and channel estimation have not been investigated yet. Syn-chronization is required at the receiver for multi-carrier systems to determine the starting po-sition of symbols and to correct the carrier frequency offset caused by Doppler-effect andfrequency mismatch of local oscillator. Additionally, without channel state information, thetransmitted data cannot be recovered at the receiver. Lack of cyclic prefix in UFMC systems,the synchronization and channel estimation become challenging and interesting tasks. This isbecause the delay spread effect of channel causes inter-carrier-interference and inter-symbol-interference for UFMC systems, while it can be completely mitigated with long enough cyclicprefix in OFDM systems.

In this thesis, aspects of time-frequency synchronization and channel estimation are inves-tigated and compared between OFDM and UFMC systems. The discussed methods are in-tended for hardware implementation in a demonstrator to test the performance of UFMC. Inchapter 2, the background knowledge for understanding this thesis is introduced. The statisti-cal properties of wireless channel and the system model of OFDM and UFMC are discussedin this chapter. Since no standardized frame structure is available for 5G, we use LTE framestructure and pilot sequences to evaluate the system performance. In chapter 3, we discussthe effect of timing and frequency offset first of all and show the different behavior of UFMCand OFDM. Then, methods for performing synchronization are discussed. At the end of thischapter, performance is shown and compared regarding different system parameters. Channelestimation is discussed in chapter 4 regarding different channel models, different scenariosand many other different aspects. The last chapter 5 provides a conclusion of this thesis andgives an overview into possible future works.

2. Fundamentals

In this chapter, some aspects of wireless channel is introduced in the section 2.1. In section 2.2,the classic CP-OFDM system and a novel multi-carrier modulation scheme, Universal FilteredMulti-Carrier (UFMC), are discussed. The last section 2.3 gives a short introduction into LTEpilot sequences and frame structure.

2.1. Wireless Channel Aspects

The data transmission over wire-line is mainly corrupted by thermal noise, which is wellknown as Additive White Gaussian Noise (AWGN). Usually, the thermal noise can be wellapproximated by statistically independent Gauss process. This statistical process is charac-terized by its variance. Besides thermal noise, data transmission over wireless channel alsosuffers from Inter Symbol Interference (ISI), which must be dealt with to satisfy a certainquality of transmission. The impulse response of the channel is more complicated in wirelesscommunication systems than that in wire-line communication, due to the multi-path propaga-tion and fading characteristics.

The transmitted signal undergoes several shadowing, refractions and reflections by varioussurrounding obstacles. This phenomenon leads to the multipath propagation nature of wirelesschannel. Each path is determined by three factors: delay, attenuation and phase shift. Ingeneral, the discrete time-variant Channel Impulse Response (CIR) h(, t) can be written as[9]

h(, t) =nan(t)e j2pi fcn(t) [ n(t)] (2.1)

where

an(t) is the attenuation factor for the signal received on the n-th path at time instant t

n(t) is the propagation delay at the n-th path and time t

e j2pi fcn(t) is the phase rotation of the signal component at delay at carrier frequency fc

[] is the Dirac Delta function

2.1. Wireless Channel Aspects 4

and the Dirac Delta function is given by

() =

{1 if = 00 otherwise

(2.2)

By taking the Fourier transform of h(, t)with respect to the delay , the time-varying ChannelTransfer Function (CTF) H( f , t) in frequency domain can be obtained. In general, the CTFcan be written as [9]

H( f , t) =

h(, t)e j2pi f d (2.3)

Note that the CTF is also time-varying.

In order to investigate the effect of wireless channel, one implementation of fading wirelesschannel is so called tapped-delay line channel model. The infinite channel impulse response ismodeled as an Finite Impulse Response (FIR) filter by truncating the taps below a threshold.Without loss of generality, the first tap is always assumed to have no delay.

Depending on the impulse response of the channel, one can classify the fading channel intotwo groups: frequency-flat fading channel and frequency-selective fading channel. In a frequency-flat fading channel, the signal is almost equally weighted so the ISI can be neglected. Ina frequency-selective channel, ISI occurs due to the overlapping of consecutive transmittedsymbols.

2.1.1. Tapped-delay line channel model

The FIR filter description of multipath fading channel is based on truncating the taps withsmall power below a threshold. Thus, (2.1) can be simplified as [10]

h(, t) = h0(t) ( 0(t))+h1(t) ( 1(t))+ +hLch1(t) ( Lch1(t)) (2.4)

where Lch denotes the number of considered fading channel paths, hi(t) = ai(t)e j2pi fci(t) isthe complex valued channel gain of the i-th path including attenuation factor and phase shiftand i(t) is the delay time of i-th path at the time instant t. Usually, the delay of the first pathis set to be zero 0(t) = 0. The FIR filter structure model of the fading channel is illustrated inFig. 2.1. Both the complex valued channel gain hi(t) and delay i(t) for the i-th path are timevarying.

If an arbitrary input signal x(n) is fed into the channel, modeled as an FIR filter, the corre-sponding output signal y(n) is thus

y(n) = x(n)h(, t) (2.5)

where is the linear convolution operator. That results in an output signal length of N+Lch1, provided an input signal length of N.


Figure 2.1.: Tapped-delay line channel model

2.1.2. Statistical description of the wireless channel

To describe the statistical properties of the channel gain hi(t), two setups are distinguished:Line Of Sight (LOS) and Non-Line Of Sight (NLOS). If there exists a line of sight (a directpath, which is not reflected by obstacles) between transmitter and receiver, it is called LOS.Otherwise, every path is reflected by obstacles at least once and received by the Mobile Sta-tion (MS). This scenarios refers to NLOS. It is shown in [10] that the amplitude of channeltap r = |hi(t)| follows Rician distribution and Rayleigh distribution in LOS and NLOS sce-nario, respectively. The Probability Density Functions (PDFs) of Rician distribution [11] andRayleigh distribution [12] are given by

fRician(r| ,) = r2 exp

[(r2+2)

22

]I0(

r2

)for r 0

0 otherwise(2.6)

and

fRayleigh(r|) ={

r2 exp

[ r222

]for r 0

0 otherwise(2.7)

where I0() denotes the modified Bessel function of the first kind with order zero. The Riciandistribution is characterized by two factors and . Since NLOS scenario is considered in thisthesis, we refer to [11] for further details about Rician distribution. The Rayleigh distributionis a special form of Rician distribution, if = 0 is satisfied. In the following Fig. 2.2, thePDFs are shown for Rayleigh distribution with = 1,2,3 and 4. The amplitude of a complexnumbered random variable R= |Z|=X2+Y 2 is Rayleigh distributed, if X N (0,2) andY N (0,2) are independent zero-mean Gaussian processes. Thus, the complex numberedchannel tap hi is the so called circularly-symmetric complex Gaussian distributed, denoted byCN (0,Pi). Pi is the power density of the ith channel tap.

By interpreting the CIR and CTF as stochastic process, the autocorrelation function R( f , f , t, t )is of interest. The autocorrelation function indicates the channel variation in time and fre-


0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ampltitude

Prob

.

=1 =2 =3 =4

Figure 2.2.: PDFs of Rayleigh distribution with different values

quency and it is defined as [9]

R( f , f , t, t ) =12E{H( f , t)H( f , t )} (2.8)

where E{} denotes the expectation operator and () means conjugate complex. If the channelfulfills the so-called Wide Sense Stationary Uncorrelated Scatters (WSSUS) assumption, (2.8)can be further simplified as [13]

R( f , f , t, t ) = R( f ,t) (2.9)

where f = f f and t = t t denote the frequency and time difference respectively.With the WSSUS assumption, the Auto-Correlation Function (ACF) depends only on the timeand frequency differences, t and f , but not on the absolute time and frequency instancesf , f , t, t . Usually, the WSSUS assumption holds for small-scale motion of users (over an areaof about 10 diameter) [13]. Since we are interested in the small-scale fading scenarios, theWSSUS assumption is always fulfilled in this thesis, if not otherwise stated.

By letting t = 0 or f = 0, the spaced-time correlation function R(t) and the spaced-frequency correlation function R( f ) can be computed respectively. They provide measuresof time coherence and frequency coherence of the channel [14]. The coherence bandwidthBcoh and coherence time Tcoh can be obtained by taking the differences between 3 dB frequen-cies and time of the frequency correlation function R( f ) and the time correlation functionR(t) respectively. With the coherence bandwidth Bcoh, the channel can be categorized intotwo groups:


frequency-flat fading channel, if the signal bandwidth is smaller than the coherencebandwidth, BS < Bcoh. In this case, all spectral components of the signal are approxi-mately equally distorted.

frequency-selective fading channel, if the signal bandwidth is larger than the coherencebandwidth, BS > Bcoh. In this case, different spectral components of the signal aredistorted with different attenuation and phase shift.

The coherence time Tcoh gives a measure of how fast the channel varies with time. A channelis said to experience [14]

fast fading, if the coherence time is less than the symbol time duration, Tcoh < TS. In thiscase, the channel fading characteristic changes significantly during the symbol transmis-sion time.

slow fading, if the coherence time is smaller than the symbol time duration, Tcoh > TS.In this case, the channel fading characteristic remains approximately the same duringthe symbol transmission time.

Obviously, the correlation function is highly dependent on the velocity v, at which the MS ismoving. Clarke derived the normalized ACF R(t) of a Rayleigh fading single tap channel in[15] as

R(t) = J0(2pi fDopplert) (2.10)

withfDoppler =

v

(2.11)

where J0() is the zero-th order Bessel Function of the first kind and is the wavelength of thesignal carrier frequency fc. In [15], Clarke proposed an 2D isotropic scattering model in whicha large number of obstacles are randomly and independently placed around a considered MS.The derivation in [15] is based on the assumptions:

large amount of scatters, which are independent of each other (Thus, the central limittheorem can be applied).

the attenuation factor ai and phase rotation i (when the signal is reflected by scatter i)are independent of that of other scatters j 6= i.

the phase rotation and scatter angles are independent identical distributed (i.i.d) anduniformly distributed in [pi,pi].

the velocity of MS should be much smaller than the speed of light v c.By taking Fourier transformation of the time correlation function R(t) with respect to thetime difference t, we get the so called Doppler spectral density function s()

s() =F{R(t)} (2.12)


whereF{} denotes the Fourier transformation operator. With (2.10) and (2.12), the Dopplerspectral density function s() can be thus calculated as [10]

s() =

{ 1pi fDoppler

1(/ fDoppler)2

, | |< fDoppler0 otherwise

(2.13)

In the Fig. 2.3, the time correlation function R(t) of a single-tap Rayleigh fading channel (inFig. 2.3a) and its Doppler spectral density function s() (in Fig 2.3b) are illustrated. It is clear

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.5

0

0.5

1

time lag

R(

t)

(a) Time correlation function of a Rayleigh fading single-tap channel

500 400 300 200 100 0 100 200 300 400 5000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

frequency

s()

(b) Doppler spectral density function

Figure 2.3.: Time correlation function and its Doppler spectral density function

from Fig. 2.3b that the spectrum is broadened due to the motion of the user.

Analogously, Power Delay Profile (PDP) Ph() can be obtained by taking inverse Fouriertransformation of frequency correlation function R( f ). It is given by

Ph() =F1{R( f )} (2.14)

whereF1{} denotes the inverse Fourier transformation operator. The PDP Ph() describesthe amount of signal power arrives at the receiver with the delay of . Thus, it is straightfor-ward for the tapped-delay line channel model in section 2.1.1.

Ph() = P0 ( 0)+P1 ( 1)+ +PLch1 ( Lch1) (2.15)

where Pi is the expected power of signal at the receiver with the corresponding delay i. With(2.14), the frequency correlation function can be easily obtained as

R( f ) =Lch1i=0

Pi e j2pi f i (2.16)

Furthermore,the mean delay m and root mean square (rms) delay spread rms can be defined


as the normalized first-order moment and normalized second-oder central moment of the PDPand they are given by [13]

m =

Ph()d

Ph()d(2.17)

and

rms =

Ph()2d

Ph()d 2m (2.18)

2.1.3. Various wireless channel models

Throughout this thesis, a various of wireless channel models are investigated. Thus, we discussall the channel models that are investigated in this thesis now.

A simple single-tap Rayleigh fading channel is first of all discussed. The properties of thissingle-tap Rayleigh fading channel are thoroughly studied in the previous section. The corre-sponding CIR is thus simply

h(, t) = h0(t) () (2.19)

Obviously, it is a frequency-flat fading channel and it does not cause any ISI. Hence, it isrefer to as flat fading channel throughout this thesis. The complex channel gain h0 followsRayleigh distribution as described in (2.7) and its time correlation function is given by (2.10).Furthermore, its Doppler spectral density function follows the classical Jakes spectrum, whichis shown in (2.13) and Fig. 2.3.

Second of all, a two-path channel model is introduced. Its CIR is given by

h(, t) = h0(t) ()+h1(t) ( 1) (2.20)

We assume that the complex channel gain h0 and h1 are i.i.d Rayleigh distribution. Further-more, the expected power of the two paths is the same, i.e. P0 = P1.

For the purpose of evaluating wireless channels for vehicular users, International Telecommu-nication Union (ITU) has standardized several channel models for vehicular test environment.In the following table 2.1, the PDPs are shown for Vehicular A (VEHA) and Vehicular B(VEHB) channel models [16]. Both of VEHA and VEHB channels consist of 6 taps. Butthe PDPs are quite different. VEHA has a significantly shorter delay than VEHB, thus thecoherence bandwidth of VEHB is expected to be smaller. Additionally, a larger ISI will alsobe introduced in VEHB channel. Furthermore, the received signal power decreases for VEHAwhile the delay increases and the strongest path is with zero delay. However, the strongestpath for VEHB channel has a delay of 300 ns.


Vehicular A Vehicular BDelay (ns) Relative Path Power (dB) Delay (ns) Relative Path Power (dB)

0 0 0 -2.5310 -1.0 300 0710 -9.0 8900 -12.8

1090 -10.0 12900 -10.01730 -15.0 17100 -25.22510 -20.0 20000 -16.0

Table 2.1.: PDP of Vehicular A and B channels

Another commonly used channel model is so called exponentially decaying impulse responsemodel. The power of channel taps Pi decays exponentially with increasing delay. If a totalnumber of considered path is Lch, then the expected power of each taps is given by [17]

Pi =1

1Lchi, i= 0, ,Lch1 (2.21)

where 0 < < 1 determines the rate of power decaying. The mean delay m and rms delayspread rms are also investigated in [17]. They can be written as

m =Lch1i=0 i

i

Lch1i=0 i

1 , LchLch 1 (2.22)

and

rms =Lch1i=0 (i m) i

Lch1i=0 i (1)2 , L

2ch

Lch 1 (2.23)

Thus, both the mean delay and rms delay spread are determined by the decaying factor .

All the aforementioned channel models are considered in this thesis. The single-tap Rayleighfading is frequency-flat, while all the other channel models are frequency-selective. For thetwo-path channel model and exponentially decaying impulse response model, the mean delayand rms delay spread can be varied by changing the delay time of second path 1 and thedecaying factor respectively. Vehicular A and Vehicular B on the other hand have standard-ized and fixed mean delay and rms delay spread values. Furthermore, the total power of allthe considered channel models is to be normalized in the following.

Lch1i=0

Pi = 1 (2.24)

The reason is to keep the total channel gain of all paths constant for fair comparison purpose.

2.2. Multi-Carrier Modulation Techniques 11

2.2. Multi-Carrier Modulation Techniques

Instead of transmitting data over the whole available bandwidth in single carrier systems, thewideband channel is divided into several subchannels with narrow bandwidth in multi carriersystems. Each information-bearing subchannel transmits with a lower bit rate over separatecarrier signals [9]. Multi carrier systems have several advantages and disadvantages comparedwith single carrier systems. The advantages of data transmission over multi carrier are

higher spectral efficiency since the spectrum of each subchannel can be overlapped.Thus, it can be used to achieve higher data rate.

immunity to frequency-selective fading channels, because the bandwidth of each sub-channel is so small that CTF can be assumed to be constant. Thus, each subchannelexperiences a flat fading. That allows a simpler equalization at the receiver.

adaptive power allocation and data modulation per subchannel is possible. If somesubchannels experiences deep fading, the power or data modulation format in that sub-channel can anticipate accordingly.

The disadvantages include

higher Peak to Average Power Ratio (PAPR) is to be expected, which raises difficultyfor amplifier.

sensitive to synchronization errors because the subchannal data must be separated at thereceiver.

The focus of this work is to investigate multi carrier systems because of its advantages, thusmulti carrier systems are discussed in the following.

In this section some basics of two kinds of multi-carrier modulation techniques are introduced.In the first section 2.2.1, we can get an overview into classical CP-OFDM system. In the lastsection 2.2.2, the properties of a novel modulation technique UFMC is analyzed.

2.2.1. OFDM

OFDM stands for Orthogonal Frequency Division Multiplexing, which is a special form ofFrequency Division Multiplexing (FDM). It has been todays most prominent multi-carriermodulation technique for broadband communications, being used in standards such as LTEand WiFi. OFDM is very simple and efficient with Fast Fourier Transformation (FFT) basedmodulation and Inverse Fast Fourier Transformation (IFFT) based demodulation. It can relyon per-subcarrier scalar equalization, which allows to reduce the receiver complexity. Fur-thermore, a higher spectral efficiency can be achieved by overlapping the partial spectra of thesubcarriers. In OFDM systems, the subchannels are orthogonal to each other. Its main draw-backs are the high spectral side-lobe levels, due to the rectangular symbol shape in time. This


makes OFDM vulnerable against time-frequency misalignments. In practical usage, OFDMis usually filtered in order to ensure proper out-of-band radiation.

In the Fig. 2.4, the system model of a conventional OFDM system is shown. First of all,the serial binary data are divided into several parallel subcarriers and modulated there byusing independent orthogonal subcarrier frequencies. Important in an OFDM system is theorthogonality between the subcarriers so that the signals at the receiver side can be separatedagain. Two signals xk and xl are referred to as orthogonal according to [18], if it is satisfied:

xkxl dt =

{0 if k 6= lc if k = l

(2.25)

where c is an arbitrary constant and c 6= 0. In OFDM systems, the orthogonality is achievedby using orthogonal carrier frequencies at different subcarriers. Usually, Quadrature Ampli-tude Modulation (QAM) with Grey coding is used to map bits into complex symbols. After

Figure 2.4.: A System Overview of OFDM

mapping, the frequency domain signal Xk is converted into time domain signal xk by IFFT.The relation between Xk and xk can be written as follows [18]:

x(k) =1N

N1l=0

X(l)e j2pilk/N ,k = 0,1, . . . ,N1; (2.26)

where N is the total number of subcarriers. Because of multi-path propagation in the reality,


a guard interval or Cyclic Prefix (CP), which is a copy of a certain length LCP of the timedomain signal xk, is inserted at the beginning of symbol after IFFT. Thus, the transmittedOFDM signal yO is of the length of N+LCP and it is given by

yO(k) =

{x(NLCP+ k) if k < LCPx(kLCP) otherwise

(2.27)

The cost for insertion of guard interval is a reduction of spectral efficiency. Afterwards, theparallel signal is again converted into serial signal and transmitted over a channel. Hence, thereceived signal rO, which is also corrupted by thermal AWGN, can be written as

rO(n) = h(n) yO(n)+w(n) (2.28)

where w(n) denotes the AWGN with zero mean and variance of 2n . The OFDM receiverfirstly splits the serial signal to parallel and then removes the inserted guard interval, whichmay be overlapped with previous OFDM symbol because of the linear convolution betweenCIR and the transmitted signal. It is shown that ISI can be perfectly mitigated [9], given thatthe maximum time delay of the channel is smaller than the guard interval duration i.e.

Lch1 < LCP (2.29)

In order to get the frequency domain signal, FFT operation is thus performed.

YO(k) =1N

N+LCP1

l=LCP

rO(l)e j2pi(lLCP)k/N , k = 0,1, ,N1 (2.30)

Given that (2.29) is satisfied, (2.30) can be further simplified using (2.27) and (2.26) as

YO(k) = H(k)X(k)+WO(k) (2.31)

with WO(k) is the N-point FFT of w(n) [14]. Moreover, the N-point FFT does not change thestatistical properties of w(n). Thus, WO(k) is also zero mean AWGN with the same variance2n . With the above equation (2.31), it is clear that ISI is fully mitigated and the subchannelsexperience a flat fading channel thus only a one-tap equalizer is needed at the receiver. If theCTF at each subcarrier k is known by the receiver, the transmitted symbol X(k) can be easilyobtained by

X(k) =YO(k)H(k)

= X(k)+WO(k)H(k)

(2.32)

Thus, the estimation of H(k) plays a very important role in data communication systems. Inthe end, the estimated symbols X(k) are decoded by demapper.


2.2.2. UFMC

The system model of UFMC is shown in Fig. 2.5 [6, 8]. The overall bandwidth is divided into

Figure 2.5.: System model of UFMC

B sub-bands. Each sub-band can be allocated with NB consecutive subcarriers and the sub-band may correspond to Physical Resource Block (PRB) in LTE. The total number of subcar-riers is N. A N-point Inverse Discrete Fourier Transformation (IDFT) operation is performedfor every sub-band i to transform the frequency domain signal into time domain. Data sym-bols are modulated in the allocated subcarrier positions for sub-band i and zeros are padded infrequency domain in the unallocated subcarrier positions to perform IDFT. Thus, the outputsignal after IDFT is N. Then, the output signal xi is filtered by a FIR-filter fi with the lengthof L. Hence, the output signal of the subband i is given by

yi(k) = xi fi =L1l=0

fi(l)xi(k l), k = 0, ,N+L1. (2.33)

That results in a symbol length of N + L 1, due to the linear convolution between xi andfi. The purpose of introducing a FIR filter to filter each subband is to reduce the out-of-band radiation. It is well known that the rectangular symbol shape in OFDM is neither welllocalized in time nor in frequency. The comparatively high spectral side lobe level of the sinc-function, i.e. the Fourier transformation of the rectangular symbol shape, causes high out-of-


band radiation to neighboring subbands if the orthogonality between subcarriers is destroyedby e.g. synchronization errors. With the block-wise filtering approach in UFMC, out-of-bandradiation can be significantly reduced by appropriately designing FIR filter. Dolph-Chebyshevfilters can be parameterized in terms of side-lobe attenuation and it minimizes the maximumout-of-band radiation. Thus, they are used in this work. In the Fig. 2.6, we plot a Dolph-Chebyshev filter for a exemplary settings (FIR filter length: L = 80, side-lobe attenuation:60 dB) in the time and frequency domain [19]. To illustrate the effect of reduced out-of-band

Figure 2.6.: Dolph-Chebyshev filter with length of 80 and side-lobe attenuation 60 dB

radiation by filtering in UFMC, the waveforms are compared between OFDM and UFMCwith the Dolph-Chebyshev filter mentioned above for one subband in Fig. 2.7. Compared to

Figure 2.7.: Waveforms of OFDM and UFMC for one subband

OFDM systems, the out-of-band radiation is very significantly reduced in UFMC. Thus, users


or devices with a relaxed synchronization condition, i.e. timing and frequency misalignment,cause less interference to other well-synchronized users in UFMC.

Filtering approach is also used in Filter Bank Multi-Carrier (FBMC) systems. In FBMC sys-tems, each subcarrier is individually filtered, strongly enhancing robustness against Inter Car-rier Interference (ICI) effects. However, typical FBMC systems utilize filters, whose length ismultiple times of the number of total subcarriers. Hence, its drawback is its long filter length,making it disadvantageous for communication in short uplink bursts, as required in potentialapplication scenarios of 5G systems [1], like low latency communication or energy-efficientMachine Type Communication (MTC). UFMC can be seen as a generalization of filteredOFDM and FBMC (in its Filtered Multi Tone (FMT) variant). While the former filters theentire band and the latter filters each subcarrier individually, UFMC filters subband-blocks,thus groups of subcarriers. This allows reducing the filter length considerably, compared toFBMC. Furthermore, QAM is still efficient (in contrast to the FBMC case [3]), making UFMCcompatible to all kinds of Multiple Input Multiple Output (MIMO). UFMC can also rely onFFT-based receive processing with per-subcarrier equalization. As UFMC is very close innature to OFDM, it is also known as Universal Filtered OFDM (UF-OFDM) [5].

After every subband is filtered, all the sub-band signals are added together and transmitted.The transmitted signal yU is given by

yU(k) =B

i=1

yi(k) (2.34)

After passing a wireless channel with the the CIR h(k), the received signal rU is then

rU(k) = h(k) yU(k) = h(k)(

B

i=1

xi fi)+w(k) (2.35)

The received signal can be considered firstly to be weighted with a window wm. As an exam-ple, a possible window can be with the raised-cosine shape

wm(k) =

12

[1 cos

(k

L21

pi)]

m [0, L2 1]1 m [L2 , L2 +N]12

[1+ cos

(kN L2+1

L21

pi)]

m [L2 +N+1,N+L1](2.36)

The time domain windowing pre-processing leads to two effects [7]

self interference is introduced due to the convolution with window function in frequencydomain.

out of band radiation of other neighboring users or devices, with respect to frequencyallocation, with relaxed synchronization is attenuated.


The windowing process is not considered in this thesis. We refer to [7] for further results withwindowing approach, advantages of windowing are shown there considering time-frequencymisalignment.

After windowing preprocessing, the received time domain signal is to be transformed intofrequency domain. Since the UFMC symbol has the length of N+L1, zeros are padded inorder to perform the 2N-point FFT. Thus, the corresponding frequency domain signal YU is

YU(k) =1N

N+L2l=0

rU(l)e j2pilk/2N , k = 0,1, ,2N1 (2.37)

It should be noted that all N+L 1 samples are used for detection rather than only N sam-ples are used in OFDM. Lacking of CP, ISI because of multipath fading channel cannot becompletely mitigated like OFDM. If the channel has only a single-tap or ISI and ICI is negli-gible,the frequency domain signal YU is given as

YU(k) = H(k)B

i=1

Xi(k)Fi(k)+WU(k) (2.38)

where Xi and Fi(k) are 2N-point FFT of xi and fi respectively. If Xi is the N-point FFT of xi,Xi can be written as

Xi (k) =

Xi( k

2

)if k is even

mSi

Xi (m)sin(pi

2 (2m k))

N sin( pi

2N (2m k)) e j pi2 (2mk)(1 1N ) if k is odd (2.39)

where Si is a set which contains the subcarrier indexes that are allocated to subband i. Further-more, Xi can be formulated as

Xi(k) =

{0 if k / SiXi(k) if k Si

(2.40)

It is clear from (2.39) that on one hand all even subcarriers contain data symbols and on theother hand all odd subcarriers contain interferences. Thus, all the signals in odd subcarriers aredropped as indicated in Fig. 2.5. Furthermore, WU is the 2N-point FFT of AWGN w(k) withvariance 2n . Thereby, the variance 2U of WU is slightly enhanced with the factor of

N+L1N

2U =N+L1

N2n (2.41)

The reason for the noise enhancement is that the scaling factor of 2N-point FFT at the receiverremains the same as in OFDM, namely 1/

N, while the time domain samples within a receive

window is increased from N to N+L1. The mathematical derivation of (2.41) is shown inA.1. Moreover, the white time domain noise is transformed into a colored noise, i.e. noise iscorrelated between different subcarriers. In A.2, the covariance of WU is discussed and it is


given by

c(l,k) =1N

sin(pik

N (N+L1))

sin(pik

N

) e j pikN (N+L2)2n (2.42)where l and k are even subcarrier indexes and k = l

k2 . The reason for correlation in

frequency domain is so called Leakage-Effect of FFT, since 2N-point FFT is performed at thereceiver using N+L1 time domain samples. In the following Fig. 2.8, the auto-covarianceof the frequency domain noise is shown for OFDM and UFMC. From Fig. 2.8a, it is clear that

(a) Simulated auto-covariance of noise in frequency do-main for UFMC and OFDM

100 200 300 400 500 600 700 800 900 10000

0.2

0.4

0.6

0.8

1

simUFMCanalyticalUFMC

(b) Simulated and analytical covariance of noise forUFMC

Figure 2.8.: Comparison of covariance of noise between OFDM and UFMC

the noise in OFDM has approximately no correlation between different subcarriers, while asmall correlation can be observed in UFMC. Furthermore, the analytical covariance in (A.8)is compared with simulated covariance for UFMC in Fig. 2.8b. It can be concluded thatanalytical results match the simulated covariance quite well.

Now, we come back to the assumption of negligible ISI and ICI. In general, ISI and ICI arisein UFMC systems if the channel has multi-taps. However, the filter ramp-up and ramp-downact as soft protection against delay spread of the channel, shown in Fig. 2.9a [8]. The signalenergy of ramp-up and ramp-down due to filtering approach in UFMC is relatively small.Thus, it can be expected that if the delay spread of channel is less than a certain percentage offilter length L, the resulting ISI and ICI is not very significant and can be neglected. In contrastto UFMC, CP is inserted in OFDM systems to provide robustness against delay spread andtiming offset, shown in Fig. 2.9b. As long as the inserted CP length is larger than the channeldelay spread, ISI can be completely mitigated. In chapter 4, further discussion regarding ISIand ICI under different channel models is provided. As an example, the energy of ISI andICI is shown to be below -40 dB in Vehicular A channel model. Practically, it can thus beneglected since the noise power and other inference power is dominant. Furthermore, theinserted CP is again removed at the receiver since it contains ISI from previous symbol whileall N+L1 samples are used for symbol detection. So, UFMC is expected to be slightly more


(a) Temporal property of UFMC signals

(b) Temporal property of OFDM signals

Figure 2.9.: Comparison of signal temporal property between OFDM and UFMC [8]

advantageous in reducing the transmission power of signal and have slightly better spectralefficiency, compared with CP-OFDM. Since every sub-band is filtered to reduce the out-of-band radiation, guard subcarriers between sub-bands (used in OFDM to protect againstinterference from neighboring sub-bands) can be reduced or are not required any more inUFMC systems. This will further increase spectral efficiency of UFMC.

If the assumption of single tap channel or negligible ICI and ISI is not hold, the receivedfrequency domain signal can be derived as (see A.3)

YU(k) = H(k)Fi(k)Xi(k)S(k)Xi(k)+ IICI(k)+ IISI(k)+WU(k) (2.43)

Without loss of generality the considered subcarrier k is assumed to be allocated to the sub-band i. Furthermore,

2.3. Pilot sequences and LTE frame structure 20

S(k) is a signal amplitude reduction factor due to loss of orthogonality

IICI(k) is the ICI caused by all other subcarriers at the subcarrier k

IISI(k) is the ISI caused by previous symbol at the subcarrier k

2.3. Pilot sequences and LTE frame structure

The transmitted signal passes a time-varying channel with discussed properties (in section 2.1).In order to recover the transmitted symbols at the receiver, Channel State Information (CSI)i.e. CIR or CTF have to be estimated. Besides channel estimation, the synchronization oftiming and frequency mismatch at the receiver is another issue. Transmitter and receiver usu-ally have no common sense to the timing, at which a transmission starts. Additionally, Car-rier Frequency Offset (CFO) occurs because of Doppler effect and local oscillator frequencymismatch. The time-frequency misalignment causes system performance degradation. Thus,known sequences called pilot sequences or training sequences are transmitted. With theseknown sequences, the receiver can estimate the CSI and perform time- frequency synchro-nization between transmitter and receiver.

2.3.1. LTE frame structure

In LTE, a radio frame with 10 ms contains 20 slots, shown in Fig 2.10 [20]. Each slot consistsof 7 multi carrier symbols with the time duration of 0.5 ms. A sub-frame with transmission

Figure 2.10.: EUTRAN frame structure

duration of 1 ms contains two slots i.e. 14 symbols, illustrated in Fig. 2.11 [21]. Every 4-thmulti carrier symbol within a slot is used as pilot sequence and all other 6 symbols are data-bearing symbols. The insertion of pilot sequences enables the receiver to perform channelestimation and synchronization, while it reduces the data-rate. There exist various types ofpilot arrangements, in EUTRAN the so called time-spaced all frequency pilot arrangementis applied. In this arrangement, all the available subcarriers or subchannels are modulated


Figure 2.11.: EUTRAN sub-frame structure [21]

with known pilot sequences. No subcarrier is used to transmit data i.e. the symbol is purelypilot sequences. In other pilot arrangement, information-bearing symbols are superimposedwith pilot sequences, since some subcarriers are used to transmit date while others are usedto transmit pilot sequences. This kind of pilot arrangement is not discussed in this thesis.Furthermore, the subcarrier spacing is set to be 15 kHz and one PRB contains 12 consecutivesubcarriers.

2.3.2. Pilot sequences

Pilot sequences, also known as training sequences and reference signals, can be used for chan-nel estimation and time-frequency synchronization. A well-known pilot sequence is Zadoff-Chu sequences. The u-th root Zadoff-Chu sequence is defined by

xZC,u(m) = e jpi um(m+1)NZC (2.44)

where NZC is a prime number and denotes the length of the sequence [22]. Zadoff-Chu se-quences are Constant Amplitude Zero Auto Correlation (CAZAC) sequences, since the cycli-cal shifted version of this sequence is orthogonal to itself. Furthermore, the cross correlation


between Zadoff-Chu sequences with different roots is constant [23].

In LTE, users are allocated with an integer multiple of PRBs. Thus, the length of allocatedsubcarriers is not a prime number. In case of a allocation length spanning at least 3 PRB,cyclical extension of a Zadoff-Chu sequence is applied to fill up the allocation length NAlloc.The pilot sequence in this case is given by

su(n) = xZC,u(n mod NAlloc) (2.45)

And the length NZC of Zadoff-Chu sequence is chosen to be the largest prime number such thatNZC < NAlloc [22]. Users can thus be separated by different roots of Zadoff-Chu sequences. In[22], the pilot sequences are divided into 30 groups using different roots. Intended for MultiUser (MU)-MIMO, 3rd Generation Partnership Project (3GPP) also introduces cyclical shiftof the pilot sequence su with the same root u.

s()u (n) = e jnsu(n) (2.46)

The linear phase shift in frequency domain creates a cyclic shift in time domain. By doing so,the orthogonality of Zadoff-Chu sequences is preserved [21].

3. Time-Frequency Synchronization

Before the actual channel estimation starts, the start position of FFT window should be deter-mined because there is a transmission delay between transmitter and receiver. Besides timingerror, carrier frequency offset is another issue caused by Doppler Effect of moving user andmismatch of local oscillator at the transmitter and receiver. In the Fig. 3.1, the transmitted

Figure 3.1.: Time-frequency misalignment between transmitter and receiver

(black and solid box) and received (green and dashed box) signal with corresponding time andfrequency lag are illustrated. Because of the time-frequency mismatch, ICI and ISI are to beexpected which results in a lower value of Signal to Noise Ratio (SNR). Furthermore, it alsocauses out-of-band radiation which is an interference to all the neighboring users.

OFDM is very sensitive to CFO because of the comparatively high side-lobe levels of the rect-angular symbol shape. It is very robust against positive timing offset (signal arrives later thanreceiver expected) due to CP as long as the timing offset is within the CP duration. Comparedto OFDM, UFMC can achieve more robustness against time-frequency misalignment with theFIR filter [7]. The reason for robustness against CFO is because of the reduced out-of-bandradiation. Robustness against timing offset is achieved by soft protection of filter ramp-up andramp-down.

Receive side synchronization becomes more important when discarding the closed-loop syn-chronized operation mode of LTE with the timing advance adjustments. In this chapter,

3.1. The effect of timing and frequency offset 24

pilot-based time and frequency synchronization approach is investigated for both OFDM andUFMC systems and compared with CP-based synchronization approach (only applicable inOFDM systems, since no CP is inserted in UFMC systems). In section 3.1, the effect of tim-ing and frequency offset is discussed for OFDM and UFMC systems. Then, two approaches,CP-based and pilot-based synchronization, are introduced in section 3.2. The last section 3.3shows simulation results and compares the performance of synchronization.

3.1. The effect of timing and frequency offset

The effect of timing and frequency offset in OFDM systems have been thoroughly studiedin [24, 25]. In OFDM systems, positive timing offset (signal arrives later than the receiverexpected), has no effect on the SIR as long as it is within the CP duration. Once the timingoffset exceeds the CP-length or it is negative (signal arrives earlier than the receiver expected),it starts to degrade the system performance. This non-symmetric effect of timing errors isshown in [26]. In contrast to OFDM, any timing offset in UFMC systems affect the systemperformance, since no CP is inserted. Even with a small timing offset, the orthogonalitybetween subcarriers is destroyed, which causes ICI. Additionally, the previous (positive delay)or subsequent (negative delay) symbol introduces ISI. But the filter ramp-up and ramp-downindicate a soft protection against timing offset, since relatively small energy is contained.

In Fig. 3.2, the Mean Square Error (MSE) of symbol estimates are plotted over relative timingoffset with relative CFO (rCFO) 0.1 (Fig. 3.2a) and 0.5 (Fig. 3.2b) subcarrier spacing. The

0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.528

26

24

22

20

18

16

14

12

10

relative timing offset

MSE

in d

B

OFDMUFMC

(a) Effect of timing offset in UFMC and OFDM underrCFO 0.1 subcarrier spacing

0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.514

13.5

13

12.5

12

11.5

11

10.5

10

relative timing offset

MSE

in d

B

OFDMUFMC

(b) Effect of timing offset in UFMC and OFDM underrCFO 0.5 subcarrier spacing

Figure 3.2.: System performance comparison between OFDM and UFMC under timing andfrequency offset

relative timing offset and rCFO is normalized to total number of samples per symbol andsubcarrier spacing respectively. The simulation settings are shown in table 3.1. We considered

3.2. Approaches of synchronization 25

Multicarrier scheme UFMC OFDMFFT size 128 128

subband size 12 12Number of subbands 10 10

CP-length 0 15FIR-filter type Chebyshev (40 dB side lobe attenuation) none

filter length 16

Table 3.1.: Simulation settings to evaluate the effect of timing and frequency offset in OFDMand UFMC systems

a scenario in the simulation that one subband ,User of Interest (UoI), is perfect synchronizedat the receiver, while all 9 other subbands interfere the UoI. From the results, it is clearthat UFMC has a symmetric effect of timing offset rather than the non symmetric effect inOFDM systems. For further results regarding the effect of timing and frequency offset and thecomparison between OFDM and UFMC, we refer to [7, 27, 28].

3.2. Approaches of synchronization

To recover the transmitted symbols by performing FFT at the receiver, starting position of FFTwindow have to be determined to avoid the effect of ISI. The procedure of finding start positionof FFT window refers to as timing synchronization. In addition, CFO should be compensatedas well to reduce the effect of ICI. Thus, the inserted pilot sequences, intended for channelestimation, are also utilized for timing and frequency synchronization. It is also known aspilot-assisted synchronization. Another approach uses the redundant information of CP toperform synchronization, known as blind synchronization. However, it is only applicable inOFDM systems since CP is not available in UFMC systems.

3.2.1. Timing offset estimation

In the following Fig. 3.3, we illustrate the timing offset between transmitted and received sig-nal due to propagation delay. The underlaying timing offset degrades system performanceby introducing ISI and destroying orthogonality between subcarriers. Thus, it should be esti-mated and corrected at the receiver. The inserted pilot symbols at the transmitter can be alsoutilized to estimate the timing offset. Since the pilots are already known by the receiver, theCross Correlation Function (XCF) A(k) between the known pilots in time domain s(n) and thereceived signal r(n) can be calculated.

A(k) =ns(n k)r(n) =

ns(n k)y(n)+

ns(n k)w(n) (3.1)


Figure 3.3.: Illustration of timing offset between transmitter and receiver

where () is conjugate complex. The peak position k of the XCF indicates the timing offset.Consider a Transmission Time Interval (TTI) of one sub-frame in LTE (in section 2.3.1), itcontains two pilot symbols and the time lag between these two pilots are known. In idealcase, the XCF A(k) should have two peaks with the known sample distance ld . However, thepeak position can be wrongly estimated due to noise and ISI. In the Fig. 3.4, we show theXCF for a TTI of 2 slots in a UFMC system with SNR 0 dB. We are able to observe two

0 2000 4000 6000 8000 10000 12000 140000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Sample index

Corre

latio

n

Figure 3.4.: Exemplary XCF in UFMC system with SNR 0 dB and TTI 2 slots

peaks corresponding to the pilot position. In order to increase robustness of the algorithm, weconsider the sum of peak amplitude instead of a single peak for one pilot. The final timingoffset estimator can be written as

n= arg maxk(|A(k)|+ |A(k+ ld)|) . (3.2)


In general, if Npilot pilot symbols are contained in the TTI, the estimator is given by

n= arg maxk

Npilot1n=0

|A(k+(n1)ld) |. (3.3)

Obviously, the performance of this method highly depends on the auto-correlation (AC) prop-erties of the pilot symbol. The well-known Zadoff-Chu sequence (in section 2.3.2) has anoptimal AC-properties, whereby the cyclically shifted versions of the sequence results in aCAZAC sequence, provided that the length of sequence NZC is a prime number.

3.2.2. Joint timing- and carrier-frequency-offset estimation

After the procedure of timing offset estimation is discussed, a further step is joint timing- andfrequency-offset estimation. Because of the Doppler-Effect and frequency mismatch of localoscillator, frequency error occurs. In order to extend the timing offset estimator to a jointtiming- and carrier-frequency-offset estimator, hypotheses tests for various frequency offsetscan be performed, shown in Fig. 3.5. First of all, we assume that the normalized CFO is

Figure 3.5.: Procedure of joint timing- and carrier-frequency offset estimation via pilots

within the interval -0.5 and 0.5 subcarrier spacing. We quantize this normalized CFO between-0.5 and 0.5 subcarrier spacing into lq levels. These quantized discrete normalized CFOs forma set SqCFO. For every CFO from this set q SqCFO, the timing offset estimation algorithmdescribed in previous section is performed and the peak amplitude and estimated timing offsetis recorded. Instead of using the conjugate complex original known pilot sequence in timedomain s(k), the CFO-compensating version of the known pilot s(k) e j2piqk/N is used


to perform timing offset estimation. Among all the peak values, the largest peak is selected.Finally, the frequency and timing offset can be roughly estimated by the corresponding indexesof the largest peak. The estimator can be formulated as

(,n) = arg maxk,q

Npilot1n=0

|A(k+(n1)ld) | (3.4)

withA(k) =

ns(n k)r(n) (3.5)

s(n) = e j2piqn/Ns(n) (3.6)

The performance of this estimator is thus dependent on the used pilot sequences, SNR andnumber of pilots Npilot within the considered TTI.

However, the inserted CP in OFDM systems is also a redundant information that can be usedto estimate timing and frequency offset. Firstly, an observation window r(k) of the length2N+LCP is selected, where LCP is the length of CP. It is assumed that one complete symbolof N+LCP length is always contained in the observation window, so that a correlation peakexists between the copied CP and the data symbol, shown in Fig. 3.6. The XCF is given by

Figure 3.6.: Observation interval of CP-based timing- and frequency synchronization

A(k) =m+L1m=k

rO(m)rO(m+N). (3.7)

Under timing and frequency offset, the log-likelihood function (n,) can be formulated tobe [29]

(n,) = |A(n)|cos(2pi+A(n))(n) (3.8)where denotes the argument of a complex number and they are given by

(m) =12

m+L1k=m

(|r(k)|2+ |r(k+N)|2) (3.9)

3.3. Results 29

=SNR

SNR+1(3.10)

They act as a normalization term of the correlation magnitude, since (m) computes theenergy of the CP and this energy is weighted by due to the presence of noise. Furthermore,they are independent of rCFO . Additionally, the maximum of the log-likelihood function(n,) is achieved, if

cos(2pi+A(n)) = 1 (3.11)is satisfied. The other terms do not dependent on the rCFO, thus the joint maximization oflog-likelihood function can be separated into two steps, maximizing with respect to n and .Thus the joint Maximum-Likelihood (ML) estimation of n and becomes

nML = arg maxn|A(n)|(n) (3.12)

ML = 12piA(nML) (3.13)Notice that the frequency offset is contained in the phase shift of the peak value, so the com-putational complexity is reduced compared to the two dimensional search approach of pilot-based method. However, CP is not available in UFMC so that this CP-based ML estimationcan only be used in OFDM systems.

3.3. Results

The performance of discussed synchronization algorithms are evaluated based on Monte-Carlosimulation in this section. As aforementioned, the performance of pilot-based synchronizationmethod depends on

the pilot itself, since the auto-correlation properties affects the performance signifi-cantly.

the SNR. The larger the SNR is, the less the random error is because of noise.

the length of TTI. The more number of pilot is contained within the TTI, the better theperformance is.

the wireless channel.

Thus, simulation are carried out for different SNRs, pilots, length of TTI and various channelmodels. The considered channel models are

AWGN-channel, where only noise is present without fading effect.

the single-tap Rayleigh fading channel (refer to as flat fading). Besides noise, the fadingeffect is also taken into account.

3.3. Results 30

the Vehicular A channel model (refer to as VEHA). In this channel model, we take alleffects into account including fading, delay spread and noise.

Furthermore, the performance of pilot-based synchronization is compared between conven-tional CP-OFDM systems and the novel UFMC systems. Additionally, the CP-based synchro-nization is also simulated for OFDM systems as a reference to investigate the performance ofpilot-based synchronization approach.

3.3.1. Timing offset

First of all, we evaluate the performance of the pilot-based timing offset estimator, discussedin section 3.2.1. The basic simulation settings are shown in table 3.2. The used FIR filters are

FFT size Filter/CP Length PRB size No. of PRBs Timing Offset (TO) TTI1024 74/73 12 10/2 10 samples 2 slots

Table 3.2.: Simulation parameters

Dolph-Chebyshev filters with its center frequency shifted to that of every PRB. The side-lobeattenuation of Dolph-Chebyshev filters are set to be 40 dB. Timing offset is set to be of thelength 10 samples. At the transmitter, one sub-frame, which contains 12 data symbols and 2pilot symbols, is transmitted. At the receiver, a timing synchronization algorithm describedabove is to be performed. The number of allocated PRB for users affects the system perfor-mance in such a way that it affects the SNR. The larger the number of allocated PRB for auser, the larger the SNR is for constant power spectral density of data symbols. In order toshow the influence of pilot sequences on the performance of the estimator, we introduce a all-ones pilot sequence in the simulation as a reference. The all-ones pilot refer to a pilot, whichcontains only ones in all the allocated subcarrier positions. For comparison purpose, LTE stan-dard compliant pilots [22] are also evaluated. The user is assumed to move at the speed of 50kmh, which results in a Jakes Doppler spectral power density described in section 2.1.2 (notvalid for AWGN-channel). To evaluate the performance of this pilot-based timing estimator,the PDF of the estimated timing offset is calculated.

In Fig. 3.7, we investigate the effect of PRB allocation size and pilot type. The SNR is fixed tobe 10 dB for both UFMC and CP-OFDM systems. The used pilots are all-ones vector and pi-lots according to LTE standard. The PDF of estimated timing offset are plotted for UFMC (leftside) and OFDM (right side) under the three considered channel models separately. It is clearfrom the simulation results that the method works well under AWGN and flat fading channelmodel with quite satisfying detection probability. The all-ones and LTE standard compliantpilot sequences have almost the same performance in UFMC systems, while the LTE stan-dard compliant pilot sequences outperform the simple all-ones pilot in OFDM systems. Thereason is that the auto-correlation properties of the pilot standardized in LTE is optimized forOFDM systems and these properties are again destroyed in UFMC systems. The optimal auto-correlation properties of Zadoff-Chu sequences is destroyed by the filtering approach, since

3.3. Results 31

7 8 9 10 11 12 130

0.2

0.4

0.6

0.8

1UFMC AWGN SNR 10 dB TO 10 Samples

TO/Samples

Prob

.

2PRBAllones2PRBLTE10PRBAllones10PRBLTE

(a) UFMC

2 4 6 8 10 12 140

0.2

0.4

0.6

0.8

1

TO/Samples

Prob

.

OFDM AWGN SNR 10 dB TO 10 Samples


(b) OFDM

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

TO/Samples

Prob

.

UFMC flat fading SNR 10 dB TO 10 Samples


(c) UFMC

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

TO/Samples

Prob

.OFDM flat fading SNR 10 dB TO 10 Samples


(d) OFDM

0 5 10 15 200

0.1

0.2

0.3

0.4

TO/Samples

Prob

.

UFMC VEHA 50 kmh SNR 10 dB TO 10 Samples


(e) UFMC

0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

TO/Samples

Prob

.

OFDM VEHA 50kmh SNR 10 dB TO 10 Samples


(f) OFDM

Figure 3.7.: Performance of timing offset estimator

3.3. Results 32

the symbols are not equally weighted in different subcarrier positions in UFMC. Furthermore,it is noteworthy to mention that UFMC has more tolerance on negative timing errors thanOFDM if residual timing offset remains after synchronization. Under the Vehicular A channelmodel, the performance of the estimator becomes worst because of the delay spread effect ofthe channel. The estimator shows large variance for both OFDM and UFMC. While still thepilots do not affect the performance much in UFMC systems, an obvious difference can beobserved for different pilots in OFDM systems. Moreover, the more the allocated PRB is, themore accurate the estimation is.

Now, we study the performance behavior with respect to SNR of the estimator. For the sakeof simplicity, we compare the results for different SNRs in the range of -10 dB to 30 dB for asettings of 10 PRB allocation with standard compliant pilot sequence. The results are shown inFig. 3.8. It can be easily observed that this method works already well for -10 dB SNR for bothOFDM and UFMC systems. Starting from SNR of the value 0 dB, no further improvement canbe achieved any more. Furthermore, the results are almost the same for OFDM and UFMC.

Because the estimation method is based on correlation between the known pilot and receivedsignal, another aspect that can affect the performance of the estimator could be the length ofreceived signal. The more slots that are included in the received signal, the more correlationpeaks exist. In the Fig. 3.9, PDFs are shown for different settings. In each figure, the PDFs arecalculated for 10 PRBs with 2 slots, 2 PRBs each with 2, 5 and 10 slots scenarios. In all thescenarios, the standard compliant pilot sequences are used. For the considered three differentchannels, it can be concluded based on the simulation results that the larger the correlationsize is, the better the estimation performance is. Moreover, increasing the allocation size ismore advantageous than increasing the correlation sequence length.

A performance comparison between CP-based and pilot-based timing offset estimation is dis-cussion in the following section.

3.3. Results 33

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TO/Samples

Prob

.

UFMC AWGN 10 PRB LTE pilot TO 10 Samples

10dB0dB10dB20dB30dB

(a) UFMC

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TO/Samples

Prob

.

OFDM AWGN 10 PRB LTE pilot TO 10 Samples

10dB0dB10dB20dB30dB

(b) OFDM

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TO/Samples

Prob

.

UFMC flat fading 10 PRB LTE pilot TO 10 Samples

10dB0dB10dB20dB30dB

(c) UFMC

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TO/Samples

Prob

.OFDM flat fading 10 PRB LTE pilot TO 10 Samples

10dB0dB10dB20dB30dB

(d) OFDM

0 2 4 6 8 10 12 14 16 18 200

0.02

0.04

0.06

0.08

0.1

0.12

0.14

TO/Samples

Prob

.

UFMC VEHA 50 kmh 10 PRB LTE pilot TO 10 Samples

10dB0dB10dB20dB30dB

(e) UFMC

0 2 4 6 8 10 12 14 16 18 200

0.02

0.04

0.06

0.08

0.1

0.12

0.14

TO/Samples

Prob

.

OFDM VEHA 50 kmh 10 PRB LTE pilot TO 10 Samples

10dB0dB10dB20dB30dB

(f) OFDM

Figure 3.8.: Performance behavior w.r.t. SNR of timing offset estimator

3.3. Results 34

7 8 9 10 11 12 130

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1UFMC AWGN SNR 10dB

TO/Samples

Prob

.

2slots10PRBLTE2slots2PRBLTE5slots2PRBLTE10slots2PRBLTE

(a) UFMC

7 8 9 10 11 12 13 140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TO/Samples

Prob

.

OFDM AWGN SNR 10dB


(b) OFDM

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

TO/Samples

Prob

.

UFMC flat fading SNR 10dB


(c) UFMC

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

TO/Samples

Prob

.OFDM flat fading SNR 10dB


(d) OFDM

0 5 10 15 20 25 300

0.02

0.04

0.06

0.08

0.1

0.12

0.14

TO/Samples

Prob

.

UFMC VEHA SNR 10dB


(e) UFMC

5 10 15 20 25 30

0.02

0.04

0.06

0.08

0.1

0.12

0.14

TO/Samples

Prob

.

OFDM VEHA SNR 10dB


(f) OFDM

Figure 3.9.: Effect of correlation size of timing offset estimator

3.3. Results 35

3.3.2. Joint timing- and frequency offset

Besides timing offset, carrier frequency offset is also to be estimated using the joint timingand frequency estimator based on pilot and CP. For OFDM systems, both CP-based and pilot-based method can be used to jointly estimate timing and frequency offset. But only pilot-basedmethod can be used for UFMC systems, lacking of CP. Thus, the performance is discussedand compared in this section.

In the pilot-based method, the normalized CFO is quantized into lq = 21 levels from -0.5to 0.5 with quantization accuracy of 0.05. Because of quantization error, the estimation isexpected to be biased. However, the larger the quantization level lq is, the more accurate theestimation can be. But it also results in higher computational complexity, since the numberof hypotheses increases. Thus, there is a compromise between the estimation accuracy andcomputational complexity. The quantization accuracy of 0.05 with lq = 21 is sufficient toneglect the quantization errors. The rCFO is set to be 0.1 subcarrier spacing and timing offsetof 10 samples. The allocation size is 10 PRBs and standard compliant pilot sequences are usedin pilot-based estimation method. In the Fig. 3.10, the resulting PDFs of the estimated timingoffset are shown for OFDM with CP-based and pilot-based method for different SNRs. Fromthe results for timing offset estimation, it is obvious that pilot-based method is more robust forfrequency unselective channel (AWGN and flat fading channel) . Satisfying performance canbe achieved under -10 dB SNR and good performance already from 0 dB SNR for the pilot-based synchronization. But the CP-based method requires SNR larger than 10 dB to achievethe same performance of pilot-based synchronization. The obtained results for UFMC systemsusing pilot-based approach are similar than that for OFDM, since they are not again plottedin Fig. 3.10. But under Vehicular A channel, CP-based method is more probable to estimatethe real timing offset. The corresponding frequency offset estimation performance are shownin the Fig. 3.11. The MSE of estimated CFO and the real CFO is computed for UFMC withpilot-based method and OFDM with pilot- and CP-based method. Thus, the MSE id definedas

MSE = ( )2 (3.14)For AWGN channel, pilot-based method outperforms CP-based method especially for SNRswhich are higher than 5 dB. For flat fading, CP-based method is more robust for SNRs under0 dB, while the MSE decreases fast for pilot-based method with increasing SNR. In Vehicular-A channel model, CP-based method is more advantageous for SNRs under -5 dB and alsofor SNRs higher than 10 dB. Furthermore, the performance of pilot-based method is almostthe same for OFDM and UFMC. Although the received signal is impaired with CFO, theperformance of timing offset seems not to be affected by CFO.

A value of CFO, which exactly matches the quantized CFO, does not exist in the practice. Thelargest estimation error due to the quantization of CFO occurs, if the real CFO value is locatedexactly between two quantized CFOs. Thus, we also simulate and evaluate the performance offrequency estimation for a CFO of 0.075. The MSE of this pilot-based frequency estimationare shown in fig. 3.12 and compared between OFDM and UFMC. It is shown that OFDM ismore sensitive to quantization errors than UFMC.

3.3. Results 36

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TO/Samples

Prob

.

CPbased OFDM AWGN 10 PRB LTE pilot TO 10 Samples rCFO 0.1

10dB0dB10dB20dB30dB

(a)

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TO/Samples

Prob

.

Pilotbased OFDM AWGN 10 PRB LTE pilot TO 10 Samples rCFO 0.1

10dB0dB10dB20dB30dB

(b)

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TO/Samples

Prob

.

CPbased OFDM flat fading 10 PRB LTE pilot TO 10 Samples

10dB0dB10dB20dB30dB

(c)

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TO/Samples

Prob

.Pilotbased OFDM flat fading 10 PRB LTE pilot TO 10 Samples rCFO 0.1

10dB0dB10dB20dB30dB

(d)

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

TO/Samples

Prob

.

CPbased OFDM VEHA 10 PRB LTE pilot TO 10 Samples

10dB0dB10dB20dB30dB

(e)

0 5 10 15 20 25 300

0.02

0.04

0.06

0.08

0.1

0.12

0.14

TO/Samples

Prob

.

Pilotbased OFDM VEHA 10 PRB LTE pilot TO 10 Samples rCFO 0.1

10dB0dB10dB20dB30dB

(f)

Figure 3.10.: CP-based and Pilot-based timing estimator in OFDM

3.3. Results 37

10 5 0 5 10 15 20 25 30106

104

102

SNR/dB

MSE

AWGN Channel 10 PRB rCFO 0.1 TO 10 Samples

OFDMCPOFDMPilotUFMCPilot

(a)

10 5 0 5 10 15 20 25 30106

104

102

SNR/dB

MSE

Flat fading Channel 10 PRB rCFO 0.1 TO 10 Samples


(b)

10 5 0 5 10 15 20 25 30104

103

102

101

SNR/dB

MSE

VEHA Channel 10 PRB rCFO 0.1 TO 10 Samples


(c)

Figure 3.11.: CP-based and Pilot-based frequency estimator

3.3. Results 38

10 5 0 5 10 15 20 25 30103

102

101

SNR/dB

MSE

AWGN Channel

OFDM2PRBOFDM10PRBUFMC2PRBUFMC10PRB

(a)

10 5 0 5 10 15 20 25 30103

102

101

SNR/dB

MSE

flat fading Channel


(b)

10 5 0 5 10 15 20 25 30103

102

101

SNR/dB

MSE

VEHA Channel


(c)

Figure 3.12.: Pilot-based frequency estimator

3.3. Results 39

From the simulation results, it can be concluded that OFDM and UFMC have almost same per-formance of timing and frequency synchronization via pilot. Furthermore, CP-based timingsynchronization requires higher SNR than pilot-based. For the investigated two kinds of pilotsequences, UFMC systems exhibit approximately the same performance while the standard-ized pilot shows some advantages in OFDM systems. The reason is that the standardized pilot(e.g. Zadoff-Chu sequences) is designed with good auto-correlation properties for OFDM,while these properties are not hold in UFMC.

4. Channel Estimation

After timing and carrier frequency offset are corrected, the CSI have to be estimated to get thesymbol estimates. In this chapter, we investigate pilot-assisted channel estimation for the novelmulti-carrier modulation technique UFMC and compare the performance with conventionalCP-OFDM systems. UFMC is expected to have several advantages compared with OFDMdue to its reduced out-of-band radiation and reduced guard subcarriers between sub-bands [5].The channel estimation in UFMC systems is also interesting because of its absence of CP.

4.1. The effect of channel-assisted ISI

Because of the insertion of CP in OFDM systems at the transmitter, the overlapping part whichcontains ISI is within CP, if the channel impulse length is smaller than the CP duration. TheOFDM receiver can efficiently mitigate channel-assisted ISI by removing the CP part withoutcausing any distortion. As we know, CP is not available in UFMC systems. This fact can leadto higher ISI and destroy the orthogonality between subcarriers in a frequency-selective fadingchannel, compared with CP-OFDM. However, the filter ramp-up and ramp-down act as a softprotection against the channel delay spread since the signal energy contained within this partis comparatively small.

To investigate the effect of channel-assisted ISI, simulations are carried out for three differentchannels

Vehicular-A channel model with the Power Delay Profile (PDP) according to C802.20[16]

A fading channel with two equal power density fading taps, but the delay between thetwo taps can be varied

Exponentially decaying PDP channel [17] with various asymptotic rms delay spread

Simulation parameters are shown in the following table 4.1. Every PRB is filtered by Dolph-

FFT size Filter/CP Length PRB size No. of PRBs Modulation1024 74/73 12 10 QPSK

Table 4.1.: Simulation parameters of investigating channel-assisted ISI

Chebyshev filter with a side lobe attenuation of 40 dB and the filters are frequency-shifted to

4.1. The effect of channel-assisted ISI 41

the center frequencies of each PRB. Furthermore, perfect channel knowledge is available atthe receiver and the noise is neglected, since we only interest on the effect of channel-assistedISI. The MSE is then calculated for the symbol estimates obtained at the receiver.

According to [16], the Vehicular-A channel model with the settings in 4.1 has 40 taps in sampleand this channel impulse length is smaller than the CP length in OFDM. In Fig. 4.1, MSE ofthe received symbol estimates are plotted over different Vehicular-A channel realizations. The

10 20 30 40 50 60 70 80 90 10080

70

60

50

40

30

20

10

0

VEHA channel realization

MSE

/dB

UFMC and OFDM with VEHA channel

mean MSE:42.7dB

Figure 4.1.: Channel-assisted ISI for Vehicular-A channel

mean MSE for 100 channel realizations is -42.7 dB for UFMC. This mean MSE indicatesthat the channel ISI is negligible for this channel model. In CP-OFDM, the channel-assistedISI is completely mitigated because CP length is so designed that it is greater than channelimpulse length. A channel with exponentially decaying PDP is determined by asymptotic rmsdelay spread, which describes the decaying speed of power density. In Fig. 4.2, the MSEs arecalculated for various rms delay spread, which is already normalized to the sample time. As

0 20 40 60 80 100 120 140 16050

40

30

20

10

0

asymptotic rms delay spread/samples

MSE

in d

B

Exponentially Decaying PDP channel, Path Number 1000

OFDMUFMC

Figure 4.2.: Channel-assisted ISI for exponentially decaying PDP channel

4.2. Single user channel estimation 42

the results show that CP-OFDM can tolerate larger rms delay spread than UFMC for a sametarget MSE. For the two fading taps case, shown in Fig. 4.3, CP-OFDM is also more robustthan UFMC. Furthermore, the x axis is delay between the two taps and normalized to FIR-

0 2 4 6 8 10 12 1450

40

30

20

10

0

10

/L

MSE

in d

B

Two Same Fading Taps Channel

CPOFDMUFMCCW40

21% filter length

36% filter length

Figure 4.3.: Channel-assisted ISI for two path channel

filter length, which is used in UFMC. As aforementioned, ISI can be completely mitigated inCP-OFDM as long as the channel impulse length is smaller than CP duration. Compared toCP-OFDM, the MSE increases while the delay increases. If a target MSE of -40 dB shouldbe achieved, then one might choose a filter with a appropriate length Lch/21%. If a targetMSE of -30 dB should be achieved, then one might choose a filter with a appropriate lengthLch/36%.

4.2. Single user channel estimation

In the previous section, we show that the channel-assisted ICI is negligible in UFMC andOFDM systems. By appropriately designing the FIR-filter and CP length in UFMC andOFDM systems respectively, the channel-assisted ISI can be limited to below a certain valueof MSE such that it does not affect the system performance significantly. If UFMC and CP-OFDM system are so designed that the channel-assisted ISI is negligible, we can write thesymbol estimates at the receiver for OFDM as (equation (2.31))

YO(k) = H(k)X(k)+WO(k) (4.1)

and for UFMC as (from equation (2.38))

YU(k) = H(k)B

i=1

Xi(k)Fi(k)+WU(k) (4.2)

4.2. Single user channel estimation 43

Without loss of generality, we can assume that the considered subcarrier k is allocated to thePRB i and we also drop all odd subcarrier outputs of the 2N-point FFT in UFMC. Thus, (4.2)can be further simplified as

YU(k) = H(k)Xi(k)Fi(k)+WU(k) (4.3)

Since the pilot symbol X(k) or Xi(k) is already known at the receiver, so we are able to estimateH(k). It is straightforward that the channel estimates for OFDM and UFMC at subcarrier kcan be written as

H(k) =YO(k)X(k)

= H(k)+N(k)X(k)

. (4.4)

H(k) =YU(k)

Xi(k)Fi(k)= H(k)+

N(k)Xi(k)Fi(k)

. (4.5)

Thus, the channel estimation differs only in the equalization of the filter shape in UFMC fromOFDM. In Fig. 4.4, the scheme of equalization of filter shape before channel estimation isshown for UFMC. At the output of 2N-point FFT, the symbols are firstly divided by its filter

Figure 4.4.: Equalization of filter shape in UFMC

response in the corresponding subcarrier position in UFMC. Once the filter s

2014 - channel estimation and equalization for 5g wireless communication systems (ufmc)

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the effect of timing