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CHIP EQUALIZATION AND TRANSMIT

ANTENNA DIVERSITY FOR

HIGH-SPEED SS/TDM SYSTEMS

Farhad Meshkati

Ji thesis subrriitted in coriforrriity with the reyuireme~its for tlic degrcc of blastcr of Applicd Scicncc

Graduate Department of Electrical and Cornputer Engineering University of Toronto

@ Copyright C Farliad hrleshkati, 2001

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Chip Equalization and Transmit Antenna Diversity

for High-Speed SS/TDM Systems

Farhad Meshkati

Master of Xpplied Science, 2001

Department of Electrical and Computer Engineering

University of Toronto

Abstract

Hybrid Spread SpectrumlTime Division Multiplex (SS/TDM) is a promising scheme for

the air interface of future high-speeci wireless packet-based networks, especially for the

downlink. In this thesis, we first present an alternative receiver to the Rake for the

downlink of SSITDhl systems. This receiver, which consists of a Fractionally Spaced

Chip Equalizcr (FSCE) and a dcsprcadcr, is shown to havc supcrior pcrformancc to thc

conventional Rake receiver and can be used in systems with long spreading codes. LVe

propose an adaptive implementation of the FSCE receiver and use simulations to study

the effect of various system parameters on the performance of the receiver. In addition.

for channels wit.h short delay spread in wliich spread spectrum does not provide enough

diversity to combat fading, ive combine chip equalization with transmit antenna diversity

to achieve botli interference suppression arid robustriess agairist fadirig. We dernoristrate

the performance of the conibined scherne iising simulations.

Acknowledgments

1 would like to thank Professor Elvino S. Sousa, my advisor. for his invaluable guidance

and support. 1 am also thankful to the members of the Wireless Lab for the helpful

discussions. 1 am deeply grateful to my family, especially my parents? for their continual

support and encouragement. 1 would also like to acknowledge the financial support of

the Natural Sciences ancl Engineering Research Council of Canada (NSERC) and the

Communications Group.

'To my parents

Contents

Abstract

Acknowledgments

Contents

iii

List of Figures viii

1 Introduction 1

. . . . . . . . . . . . . . . . . . . . . . . 1.1 Direct-Sequerice Spread S y ect runi 2

. . . . . . . . . . . . . . . . . . . . . . 1.2 Spread Spectruin Cellular Networks 5

. . . . . . . . . . . . . . . . . 1.3 hlultipath Fading arid Diversity Tecliniques 6

. . . . . . . . . . . . . . . . . . . . . . 1.4 Receiver Design for CDMA Systems 8

. . . . . . . 1.5 Hybrid Spread Spectruni/Time Division Multiplex (SS/TDh. 1) 10

. . . . . . . . . . . . . . . . . . . . . . 1.6 Thesis blotivation arid Orgaiiization 12

2 The Fractionally Spaced Chip Equalizer (FSCE) Receiver 14

. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 SS/TDhl Downlink hlodel 15

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Signal Detection 18

. . . . . . . . . . . . . . . . . 2.2.1 Optimal Receiver for AWGN Channel 18

2.2.2 Optimal Detection in Presence of Intersymbol Interference (ISI) . . 19

. . . . . . . . . . . . . . . . . 2.2.3 Fractionally Spaced Equalizer (FSE) 19

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Rake Receiver 22

. . . . . . . . . . . . 2.3.1 Tapped Delay Line Mode1 for Radio Channels 23

. . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Rake as a Matched Filter 23

. . . . . . . . . . . . . . . . . . . 2.3.3 Limitations of the Rake Receiver 25

. . . . . . . . . . . . . 2.4 -An Improved Receiver Based on Chip Equalization 27

. . . . . . . . . . . . . . . . . . . . . . 2.4.1 The MMSE Chip Equalizer 28

. . . . . . . . . . . . . 2.4.2 Fractionally Spaced Chip Equalizer (FSCE) 30

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Chapter Summary 35

3 Simulation Results for the FSCE Receiver 36

. . . . . . . . . . . . . . . . . . . . . . 3.1 Simulation Mode1 and .A ssumptions 37

. . . . . . . . . . . . . . . . . . . . . . 3.2 Simulation Results and Discussions 43

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 QPSK 44

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 lGQ.Abl 53

3 .23 Corriparisori Betweeri QPSK and 16-Q.AA.1 . . . . . . . . . . . . . . 54

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Correlated Fading 60

. . . . . . . . . . . . . . . . . . . . . . 3.2.5 Decisiori-Feedback Equalizer 60

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Cliapter Summary 62

4 Combined Transmit Antenna Diversity and Chip Equalization 64

. . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 .l lar~iou t i's Diversity Scl~errie 66

4.2 Trarisrriit Axiterrria Diversity ivith Cliip Equalizatiori for SS/TDM Systerris 68

. . . . . . . . . . . . . . . . . . . . . . 4.3 Simulation Results ancl Discussions 74

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Chapter Summary 76

5 Conclusions 77

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Thesis Surrirriary l i

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 .2 Future Work 79

A The Recursive Least Squares (RLS) Algorithm

Bibliography

vii

List of Figures

. . . . . . . . . . . . . . . 1.1 Basic baseband mode1 for DS Spread Spectrum 2

1.2 Demonstration of the noise (interference) rejection property of spread spec-

trum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

. . . . . . . . . . . . . . . . . . . . . . . . 1.3 Time-varying multipath channel 6

. . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Fraiiie structure in SS/TDkI 11

. . . . . . . . . . . . . . . . . . . . . . . 2.1 Tratismitter for SS/TDM systems 16

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 hlatched Filter 18

. . . . . . . . . . . . . . . . 2.3 klatched Filter plus Lirlear Transversal Filter 19

. . . . . . . . . . . . . . . . . . . . 2.4 Iiifinitely long LTF with T tap spacing 20

2.3 r\liasing cffccts duc to insufficicnt sanipling rate . . . . . . . . . . . . . . . 21

. . . . . . . . . . . . . . . . . . . 2.6 Tappcd dclay linc modcl of radio channcl 24

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 R.akc R.cccivcr 2.5

. . . . . . . . . . . . . . 2.8 .-\ri alternative representation of the Rake receiver 26

. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 The &Il[SE chip equalizer 29

. . . . . . . . . . . . . . . . . . . 2.10 The chip eclualizer as a tapped delay line 31

2.11 The FSCE receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.12 Plot of 1 Hrll (w)12 for r = Tc . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.13 Plot of IHT, (w)12 for r = :Tc . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3-1 Discrete baseband model for SS/TDiLI downlink transmitter . . . . . . . . 40

Discrete baseband mode1 for SS/TDM downlink with FSCE receiver . . . . 41

QPSK constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Comparison between the FSCE and Rake receivers (Ar = 4, two-path chan-

ne1 with T = 2Tc, QPSK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Comparison between the FSCE and Rake receivers ( N = 16: two-path

channel with T = 2Tc, QPSK) . . . . . . . . . . . . . . . . . . . . . . . . . 46

Effect of processing gain, N : on the performance of FSCE (two-path chan-

ne1 with T = 2Tc, q = 2,r'l.i = 15, QPSK) . . . . . . . . . . . . . . . . . . . 48

Performance of the Rake receiver under three different channel profiles

(IV = 4, II: = 1, QPSK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Performance of the FSCE receiver under three different channel profiles

(N = 4, K = 1, q = 2,121 = 15, QPSK) . . . . . . . . . . . . . . . . . . . . 51

Effect of ISI on the performance of the FSCE receiver (two-path channel,

q = 2 , M = 15, QPSK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

16-QAM constellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Comparison bctwccn the FSCE and Rakc rcccivcrs (Ar = 4, two-path chan-

ncl with T = 2Tc, 16-Q-4M) . . . . . . . . . . . . . . . . . . . . . . . . . . a5

Effcct of proccssing gain: N, on the pcrformancc of the FSCE rcccivcr

(two-path channcl with T = 2Tc, q = 2. -44 = 15, 16-QUvI) . . . . . . . . . 56

Effect of ISI on the performance of the FSCE receiver (two-path channel,

q = 2, LI1 = 15. 16-Q.AM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Comparison between QPSK and 16-Q-AM (two-path channel witli T = 2Tc,

q = 2 , M = 15) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Effect of correlated fading (two-path channel, N = 4. K = 1, q = '2: 1bl = 15) 61

Comparison between FSCE and DFE (two-path channel with T = 2Tc,

11; = 4. IC = 1. QPSIO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.1 Transmitter and receiver structures for -4lamouti's diversity scheme . . . . 68

4.2 Block diagram of the receiver for the combined scheme . . . . . . . . . . . 72

4.3 The overail receit-er for the combined transmit diversity and chip equaliza-

tion scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.4 Cornparison between simple equalization and combined chip equalization

with transmit diversity (two-path channel with T = 0. lTc: N = 4. K = 1) . 75

Chapter 1

Introduction

The possibility of being able to offer multimedia services to mobile users anywhere and

at anytime has attracted enormous amount of attention and effort towards the area of

wireless communications. Multimedia applications such as Internet browsing arid video

coriferencing require high bit rates. In order to provide such services to a large number

of users over the liniited radio spectrum. the spectral efficienq. of wireless systerns has to

improve corisiderably. To desigri efficient wireless networks. it is esseiitial t ha t baridwidtli

arid trarisriiit power are rnariaged efficieritly. Towards this goal. spread spectrurri tecli-

niques tiü\-e received a great deal of att.eiitiori over t.he past feu- years. Iri this modulation

schtmc. the data signal is transmitted over a bandwidth that is much larger than the

data rate. This bandwidth esparision results in a number of properties of whicli interfer-

cncc rejection (suppression) is of primarj- importance. There are different tj-pes of sprcacl

spectrum. The three main ones are Direct-Sequence (DS): Frequency-Hopping (FH) and

Time-Hopping (TH) [II. Direct-Sequence Spread Spectriim (DS-SS) is the most popular

form of sprcad spcctrum and will bc our focus throughout this work.

spreading code Interference

*

spreading code

channel

Figure 1.1: Basic baseband modcl for DS Sprcad Spectrum

1.1 Direct-Sequence Spread Spectrum

Iri Direct-Seqtierice Spread Spectrum (DS-SS), the data signal is rriultiplied by a spreading

code wtricti has a much larger baridwidth thari the niininiurri baridwicltti typically required

for the given data rate. The spreading code should have noise-like properties to achieve

robustness against interference. -At the receiver, the DS signal is multiplied by the same

spreading code. This wax the information signal is despread back to its originaI band-

wicltli. But. the noise (interference) that was added in the channel remains spreacl over

thc largcr bandwidth. The rcsulting signal is thcn passcd through n lowpass filtcr (sce

Figurc 1.1). Thc output of the lowpass filtcr contairis only a fraction of the noisc powcr.

This noise rediiction is proportional to the amoiint of bandwicith cspansion (sec? Figure

1.2). The spreedirig code is normally n bina- pseudo random signal grneratecl by a sliift

register circuit with feedback connections. The binary pulses of this signal are referrecl

to as chips. The ratio between the symhol duration (7') and the cliip duration (Tc) is

called the processing gain and is an important factor in determining the performance of

the spread spectrurn modulation.

-4s a result of the bandwidth expansion, spread spectrum has a number of benefits

data signal ? SS signal

> -L

/ -L frequency

T I

interference f SS signal

/

I -L frcquency T

s~recid interference 1 r: I despread data signal

-L frequcncy T C

Figure 1.2: Demonstration of the noise (interference) rejection property of spread spec-

t rum

[l]: The main one is the interference rejection property. In addition. spread spectrum

provides anti-jamming capabilities. If the bandwidth of t.he SS signal is larger than the

coherence bandwidth of the cbannel, spread spectrum provides path diversity which can

be esploited to combat fading. Another benefit of spread spectrum is that because of

the low power spectral density, SS signals cannot be easily intercepted. AIso: due to

the use of randonl spreading codes, spread spectrum provides some level of secrecy. In

addition, the interference rejection (suppression) property of the spread spectrum allows

for multiple signals to be transrnitted sirnultaneously over the radio channel and hence

provides multiple access cayabilities. Multiple access communication can be achieved by

assigiiirig differerit spreadirig codes to different users. It is desirable that the spreadirig

codes have a narrow aut.ocorrelation function and the cross correlation betweerr different

spreading codes be as srnall as possible to reduce the amount of multiple access interfer-

ence. This multiple access scheme is called Spread Spectrum Multiple -1ccess (SS'Uf-4) or

Code Division Slult.ip!e Access (CDLIA) [2].

The spreading codes used for different users m a j be long or short depending on their

pcriod. If the pcriod of the scqucncc is cqual to the data syrnbol pcriocl the scqucncc

is callcd short. On the otlicr hand: if thc pcriocl is much largcr than t h data symbol

periad, t,hc sccliicncc is long. Also, dcpcnding on thc systcm dcsign. a SSM-1 systcm can bc

synchronous or asynchronous at thc chip lcvcl. In point to multipoint communication (cg.

hase station to mobile t.ertninals). it is possible to synchronize signals iit the cliip level.

This way. orthogonal spreacf ing codes can he useci t o eliminate CO-channel in terference

(orthogonal CDhl-A). U,.alsh codes are esamples of ort hogorial sprcading codes. N'hile

\j7alsh codes provide orthogonalit~v, they do not have noise-like properties such as narrow

autocorrelation function. To rectify this problem: a masking sequence can be used to

randomize the spreading codes while keeping ttieir orthogonality. In multipoint t o point

communication (mobile tcrminals to base station) it is difficult to synchronize the signals

transini tted by different users. In such cases, asynchronous transmission with short or

long pseudo noise (PX) spreading codes is used. This way? little coordination is required

among the users.

1.2 Spread Spectrum Cellular Networks

Because of its robustness against jamming, low probability of intercept and moderate

level of secrecy (encryption), spread spectrum was used mainly in military applications.

In 1978, cellular application of spread spectrum was proposed for the first time [ 3 ] . Due

to its noise rejection capability, spread spectrum reduces the intracell and interceIl inter-

ference and alion-s the entire available bandwidth to be used in every ce11 (i-e. frequency

reuse factor of one). This results in a higher system capacity compared to narrowband

modulation schemes. The capacity of spread spec trum cellular ~ietworks depends on the

level of intracell and interccll interference. Several approaches are taken to increase the

systerri capacity:

One technique is to use potver coritrol to rniriimize the aniount of iriterfererice iri the

system by adjusting the transmit pon7er according to the channel condition while satisfying

the required signal to noise ratio (SNR) level. -4nother approach is to use sectorization

along with directional antennas to reduce the interference. Ir1 the downlink (base station

to mobile) where communication is point to miiltipoint, signals can be synchronizecl at

the chip level. With synchronization, orthogonal spreading codes can be used to elimitiate

intraccll intcrfcrcncc. -41iothcr approach is to improvc tlic design of rcccivcrs so that tiicy

can achicvc thc dcsircd bit crror rates a t lowcr SNR lcvcls. This rcdiiccs thc rccliiircd

transmit power and hence reduces the overall interference in t,he system. .A11 of t h e above

techniqiies try to rnasirnize the system capacity hy minimizing the interference in the

system.

Figure 1.3: Time-varying multipath channel

1.3 Multipat h Fading and Diversity Techniques

hlultipath fading, which is a result of constructive and destructive combination of ran-

domly delayed! refiected. scattered and diffracted signal components (see Figure 1.3), is a

characteristic of almost al1 wireless channels and has to be given serious consideration in

the design of wireless networks. Variations in the envelope of the received signal result in

variations in thc rcccivcd SXR. Whcn the rcccivcd SNR is highcr than thc rcquircd SNR,

the unnecessary interference causes capacity rediiction. One the ot her hand, when the re-

ceived SNR is lower t hm the reqiiired SNR, the reqiiired qiiality of service cannot be niet.

Therefore, steps shoiild be taken to reduce the effect of fading and avoid fluctuations in

the SNR level. The rate of signal variation depends on the channel Doppler spread which

is related to a/,, ivhere 7: is the velocity of the receiver or transmitter or the siirroiinding

objects: c is the velocity of light and f, is the carrier frecpency. The coherence time of the

channel (rCoh), which is a measure of the time interval over mhich a transmitted signal will

be relatively undisturbed bÿ channel fluctuations. is approsimately equal to the inverse

of t.he Doppler spread.

The time dispersion caused by the channel as a resiilt of multipath propagation is

measured by the channel delay spread. The coherence bandwidth of the channel (f,,,,),

which measures the minimum frequency separation required for two signals to undergo

uncorrelated fading, is inversely proportional to the channel delay spread. If the signal

bandwidth is larger than the coherence bandwidth of the channel, fading is frequency

selective. In this case, although the channel causes dispersion in time, most of the signal

energy can be recovered at the receiver through proper signal processing. CVith spread

spectrum modulation, if the information signal is spread over a bandwidth larger than the

coherence bandwidth of the channel, fading becomes frequency selective. This provides

implicit path diversity ndiich can be esploited to combat fading. If the signal banciwidth

is smaller t han the coherence bandwid t h of the channel, fading is frequency non-select ive

(flat fading). Iri this case, the received signal eriergy cau fluctuate corisiderably deperidirig

on the relative phase of the rnultipatli components. To mitigate flat fading, diversity

techniques have to be used.

There are three main diversity rnethods: frequency, time and space. In frequency diver-

sity, multiple copies of the same signal are transmitted using different carrier frequencies.

In order to ensure independent fading? t,he spacing between the carrier frequencies niust

bc largcr than thc cohcrencc frcqucncy of thc channcl. Path diversity which is proviclcd in

sprcad spcctrum techniques can bc considcred as a spccial case of frcqucncy divcrsity. In

tinlc divcrsity, multiple copies of thc samc signal arc scnt diiring ciiffcrcnt timc slots. Tlic

scparation bctwccn thc timc slots should bc largcr than thc cohcrcncc timc of thc channcl

to ensure independent fading. Spme diversity is achieved iising multiple antenniis. One

cornmori way is to transmit the signal usirig one transmit antenna and receive the sigiial

with multiple receive antennas. If the receive antennas are positioned far enough [rom

each other. they \vil1 provide space diversity. It should be notecl that even if the signals

undergo correlated fading, there is still some diversity gain. However, the diversity gain

reduces as the correlation increases.

Due to the stringent limitations on the size and complexity of the mobile terminals.

receive antenna diversity is not very practical for the downIink charinel. Instead, it is

preferred to use transmit diversity. Most of the proposed transmit antenna diversity

schemes result in handwidth espansion or require feedback. -4lamouti in [4] and DaSilva

and Sousa in [5] have proposed two different transmit diversity techniques for Bat fading

channels. Alamouti uses a special case of space-time coding [6] to achieve diversity whereas

DaSilva and Sousa rotate the constellation t o obtain resistance against fading. Both

metliods are bandnidth efficient and do not require feedback. -4 rnodified version of

Alamouti's scherne has been proposed in [Tl for channels with ISI. The proposed scheme

is mainly concerned wi t h narrowband modulation and does not consider spread spectrum

modulation.

1.4 Receiver Design for CDMA Systems

We mentioned that one approach for increasing tlie capacity of spread spectrum cellular

rietworks is to irriprove the receiver design. -411 improved receiver cari satisfy the quality

of service requirernent a t a lower SNR level. This reduces the overall iriterfererice iri the

system and hence increases the capacity. The conventional receiver for spread spectrum

systems is the Rake receiver [8]. While it is simple and robust, Rake receiver performance

is limited by interference. New receivers have been proposed to mitigate tlie sliortconi-

ings of the Rake receiver [9]. These receivers can be divided into two main categories:

mult.iuser and single-user. The first multiuser detector was proposed by Verdu in 1986

[IO] and IWS bascd on hlilsinium Likclihood Sequcncc Dctcçtion (MLSD). Although t liis

rcccivcr can achicvc optimum pcrformancc. it is not practical duc t o its cxponcnt,ial com-

plesity. -4 niimber of siihoptimal reccivers have been proposed which are less comples to

implement . Decorrelator receiwr [l 11. Siiccessive Interference Cancellation (SIC) 1121 and

Parallel Interference Cancellation (PIC) [13] are examples of such suboptimal receivers.

In al1 multiuser receivers, the signal for each user is demodulated taking into account the

contribution of other users (interferers) in the system. Most of these receivers require ver'-

high computational power and hence are not suitable for the downlink. Froni a practical

point of view? size. complexity and cost of mobile terminak should be kept as Iow as

possible.

-4 single-user receiver, on the other hand, does not require any information regarding

other users in the system and demodulates the data signal of one user only. One family

of improved single-user detectors is the Minimum Mean Square Error (Mh.ISE) receiver

proposed in [14] and [ls]. These receivers have moderate complexity but the? require the

received signal to be cyclostationary. Therefore, they can only he used in systems with

short spreading codes.

-4 nuniber of receivers have beeri yroyosed for systerris with long spreading codes

116. 17, 18. 191. Ttiese receivers use chip equalization to suppress interferericc ic i the

downlink of CDhL4 systems. In [20]: Davis et al. present chip equalization as a noise

whitening approach for multiple-access noise rejection. CIiip equalization based on Zero

Forcing (ZF) and iLlinimum Meari Square Error (MhISE) criterion is discussed in [16]:

[18] and [19]. Several adaptive implenientations of chip equalization are also presented in

[lS], [21] and [22] for thc downlink of CDhjIA systcms.

Whilc chip cqualization is shown to givc supcrior pcrformancc cornparcd to t h con-

vcntional R.akc rcccivcr. thc pcrforniancc of siich rcccivcrs has not bccn sttidiccl in dctail.

hIorc rcscarch nccds to bc donc in ordcr to obtain furthcr insight into thc opcration of

these receiwrs. For esample, t he effect of varioiis system parameters siich as processing

gain and channel profile on the performance of tliese receivers needs to investigated. In

order to achieve high bit-rate transmission, the spectral efficiency of wireless systems hm

to improve. One possibility is to try to use Iiigh-order modulations siich as 16-QAM.

So far: no work has been done to study the performance of chip equalizers under such

modulation schemes.

1.5 Hybrid Spread Spectrum/Time Division Multi-

plex (SS/TDM)

Future wireless networks are espected to support various multimedia services. A large

portion of the traffic carried by these networks will be data-oriented. In contrast to voice.

which requires a constant bit rate and is sensitive to delay, data traffic is bursty in nature

and tolerant to delay. Current wireless systems (Le. 2G) are not particularly optimized for

data transmission. For example. the DS-CDhI-4 scheme that is employed in the downlink

of IS-95 standard is dcsigncd mainly for voicc transmission. Each uscr is assigncd onc

orthogonal code (Walsh codc) ovcr which thc uscrk information is sprcad. This way. a

voice channel is allocated to a user over the entire diiration of its call.

In contrast to voice services that use circuit-switching to guarantee continuous trans-

mission. data services can use packet-switching methocls to achieve higher efficiencies by

taking advantage of statistical multiplesing. Therefore, if a wireless network is to be

designed esclusively for packet transmission. it is reasonable to incorporate some form

of time multiplesing. This allows us to use fairly simple scheduling schemes to accom-

mociate both high bit-rate and low bit-rate users in the system. However. we would still

like to have some of the advantages of spread spectrum. In particular. we want to have

some degree of robustness against interference. Spread spectrum reduces the intracell

and intercell interference and allows us to use a frequency relise factor of one. LVe c m

have the benefits of both TDM.1 ancl spread spectrum by implementing a hybrid Spreaci

Spectrum/Time Dix-ision Multiples (SS/TDhI) scheme. In such a SS/TDM scheme. tin-ie

is divided into slots (frames). During eacti time slot, spread spectrun~ moclulation is usect

for data transmission. This way, users receive (or transmit) data in bursts rather than

continuously. Each frame contains one or more pilot bursts as shown in Figure 1.4. The

pilot bursts facilitate various tasks such as acquisition, synclironization. channel estima-

t ion, and signal to noise ratio (SNR) rrieasurement. Considering its structure: SS/TD LI is

I Time Slot (frame) Pilot Burst

Figure 1.3: Frame structure in SS/TDh,I

more feasible in point to multipoint communication wliere time synchronization is easier

to achieve. Implementing this scheme in multipoint to point scenarios is more difficult

and rleeds coordination among different users. Our focus throughout this thesis wilI be

the downlink (base station to mobile terminal) where the communication is point to mul-

tipoint,

The SS/TDM scheme is particularly suitable for cellular data networks due to the

following reasons:

The time niultiplex nature of this sctieme is very fitting for packet transmission.

It allows us to use schedulirig rriettiods to serve niobile users witli differerit bit-rate

requirenierits in a n efficient nianrier.

Because spread spectruni transmission is used iri each time slot, this scheine still

lias rohstriess agairlst iriterfereiice. I t . lierice? allows ttie entire available bariclwidth

to be used iri every ce11 (i.e. reuse factor of orle).

Sirice duririg auy giveri frarrie, o d y orle user receives (or trarisriiits) data, the traris-

riiissiori cari be optirriized for tlie user of iriterest. For esariipte: beariiforuiing cari

be dorie usirig ariteriria arrays tu reduce iriterfererice in the system.

If the size of the frames are chosen to be less tliaii the coherence time of the chaririel

(rCoh ). the tinie-varyirig radio charinel becoriies practically tirrie-irivariatit duririg a

frame period. This nrill allow for implementation of sophisticated signal processing

schemes nithout adding too nuc ch cornplexity.

Each user receives (or transmits) data in bursts. So, when a user is inactive, it can

either go to "sleep" mode to save power or process the data it already received.

There are different ways to implernent spread spectrum within each tinie slot. In

order t o support high bit rates and a t the same time keep the processing gain reasonably

large, multi-code DS-SS can be implemented in each time slot. In particular, in the

downlink mhere the signais can be synchronized at the chip level, orthogonal spreading

codes (e-g. IValsh codes) may be used to eliminate intracell interference. In practice,

however, mult ipath propagation destroys the ort hogonality and degrades the performance.

A SS/TDM system with Walsh spreading codes is somewhat similar to the scheme used

in the downlink of 1s-95 [2], [23]. However, tiie niain difference is that in the SS/TDM

system, users receive data in bursts. During each burst, al1 the \ITalsh codes are assignecl

to the sanie user. -An esample of such a SS/TDhl system is the High-Data-Rate (HDR)

system developed by Qualcomm lncorporated [24].

1.6 Thesis Motivation and Organization

Future wireless systems will have to support a variety of services? a majority of which

will be data-oriented. Most data applications have bursty and asyrnmetric traffic. In

many of tliese applications, the downlink traffic is greater than the uplirik traffic. In the

previous section! we ga'-e motivations for using SS/TDhl scheme in future wirelcss data

netn-orks, especially for tlie downlink. One approach is to use orthogonal spreading codes

to eliminate intracell ititerference. However, in practice, inultipat h propagation destroys

tliis ortliogoriality and results iri iriterpath arid ititerchartriel iriterfererice. Our objective

is to propose an alterriative receiver t o the Rake for tlie dowilirik of SS/TDhI systeriis to

cope with this iriterference better. Such a receiver should have rnoderate complexity and

be able to handle long spreading codes. Mre intend to study the effect of different system

parameters on the performance of this receiver. In addition, for channels with short delay

spread. in which spread spectrum may not provide enough robustness against fading, we

add antenna diversity to combat fading.

The organization of the thesis is as follows:

In Chapter 2, we give the system mode1 for the downlink of SS/TDM systems with

orthogonal (Walsh) spreading codes. We then describe the Rake receiver and discuss

its limitations. Nest, we present an alternative receiver for the downlink of SS/TDM

systems. This receiver, which consists of a Fractionally Spaced Chip Equalizer (FSCE)

and a despreader, is only slightly more complex than the conventiorial Rake receiver but

has much better performance.

Iri Cliapter 3, Ive study the perfor~nance of the FSCE receiver. Througli diip-level

siniulatiocis. me show that t his receiver yerforrns sigriificantly better than the Rake re-

ceiver. We also study the effect. of various system parameters such as processing gain and

channel profile on the performance of the FSCE receiver. In addition, we compare the

performance of the FSCE for QPSK and 16-QAhI modulation schemes.

In Chapter 4. ive combine transmit antenna diversit.' with chip equalization to achieve

robustness against fading and intcrfcrencc cancclIation for channcls with short dclay

sprcad. Tlic cornbincd schcmc whilc being more complcs than simple chip cquaIization

providcs an additional sourcc of divcrsity which is ncccssary to combat fading in cnviron-

ments siich as indoors whcrc the channcl dcIay sprcad is short. WC show t.hc pcrforrnancc

of t h e cornhined scheme iising simrilations.

Finallu, in Chapter 5, we present conclusions arrtl suggest future work.

Chapter 2

The Fract ionally Spaced Chip

Equalizer (FSCE) Receiver

ikiost of the traffic transmitted over future wireless systems will be da ta rather than voice.

As a result. there will be a need for networks that are optimized for data rather than for

voice. -4 promising scheme for the air interface of the downlink of wireless data s>-stems

is the hybrid Spread Spectrum/Time Division Multiplex (SS/TDlI). In t his scheme. tinie

is divided into slots (frames). During each time dot, spread spectrum modulation is useci

for data trarismission. Considering its structure, SS/TDAII is more pract ical for point to

multipoixit communication where time synchronization is easier to achieve. Herice, frorn

this point on. our Focus will be on the downlink. In particular, we assume that chip

synclironization can be achieved at the transniitter. Based on tliis cassumption. ive use

orthogonal (Walsh) codes to spread the data signal.

Ive start this chapter by describing the system mode1 for the above SS/TDhI scheme.

Then. on our way to presenting an improved receiver for this systern: we review some of

the basic concepts in signal detection. Nest, we describe the Rake receiver: whicti is the

conventional receiver for CDM-4 (spread spectrum) systems, and esplain its limitations.

-4fter ui~derstanding the shortcomings of the Rake, we conclude this chapter by presenting

a novel receiver which is particularly suitable for the downlink of the SS/TDM system

and has superior performance to the convent ional Rake receiver .

2.1 SS/TDM Downlink Mode1

To give a clearer pictiire of the above SS/TDLI scheme, let us assume that a processing

gain of hi is used to spread the data signal. For a processing gain of AT, ive can use K

IValsh codes simultaneously, where K 5 N. During a given franie. al1 K codes are used

to transmit data to one user (mobile terminal). The number of codes used depends on

the SNR a t the mobile and the desired bit error rate (BER).

First . the data bits are divided into A- streams using a serial to parallel converter (S/P).

The kt" stream is rnultiplied by the corresponding Walsh code (lis). Al1 li streams are

then added together and the resulting sequence is multiplied by a P N code. Since al1

cells use the same set of Walsh codes: the P N code is used to distinguish one base station

from another. The resulting chip sequence goes through a cttip filter with an impulse

response equal to f (t). The output of the filter, which is a baseband signal, is converted

to bandpass iising a carrier frequency. w,, to give the transrnitted signal as shown in

Figure 2.1. For siniplicity, only the in-phase coniponent is shown i r i this figure.

The transrnitted bandpass signal is given by

z( t ) = [$ f (t - nT,) cos(w,t) + d: f (t - nTc) sin(uict)] (2.1) n

where f ( t ) is the impulse responsc of the chip filter, sc is the carrier freqiiency, and

and

Here. cl(n) and cQ(n) are the PN codes çorresponding to the in-pliase (1) and quadra-

ture (Q) components. AL and A? are the amplitudes of the kt" stream in the 1 and Q

15

w K

Figurc 2.1: Transmittcr for SS/TDM systcnis

components, respectively. 1$5(n) is the periodic estension of the kt" LValsh code with

period N T i.e.

H,i(n) = Wi(n rnod !V) . (2.4)

where I l i (m) , with O 5 rn 5 N - 1, is the kLh Rglsh code. Finally, 8L(n) and @ ( n ) are

defined as R

= b N X J ) (2.5)

and n

b*Q(n) = bf( lTl) : (2 .6)

whcrc b i ( m ) and @(m) arc thc mth data syrnbol of thc 1 and Q cornponcnts corrcsponding

to thc kth strcam aiid arc assumcd to bc indcpendcrit. Hcrc [xj is an intcgcr such tliat

1.1 5 x < 1.1 + 1.

The receiveci signal, r ( t ) , consists of three components: signal. interference: and noise,

1.e.

d t ) = ~ l ( t ) + Io&) + n( t ) : (2-7)

where y ( t ) is the result of the convolution of the transrnitted signal with the channel,

Ioc(t) is the iritercelI interference? and n(t) is the background noise. WC car1 combine the

interference and noise cornponents to get

r ( t ) = + 7 7 w :

where

In al1 our analyses. we assume that q ( t ) is white and Gaussian. The channel can have

multiple paths, each with an amplitude and delay equal to al and 7 1 , respectively. Thus.

y ( t ) can be written as

where L is the nurnber of multipath components.

Several observations can be made regarding the above SS/TDR,I system:

O If the channel lias only one path, the orthogonality arnong the M'alsh codes wi

maintaincd and thcrc will bc no intraccll intcrfcrcncc.

0 -4 mult ipat h channel will destroy the orthogonality between different codes

cause interpat h and CO-channel interference.

1 be

and

a ,411 A- streanis go through t,he sarne channel before reaclling the recci\-er.

Based on above observations: for a single-patli channel, a simple correlator can be used

at the receiver to retrieve the transmitted data bit. In the case of a multipath channel,

howcwr, intraccll intcrfcrcncc dcgradcs thc pcrformancc of t h corrclator. Bcforc WC

discuss rccciwr dcsign for SS/TDM systcms, WC rcvicw somc basic concepts in signal

detection.

Figure 2.2: Matched Filter

2.2 Signal Detection

In almost al1 communication systems, the main challenge is to detect a desired transmitted

signal in the presence of some kind of noise. As a result? a fundamental question is: if we

receive r ( t ) corisisting of a signal component, s ( t ) , and a noise component. n( t ) :

what is the optimal receiver for detecting s(t)?

Before tve answer t his question, we have to specify the criterion foi optirnality. The

most reasonable criterion in most communication systerns is the probability of error (K..

2.2.1 Optimal Receiver for AWGN Channel

It is well known that for an additive white Gaussian noise (-;GY) charinel. a filter

rnatchecl to s ( t ) is optimal in the sense that it minimizes the probability of error (251 (see

Figure 2.2j.

If the additille noise is not white, a whiteiiing filter has to be inserted hefore the

matched filter. In this case, the matched filter should be matched to the signal component

of the output of the wtiitening filter.

Figure 2.3: hfatched Filter plus Linear Transversal Filter

2.2.2 Optimal Detection in Presence of Intersymbol Interfer-

ence (ISI)

If the channcl causes intcrsymbol intcrfcrcnce (ISi). a matchcd filtcr pltis a mlzsimiim

likelihood seqiience rlet,ector (MLSD) gives the optimum performance. However. hILSD

has esponential coinplexity and hence is not very practical. To keep the coniplesity liriear,

a Linear Transversal Filter (LTF) can be used in place of the hILSD as shown in Figure

2.3.

The coefficients of the filter can be optimized to minimize the probability of error.

But, this task is rather complicated because P, is a nonlinear function of filter coefficients.

Instead, Minimum Llean Square Error (b1MSE): mhich is a simpler but still reasonable

criterion, is used for adapting the coefficients. This resuits in suboptimal performance

which is still acceptable for most practical situations.

Theoretically, ?VISE can be minimized using an infiniteiy long LTF \vit11 tap spacing

equal to T , where T is the symbol duration (see Figure 2.4).

2.2.3 Fractionally Spaced Equalizer (FSE)

Altliough, an equalizer with tap spacing of T can theoretically achieve hlinimum 'Iean

Square Error (AIlISE). there are a few practical issues that have to be considered.

First of all, an infinitely long equalizer is not practical. Secondly, since a Nyquist pulse

with zero escess bandwidth decays slowly7 in practice some excess bandwidth is reqiiired.

Due to this excess bandwidth, sampling a t rate results in aliasiiig in the frequency

Figure 2.4: Infinitcly long LTF with T tap spacing

domain (see Figure 2.5). Therefore, the equalizer will try to equalize the aliased spectrum.

To show this more clearly: let x ( t ) be the output of the matched filter with .Y(w) as

1 its Fourier Transforrn. Sampling x(t) a t rate T gives us

Zn = z ( ~ z T + T ) ,

where r is the samplirig error. Based o n (2.12), the folded spectrum of x ( t ) is ['26]

Based on (2.13). spectral niills can occur due to timing errors. If they do, the equalizer

has to compensate for them by putting a large gain at those freqiiencies. This 1\41 resiilt

in noise en hancernent.

To avoid this ali,?sing effect, we should sample the output of the matchecl Cilter at a

rate higher than (or eclual to) t h e Nyquist rate. For ease of irnplementation, the sampling

rate is chosen to be an integer multiple of the symbol rate. In other words, we choose the

sampling rate, f 5 ? to be

Figure 2.5: -4liasing effects due to insufficient sampling rate

where T, = and q is an integer. An equalizer with tap spacing equal to Tq < T is

called a Fractionally Spaced Equalizer (FSE). In this case: since the sampling rate is hi&

enough, the operation of the matched filter can be included in the FSE.

The FSE has several advantages over the symbol rate eqiializer:

0 Sincc the channcl is unknown in most cascs, thc rcccivcr filtcr is usually matched

to thc transmittcd signal and not to thc rcccivcd oric. In thc casc of a symbol ratc

eqi~alizer~ the performance becomes very sensitive to sarnpling phase. The FSE, on

the other hand, is tolerant to timing errors.

a Since the FSE does both matched filtering and equalization a t the sanie tirne: a

simple front-end R F filter can be used to reduce the receiver cost.

0 In al1 practical cases where the equalizer has a finite length. the FSE can handle

spectral nulls better than the symbol rate equalizer.

For detailed analyses of the Fractionally Spaced Equalizer, refer to [27]. [28]. and [29].

N7e now return to our main topic which is receiver design for the dowilink of SS/TDM

systerris. We first. look at the Rake receiver. whicli is the corive~itiorial receii-er for spread

spectruni systenis witlr frequericy-selective fading. \Ve discuss sonie of tlie stiortcoriiirigs

of this receiver. Then, we present an improved receiver which is particularly siiitable for

the dotvnlink of SS/TDM systems.

2.3 Rake Receiver

One of tlie advaiitages of spread spectrurri is tliat it cari provide patti ciiversity (frequericj-

diversity) to corribat fadirig. If the iriforrriatiori signal is spread wide eiiougli so tliat

the trarismissiori bariclwidtii esceeds the coliererice bandwidth of the diaririel (f,,~), the

multipath components of the channel can be resolved. This will provide the receiver with

several iriclepcndently fading versions of the transmittcd signal.

22

2.3.1 Tapped Delay Line Mode1 for Radio Channels

Considcr that WC arc intcrcstcd in transmitting a chip scqucncc, d,, ovcr a radio channcl.

c(t). Lct f ( t ) bc the txansmittcr filtcr (chip filtcr) with bandwidth F. Thc bascband

transmittcd signal, s(t). will bc

LV where 7'' is the chip duration. Since s ( t ) is bandlimited to 2, we can assume that the

equivalent baseband channel is also bandlimited to y. As a result, the received signal,

r ( t ) , in the absence of noise can be expressed as [25]

A If we define cm = & c ( s ) , we get

This riiearis ttiat the received sigrial cari be represerited as an infirde surii of scalecl delayed

versions of the transmitted signal. Therefore, the channel can be modeled as an infinitely

long tapped del. line with tap spacing equal to & as shown in Figure 2.6.

Based on the above channel rnodel, Price and Green proposed the Rake receiver for

demodulat ing spread spectrum signals over frequenc-select ive fading cliannels [8]. Ttiis

receiver consists of a nurnber of "fingers?'. Each finger correlates the received signal with

a delved version of the transmitted signal. The outputs of the correlators are then

combined using maximal ratio combining (MRC).

2.3.2 Rake as a Matched Filter

Thc Rakc rcccivcr can bc vic~vcd as a matchcd filter. To makc this clcar: lct us considcr

trarismitting oric bit of information, 6 , using sprcad spcctriim. Thc bit is first mult.iplied

Figurc 2.6: Tappcd dclay linc modcl of radio channcl

by a spreading sequence, { a , } ~ ~ ~ , where N is the processing gain. The resulting secpence

goes through a chip filter, f (t). Let us combine the effect of spreading and chip filter into

one filter called sT ( t )? where

iv- 1

Based on the channel mode1 presented above (see Figure 2.6): the received signal in the

absence of noise will be

.A Rake receiver with infinite number of fingers (taps) spaced & apart is a niatciied filter.

Such a receiver is shown iri Figure 2.7.

The Rake receiver output, y ( t ) ? can be written as

where .ul = c-l . Since MRC and correlation are linear operations, we can change their

order to get

MRC

Figure 2.7: Rake Receiver

This new representation of the Rake receiver, which is shown in Figure 2.8, will be useful

in our future discussions.

2.3.3 Limitations of the Rake Receiver

While the Rake receiver is robust and simple to implement, it has a riumber of limitations:

0 The performance of the Rake is limited by the interference caused by niultipath

propagation. Because of the intracell interference. Rake lias a poor performance eveu

in the case of zero thermal noise and zero interce11 interference. The interference

esists everi if one code (streani) is used and becornes worse as the nuniber of codes

(strearris) iricreases. Tlie degradatiori in perforrria.rice is sigriificant iri systerris w1iei.e

the processirig gairi is srriall.

0 ,411 practical Rake receivers have firiite rrurrher of firigers. Herice. the pcrforrriance

of the Rake receiver is greatly affected by the positioii and spacirrg of the fingeis

25

\

: MRC

Figure 2.8: -An alternative repre~entat~ion of the Rake receiver

even if we have perfect knowledge of channel coefficients [30].

Al1 practical chip filters have some excess bandwidtti, i-e. < Tc. This rneans that

firiger spacing rriust be less than Tc, even when irifiriite riurriber of firigers is used.

Now that WC havc mentioncd somc of thc limitations of thc Rakc rcccivcr. wc try to

come iip with an improvcd rcccivcr which is part.iciilarly suitablc for the downlink of thc

SS/TDM system described in the beginning of this chapter (Sect.ion 2.1).

2.4 An Improved Receiver Based on Chip Equaliza-

t ion

-4s described previously. in the downlink of SS/TDhI. users receive data in bursts. Time

is divided into slots (frarnes). During each frame, only one user receiïes data in each

cell/sector. The data bits are divided into IC parallel streams. Each stream of bits

is spread over a wide bandwidth using ortliogonal 11,-alsh codes. The streanis are then

added together and are multiplied by a P N sequence. The resulting sequence is passed

through a chip filter and transmitted to the desired user (refer to Figure 2.1).

l \ e obserl-ed that thc multipatti channel destroys the orthogonality betweeii the codes

and causes interpath and interchannel interference. -4nother important observation n-as

that al1 A* streams go through the same multipath charinel before reaching the receiver.

So. if. a t the receivcr. ive use an equalizer to equalize the multipatli channel. the ortliogo-

nality between the codes will be restored and data bits can be cleniodulated wit hout an?

interference (rieglectirig the iritercell interference). Since a11 the codes go througti the sarne

cliariiiel. the sarrie equalizer cari be used for al1 A- codes. .After passirig tlie received ctiip

sequerlce through the cqualizer. the output is niultiplied first by tlie P N code ancl theri

by the LValsh codes and is summed over AT chips. The result is then sent to a decision

delice to obtain the data bits.

.Although radio channeIs are time-varying in general. in the case of SS/TDhI. ive can

assume the channel is invariant during one frame (Le. block fading) provideci that the

frame duration (TI,) is smaller than the coherence time of the channel ( r C o h ) . In the rest

of this chapter. ive assume that T!, < T ~ ~ , , and hence during a frame the channel can be

considered tirne-invariant. Cire sliow in Chapter 3 that this assurnption is reasonable. If we

assume that the radio channel is time-invariant during a frame, we can use the pilot burst

to train the equalizer. ,Ifter the training period is passed, actual data can be transmitted.

Since the channel stays the sarne during the frame, the equalizer will equatize the channel

and, hence, will remove the intracell interference. Since the equalization is done at t h e

chip tevel, this receiver cati be used in systerris with long spreadirig codes.

2.4.1 The MMSE Chip Equalizer

To gairi niore irisight irito the operation of the equalizer described above, consider the

following:

For now ignore the fact that the chip sequence a t the transmitt.er is the result of

adding K ctiip streams, eacli corresponcling to a bit. sequence multiplied by a spreading

sequence, and let us insteacl concentrate on chip transmission. The chip seqiiencc first

goes through a chip filter f (t) and then through the multipath channel. For sirnplicity. let

us assume zcro cxccss handuidth for the chip filter (i.c. Tc = h). Noise will bc added to

the seqiience before reaching the receiver. The chip equalizer estirnates the trarisniittecl

chips a t the receivei-. Let h ( t ) be the impulse response of the chanriel plus the chip filter.

In the discrete model, if ive transmit the chip sequence di, the receiwd sequence ni11 be

where hn = h(nTC) and is Gaussian noise. If we use an infinitel-long equalizer, the

transfer function of the equalizer based on the hlinimum Mean Square Error (hlhISE)

noise

) chip filter channel Equalizer -

Figure 2.9: Thc MhISE chip cqualizcr

criterion will be [31]

where H ( c ) is the z-transforrn of h,

numerator of (2.23) can be considered

and S,(z) is t.he power spectrum of the noise. The

as a filter matched to h, (or h( t ) ) . The denominator

can be viewed as a filter that tries to equalize the output of the matched filter taking into

account ISI and background noise. So, the MMSE chip equalizer as a whole docs both

matched filtering and eclualizing at the same time as shown in Figure 2.9. It is interesting

to notc that a matchcd filtcr t o the channcl actually pcrforms inasimal ratio combining

(hlRC). To sec tliis more clearly let ils assume that signal s ( t ) is transmittcd. For

simplicity. assume that the channel tias only two patlis. The received signal, rit). in the

absence of noise is

wliere B is a comples number representing the path amplitude and phase, and T is the

path delay. The Rake receiver is a matched filter. Hence, its output is

After a few simple steps, g(t) beconies

where Es is the energy of s ( t ) and w ( t ) is the interference given by

The first term in (2 .26) is the MRC term and the second term is interference due to nonzero

correlation bet.ween the paths. The equalizer not only performs matched filtering (and

hence blRC). but also suppresses the interference. This results in significant performance

improvement as shown in the nest chapter.

To summarize: the chip equalizer coefficients, ui. are optimized to perforrn three tasks:

1. Rlatched filter to the trarismitter chip filter, f ( t ) .

2. b:lâtched filter to the charinel: which is equivalent to h81RC.

3. Channel equalization to restore the orthogonality among the spreading codes (il~alsh

codes), or equivalent ly to cancel the interference.

The output of the equalizer is then passed through a correlator (despreader) to obtain

the desired bit as shown in Figure 2.10.

The receiver structure in Figure 2.10 is very similar to thc alternative representation

of the Rake sliown in Figure 2.8. The orily difference is that the [ilter coefficients arc tiow

optimized to do equalizatiori in addition to matched filtering.

2.4.2 Fract ionally Spaced Chip Equalizer (FSCE)

In Sectiori 2.2.3, we described tlie advaiitages of tlie fractiorially spaced equalizer over tlic

coiiwritiorial synibol-rate eqiializer. Based on the reasons giveri there, it is more baieficial

to use a fractionally spaced chip equalizer (FSCE) in our receiver. Given the transmitter

Figure 2.10: The chip equalizer as a tapped delay line

moclel for the downlink of the SS/TDbI system. Figure 2.11 shows the structure of the

FSCE receiwr. For sirnplicity. only tlie in-phase component is sliown. Here. T, = - < I '

where q is an integer which represents the number of samples taken per chip. The FSCE

receiver has the following properties:

It performs not on1y diversity combining but also interference suppression and hence

its pcrformancc is supcrior to the Rakc rcccivcr.

Since the chip filter in practice has some escess bandwidth, implemeiitation of the

chip matched filter c m still be included in the operation of the FSCE. Tlierefore. a

simple and inespensive front-end RF filter can be used a t the receiver.

r Due to fractional sampling, the FSCE is tolerant to timing errors and can handle

spectral nulls better.

Sirice tliis receiwr perforiiis equalizatioii a t tlie cliip level, it cari be used in SJ-st,eiiis

31

I cos W l

Figure 2.11: The FSCE receiver

with long syreading codes.

Since the same equalizer can bc used for al1 h' streams, the FSCE receiver has

moderate coinplesity.

To demonstrate the operation of the chip equalizer more clearly, let us consider a

two-pat h channel

We choose 00 and ro as reference and set tliem to zero. We also set BI = 0 and ri = T .

The received signal is

- wliere d , is tlle trarisniitted diip sequeiice upsarnpled by q arid

h( t ) = no f ( t ) + oid0 f ( t - T ) y (2.31)

with f ( t ) ùeiiig the cliip filter impulse resporise. Sampling the received sigiial at rate '- r,

gives us

Based on (2.31), t he folded spectrum of h ( t ) is

where F ( w ) is the Fourier Transform of f (t). The chip equalizer will t ry t o equalize

HTq ( w ) If tve assume that sampling rate is liigh enough, we can focus our attention on

the interval [-- "1. In this interva1 we have TV

According to (2.23). the periodic transfer filnction of the hIMSE eqiializer will he

f o r - L < w c z . =, TP sin(?)

For esample, for f (t) = +, - i.e. a sinc pulse with zero escess bandwidth? we have 'rc

and

- Tc f o r l w l < $ F ( w ) =

O othernrise

Thus, (2.34) and (2.35) become

T c - HTq (w) = [ao + a l ej("-ur)] - for Iwl < 5 . Tq

For other cliannel profiles, a simiiar approach can be taken. \fi now use (2.37) t o

plot I ~ ~ ( w ) l * for different values of r and B. For simplicit- we assume Tc = 1 and

CLO = QI = fi . Figures 2.12 and 2.13 show I H ~ ~ ( w ) ~ ~ for different values of 0 witli

i = Tc aiid T = f Tc . respect ively.

Figure 2.12: Plot of 1 HT, (LI)/' for r = Tc

Figure 2.13: Plot of 1 HT, (w ) l2 for r = f Tc

ive observe that when T c 'Ti, the received signal energy is dependent on O and varies

significantly as O changes (flat fading). From (2.37). it can be observed that when r 2 Tc:

IHT,(w)l2 takes al1 the values betneen (aa - and (ao + a l ) 2 inclusive. This means

that the received signal energy is fixed and does not depend on the value for 8 (frequency-

selective fading). In this case? it can be seen that regardless of the value of 0: the channel

has a spectral nul1 if a. i a, (see Figure 3.12). To compensate for t hist the linear equalizer

has to put a large gain a t the frequency where the nul1 occurs. This in general results in

noise enhancement. A Decision-Feedback Equalizer (DFE) would fix this problern [25].

However, since ive are performing equalization on chips not bits, a DFE cannot be used in

this case because the ctiip values are uriknowri to the receiver. While bits cari take either

+l or -1 (in case of BPSK), the overall chip sequence has values between -K and +I<

and lience is more difFicult to estimate. In the case of IC = 1: chip values are either +I or

-1. Therefore, simple chip detection can be done and the resulting decisions can be fed

back. Homever, because chip detection does not bencfit from the processing gain. chip

decisions would not be accurate and hence the performance of the DFE would be poor.

2.5 Chapter Summary

In this chapter, we described the SS/TDRI transmission scheme as a prornising candidate

for the downlink of packet-based systems. We studied the conventional Rake receiver and

mcntioricd its limitations. 14.c thcn prcscntcd a novcl rcccivcr bascd on chip cqualization

n-liich is particularly siiitablc for the downlink of the SS/TDhI systcm. WC also dcscribcd

some of the advantages of this receiver as compared to the conventional Rake receiver. In

the following chapter, we will perform a n estensiw stiidy of the performance of the de-

scribed FSCE receiver using a series of detailed simulations and compare the performance

with that of the Rake receiver.

Chapter 3

Simulation Results for the FSCE

Receiver

In the previous chapter, tve presented a receiver for the downlink of SS/TDh,I systeins

based on chip equalization. We claimed that this receiver tvould outperforrn t,he con-

ventional Rake receiver whosc performance is interference-limited. Since the downIink

transmission is synchronoiis, if we use orthogonal spreading codes, intracell interference

can be avoided provided t hat t, he orthogonality among the spreading codes is maint ained.

But, a multipath channel will destroy this orthogonality and, hence, will cause interpath

and interchannel interference. ,A Rake receiver will perform poorly in sucli a system. How-

ever? channel equalizat.ion can restore the orthogonality and eliminate the interference.

This \vil1 considerably improve the performance of the receiver.

.Ilthough channel equalization for the dotvnlink of CDM-4 systems bas been proposed

in [1G]-[19]. the performance of such a receiver has not been discussed in detail. In

this chapter, we present an adaptive implementation of the Fractionally Spacecl Chip

Equalizer (FSCE) receiver described in Chapter 2 for the dotvnlink of SS/TDhI systems.

In addition, we study, in a comprehensive nianner, the effect of various system parameters

such as processing gain, channel profile and constellation size on the perforinance of the

FSCE receiver using a series of detailed sirnulations. Our simulation results provide insiglit

into the design of the downlink receiver for future high bit-rate SS/TDhI systerns.

3.1 Simulation Mode1 and Assumptions

In this section, ive give a detaited descriptiori of the mode1 used in our simulations and

state the assumptions made. -As we mentioned in the pre\-ious chapter. in a SS/TDM

system, time is divided into slots (frames) of length q, During each time slot' the base

station transmit data t o only one user using spread spectrum transmission. The data bits

of the user are divided into K streams. These streams are spread using orthogonal Walsh

codes and are then summed together. The overall sequence is multiplied by a P N code

unique to the base station. The resulting sequence goes through a chip filter and is tlien

transmitted.

The received signal is the surri of scaled, delayeci versioris of t lie t rarisrrii tt,ed sequerice

plus noise. The receiver corisists of a front-erid filter followed by a Fractiorially Spaced

Chip Equalizer (FSCE). The output of the equalizer is then multiplied by the P N and

Walsh codes and is summed over one symbol period. The result is sent to a decision

device (threshold detector) to get t,he data bits. Throughout this chapter, we assume

one transmit and one receive antenna. Mé do not consider sectorization. In our simula-

tions, ive mode1 the background noise and intercell interference as white Gaussian random

variables.

M.'c considcr a SS/TD-LI system with bandwidtli of B = 1 .25AfHz as uscd in 1s-95.

We assume that each time slot is 1.432ms long, i.e. Tj , = 1.432ms. From tliis 1.432mn.

ive a1locat.e 9%, which is eqiial to 130p,.s, to the pilot. The radio channel is assiimed to he

time-invariant duriiig each frame. This is a reasonable assumption because for a mobile

nioving a t a speed of 1001iPm/h, the coherence time of the channel, rCoh, is about 5.3ms

at 2GHz . This means tliat Tj, is about 4 times smaller than T ~ ~ , ~ . Hence, it is safe to

assume that the channel does not change during one frame.

The downlink radio channel is modeled as sum of L muitipath components. This can

be represented in baseband as

The amplitude of each component., al, is assumed to be a Rayleigh random variable.

The phase, &, is iiniformly distributed between O and 27;. The delay of each path. 71.

is assurned to be fised. ,As we mentioned above, throughout our simulations, we always

assume block fading. It ineans that a L 7 s and 81's stay constant during one frame. From

one frame to another, ive assume independent fading. The channel multipath components

are also assumed to fade independently.

-4s we change the processing gain, the frame Iength is kept the same (i.e. TI, =

1.432n~s). So, if the processing gain increases. siiice the chip rate is fixed, the nurnber

of syrnbols in each fraine decreases and vice teersa. To give an esample. if ive choose a

processing gain of 16. 1.e. = 16, the number of symbols in one fraine will be 110. Out

of the 110 syrribols, 10 syrribols d l be for the pilot. arid 100 syrnbols for the actual data.

If ive diange the processing gain to 4, each franie will have 440 synibols, 40 for tlie pilot

and 400 for data. This way the duration of the pilot burst and the data cornponent of

each frame stays the same independent of the processiiig gain. It should also be noted

ttiat Ive assignecl 9% of each frame to training SJ-mbols. This percentage can be reducecl

by increasing the nurnber of data symbols i r i the frarne as long as the frame duration stays

sufficiently small (i.e. TI, < T ~ , ~ ) .

In our simulations. ive consider both in-phasc (1) and quadrature (Q) channcls. Thc

same set of Walsh codcs is uscd for both channcls. Honrcvcr, the P N codes for the channcls

are different. We assume that the P N codes have long periods and hence mode1 them as

two random sequences. The overall chip secluence. dLQ7 is a complex sequence. Its real

part. d!,' is the in-phase sequence and t h e imaginary part, dnl is the quadratiire sequence.

For the transmitter chip filter, f (t), we use a square-root raised-cosine pulse [31] with

a roll-off factor of a = 0.01725 sirnilar to IS-95. Since our receiver uses a fractionally

spaced chip equalizer, the receiver chip filter: g ( t ) , does not have to be matched to the

transmitt.er filter, However, in our simulations: Ive assume that g ( t ) is also a square-root

raised-cosine filter. We combine the transmitter and receiver chip filters with the impulse

response of the channel to get

L- I

1=0

where p ( t ) = f ( t ) * g ( t ) is a raised-cosine with a roll-off factor of a. = 0.01725, i.e.

Since h ( t ) is unlimited in time domain, we truncate it to get

where ~,,,, and Tupper are the lower and upper limits of truncation. respectively. Through-

out our simulations. the time spans of the chip fiIters are chosen to be 6Tc. Xlso. we choose

the first path of the channel as the reference and set its d e l q and phase to zero, i.e. TO = O

and O0 = 0.

The discrete ciiannel (plus chip filters), h = [h,]? is obtained b j ~ sampling h( t ) : i.e.

nhere T, = 5 and q, which represents the ~iurnber of samples taken per chip, is a positive

integer. Since we are using a fractionally spacecl equalizer a t the receiver, the transmitted

cliip sequence, cl?. is upsampled by q to get diQ. This sequence is tlien convolved witli

. Soise, rlnQ. is added to get r, , . It should be noted that srQ consists of two inde-

pendent noise components and @ each with variance 02. The FSCE is represented

b~ an FIR filter, u: of Iength AI plus a downsampler. Since t,he transmitted chip values

Figure 3.1: Discrete baseband mode1 for SS/TDhI downlink transmitter

are coniples, the equalizer coefficients are also cornplex-valued. The discrete baseband

cquivalcnt rnodcls of the transmittcr and rcccivcr for thc SS/TDRI systcrn arc shown in

Figures 3.1 and 3.2.

As mentioned previoiisly, the background noise and intercell interference are modeled

as white Gaussian noise. This noise goes through the receiver front-end filter and the

result has a n autocorrelation fiinction, R ( r ) , equai to g ( r ) * g* ( - T ) . Since the sampling

rate a t the receimr is higher than the chip rate, vLQ is not white in general.

Diiring the training period, the output of the chip eqiializer is compared with the

corrcsponciing cliip in the training secluence. Based on the error. the coefficients of the

equalizer are adjusted using an adaptive algorithm. When the training period is finished,

actual data is sent and the equalizer coefficients stay the same during the rest of the frame.

The estimated chip values? dfP, at the output of the equalizer, are used to retriem the

transmitted data bits. For example, the real part of dnq is multiplieci by the PN sequence

of the in-phase channel. The resulting sequence is then miiltiplied by the Walsh codes

Figure 3.2: Discrete baseband mode1 for SS/TDM domnlink with FSCE receiwr

and summed over IV samples.

The signal to noise ratio (SNR) is defined as the ratio of t.he average signal poiver to

the average noise (background noise plus intercell interference) power. The noise power

is normalized by the processing gain t o make fair cornparisons between the cases with

different processing gains. As a measure of SNR: we can use %, where Ea is the average

bit energy and 9 is the twesided noise spectral density.

Since the equalizer used in the receiver is a chip equalizer, tlie training has to also be

done at the chip level. In the SS/TDM system, al1 Ir' Walsh codes are used by the base

station to send data to a single user in each time slot. Therefore, al1 W'alsh codes should

be available at al1 mobile receivers. Mobile users also have knowledge of the PIN code used

by the base statiori. Corisequently, seriding knowri bits is equivalerit to seridirig kriowri

chips. If tlie receiver knows the training bits it cari easily generate the corresponding chip

sequence.

Anothcr important point regarding the training sequence is that since the equalizer

acts on chips, the power of the chip sequence during the training period should be equal

t o the p o w r of t.he chip sequence during data transmission. This means that if we are to

use I< streams of bits during data transmission: we should also use Ir' t rainirig st reams or

onc training strcam with I< timcs thc powcr. If thc training chips liavc a diffcrcnt powcr

than the data chips, thc pcrformancc of thc cqualizcr dcgradcs whcia i t is switchcd from

training mode tm data niode. In our simiilations, 1c-e use I< streams of t.rairiing bits.

-4nottier key parameter in training is the achieved level of Mean Square Errnr (MSE).

This deterniines how meIl we can estimate tlie chip values during da ta transmission. -4

good estimate of the chip sequence will ultimately result in good receiver performance.

While n.e are interested in a low SE value, Ive would like to converge to this ~ a l u e as

fast as possible to minimize the amount of overhead in each frame. In other words, we

would like our adaptive algorithm to have fast convergence and achieve low mean square

error. At the same time, we want to keep the coniplesity of t h e algorithm reasonable.

X good candidate for such an algorithm is the Recursive Least Squares (RLS). The RLS

algorithm converges t o a lom MSE value in approxirnately 3.U iterations' where 113 is the

length of the eqiializer [32]. The complexity of the algorit.hm is of the order of 11f2. For

al1 our simulations, ive use RLS algorithm to adapt the equalizer coefficients during the

training period. This algorithm is briefly described in Appendis -4.

To compare the performance of our receiver with that of the conventional Rake re-

ceiver. we will perform a number of simulations for the Rake receiver. In our Rake

simulations. we assume that the sampling rate is one sample per chip. LL'e assurne that

Rake has L fingers where L is the nurnber of multipath components of the channel as

showri by (3.1). The amplitudes? piiases and delays of the rriultipath cliaririel are assurried

to be kriowri to tlie Rake receiver.

For the cernainder of this chapter, we refer t o our proposed FSCE receiver (shown in

Figure 3.2) as chip equalizer although it consists of an equalizer and I< despreaders.

3.2 Simulation Result s and Discussions

We nonr present a series of simulation results in order to study the effect of various

system parameters such as processing gain, channcl profile and constellation size on the

performance of the FSCE receiver. In our simulations. we set the delay between the

transrnittcr ancl the receiver in sucli a way that the ceriter of the eqiializer coincides with

the ccntcr of thc channcl profile (i.c. ccntcr of thc rnultipath). \\'c transmit a t Icast

1000 framcs and continue thc transmission imtil 100 framc crrors occiir. A framc crror

happens when a fi-ame has one or more bit errors. We calculat,e the total ntiniber of bit

errors and di\.itlc i t by the total nimber of transrnitted bits to ohtain the bit, error rate.

Since t hcre is a synimetry between the in-phase and quadrature channels, nre only focus

on the in-phase bit error rate. In calculation of the bit error probability. we only look a t

the receij-ed bits of tlie first Stream.

Figure 3.3: QPSK constellation

3.2.1 QPSK

Hcrc, WC study the rcccivcr performance for QPSK modulation. The constcllation is

shown in Figurc 3.3. In this modulation schcrnc, cach symbol can takc onc of four valucs:

{ + l + j , -1 + jt +l - j . -1 - j ) .

To avoid long description of the channel, wc use the following notation: { ( T , . Pl):

(F-, Pz) , . . . ). Each pair represents one path of the muitipath channel. The first compo-

nent of each pair is the path delay and the second component is the path average power

(in dB) relatil-e to the first path.

FSCE vs Rake

ive first give a comparison between the corwentional Rake receiver and the Fractionally

Spaced Chip Ecpalizer (FSCE). Figures 3.4 and 3.5 show the average bit error rate (BER)

vs $ of tliese two receil-ers for different values of Ii with LV = 4 and N = 16. respeçtively.

The channel is assurnecl to have two paths with equal average powers. The clelay between

the two paths is r = ?Tc. Based on our notation, we can represent this channel as

{ ( O , OdB), (STc, OdB) }. The chip equalizer has 15 taps and uses two samples per chip

(JI = 15. q = 2). -4s a reference, the optimum single-user BER curve for the case of

Rayleigh fading with second order diversity is also shown [25].

-4s espected, the chip equalizer performs significant ly bet ter than Rake especially as

I< increases. It is also seen t h a t the BER curves for the Rake receiver ievel off much

IOO L i i 1 1 I l 1 I I i i 1 b r 4 K=1, FSCE ] -O- K=1, RAKE 1 + X.2. FSCE 11 -x- K=2, RAKE

1 - . optimum 11

Figure 3.4: Coniparisori hctn-een t h e FSCE and Rake receivers (!Y = 4, two-path channel

with 5 = 2Tc: QPSIi;)

U K=1; RAKE * K=4, FSCE -x- K 4 , RAKE + K=8, FSCE a- K=8, RAKE + K=16, FSCE T- K46, RAKE . - . optimum

Figure 3.5: Comparisori betwe~ri the FSCE and Rake receivers ( N = 16: two-path channel

with r = 2Tc1 QPSK)

faster than tliose corresponding to the FSCE. This is because the performance of the

Rake is limited by interpath and interchannel interference. -4s K increases? the amount

of interference increases and the performance of the Rake receiver degrades considerably.

It should be noted that since the FSCE receiver performs equalization at the chip

level, the SNR seen by the equalizer is related to g: where Ec is the chip energ-. In

our SS/TDM system, Ec = 5~~ . The behaviour observed in Figure 3.5 for the case of

Ar = 16 and h' = 1 with the FSCE receiver is because the SNR seen b - the equalizer in

this case is very low and, hence, good convergence cannot be achieved during the training

period.

Effect of Processing Gain

ici Figure 3.6. we corripare the perforrriance of the diip equalizer for two differeilt processirig

gairis (N = 4 arid N = 16). I t sliould be rioted that sirice ive keep the duratiori of the

franies fised independerit of the processing gairi. as we iricrease IV? we tiüve to increase

I< with the same proportion in order to keep the bit rat.e the same. But increasing I<

means increasing the overall transrnitted pomer. So, to keep the comparisori fair! ive

normalize the signal (or noise) power. -1s i t can be seen from Figure 3.6. changing the

proceçsirig gain does not have any significant effect on the performance of the FSCE. This

makes scnsc bccausc the cqualizcr acts on chips not bits. So: FSCE secs no differcncc

bctwccn thc two cas- bccaiisc thc incoming chips look thc samc (proviclcd that tlic poncr

is normrxlized properly). Of murse, the processirig gain cannot. be niatle arbitrarily srrièt l l .

In the cstreme case of ,\i = 1: the whitening efkct of the spread spectruni will totally

disappear.

EfTect of Channel Profile

\Ve now look at the performance of the chip equalizer and the Rake receiver for three

different channel profiles:

1 O-' I 1 I I 1 l I l I I 1 I I

-2 O 2 4 6 8 10 12 14 16 18 20 22 24 26 EdN, (dB)

Figure 3.6: Effect of processing gain, N. on the performance of FSCE (thmpath channel

with T = ZT,, q = 2: hl = 15, QPSK)

1- Channel 1: Two paths with equal average poivers and delays of O and -Tc: i.e.

((0 . OdB), (2Tc , O ù B ) ).

2. Channel 2: Four paths with equal average powers and delays of O. T,: WC, and 3Tc:

i .e. {(O , OdB) , (Tc OdB) , (2Tc . OdB). (3Tc OdB) ).

3. Channel 3: Four paths with decaying average powers and the sarne delays as Channel

2 , i.e. ( ( O - OclB), (Tc . -3dB). (-Tc . -GdB), (3Tc : -9dB)).

Figure 3.7 and Figure 3.5 show the simulation results for the case of lh7 = 4 and F< = 1.

The FSCE has the same tap spacing and length as the previous section, Le. q = 2 and

J I = 15. For the Rake receiver, the two-path channel has the best performance and the

four-path channel with equal average powers has the worst performance. This is because

the channel with four pat hs of equal strengt li causes the largest iriterpat h interference.

The interference caused by the channel with decq ing average powers is srnaller. The two-

path channel introduces the least amotint of interpath interferencc. It should be noted

that although the four-path chaniiels provide 4'" order diversity. the improvement over

the Y d order diversity pro\-ided by tlic tmo-path channel is overshadowed by the extra

interpath interference. For the chip eqtializer, on the other hanci? the four-patli cliannels

perforni bet ter tlian the two-path channel. This is because of the estra diversity provided

by tliese two clianriels. Since tire equalizer is able to suppress the int,erpath interference,

tlie est ra diversit .~ contributes to thc perforrnarice iniprovemerit seen in Figure 3.5.

Effect of Intersymbol Interference (ISI)

Ses t , ive studj- the effect of iiitersyrribol i~iterfere~ice (ISI). caused by a large ctiarinel

d e l v spread, ori tlie perforrriarice of ttic chip equalizer. To do tliis, we corisider a two-

path ctiaririel with a d e l q of GT,. i.e. ( ( O , OdB), (GT,, OdB)}. Figure 3.9 looks a t two

cases: one is the case of iv = 4 which rneans ISI esists. The other case is the case

of :Y = 16 wliicli corresponds to rio ISI. -As i t can be seen frorn the figure. ISI has no

4 Channel 1 (two paths) * Channel 2 (four equal paths)

Figure 3.7: Performance of the Rake reçeiver under tliree different channel profiles (:Y = 4:

K = l ? QPSK)

Figure 3.5: Performance of the FSCE receiver iinclcr three different chanriel profiles ( N =

1 l o O

IO-'

1 o - ~

[21 W m

1 o - ~

IO-^

[ -

1 IO-^. I I I l I I I I I 1 I I I i

-2 O 2 4 6 8 10 12 14 16 18 20 22 24 26 E p J , (dB)

r 1 1 4 1 I I 1 1 L 1 I 1 I + Channel 1 (two paths) * Channel 2 (four equal paths) -6- Channel 3 (four exp paths)

: -

.- -

7 -

= -

r

Figure 3.9: Effect of ISI on the perforiiiance of the FSCE recciver (two-path channei,

significant effect on the FSCE performance provided that the equalizer is long enough to

cover the channel length. The reason for this is that the equalizer processes chips not

bits. The FSCE tries to equalize the chips without any knowledge of the iinderlying bit

patterns. Because of the long PN sequence used to randornize the chips, the case of ISI

(:V = 4) does tiot look any different t o the equalizer than the case of no ISI (3- = 16).

However, as it is shown in Figure 3.9: for the same equalizer length, larger delay spread

results in poorer performance. This, of course, cornes as no surprise because the equalizer

needs rnore taps to equalize a channel with a larger delay spread.

I t is known that 16-Q-fiRI has a higher spectral efficiency ttian QPSK. This is because

each symbol in 16-Q-AM reprêsents 4 bits wliereas in QPSK eacli syrnbol represents 2

bits. Herice, the rriaxirriurri achievable spectral efficiericies for 16-QU1 arid QPSK are 4

and 2 bits per second per Hertz, respectively. Since the radio bandwidth is ver' limited,

to achieve high bit rates, we have to increase the spectral efficiency of our system. One

approach is to try to use a high-order modulation scheme such as 16-Q-4M instead of

QPSIi. This motivates us to study the performance of the FSCE with 16-QAh,I as the

n~odulation scheme. In this section: we present simulation results for 16-QAh,i. In the

following section, WC cornparc thc performance of thc chip cqualizcr for the tmo modulation

sclicri1cs.

Iri 16-Q,\h.I, cadi symbol caii takc one of 16 \*ducs as shown in Figrirc? 3.10. For

oiir simtilations. t,he chip eqiializer is assiimed t o have 15 taps with n spncing of 2 - (Le.

51=1.5. q=2). Figure 3.11 shows the BER rs % for different values of li with N = 4.

The channel in this case has two paths with equal average powers and a delay of LTc-

Thc figure shows siniilar trends as for the QPSII; casc. Howcvcr, in this case? t.hc Rakc

receiver performance is estremely poor dile t o escessive amoiint of interference causeci by

Figure 3.10: 16-Q.AX,I constellation

16-Q-4h.I modulation sclieme.

-4s it is shown in Figurc 3.12. proccssing gain docs not have any signifiant effect on

the pcrformancc of thc cqualizcr. This, as csplaincd prcviously. is duc to thc fact t.hat

the FSCE eqtializes chips not bits. In Figure 3-13: ive compare the cases of 1SI and no

1S1 for 16-Q.414 as ive did for QPSK. Again. here we see that while a largrr delay spreacl

degracies the performance of the eqiializer, the performance is independent of whether ISI

esists or not.

i ve now would like to compare the receiver performance for the cases of QPSK and

16-QXh.1. This will help us decide when to switch the moduiation scheme from QPSIi to

16-QUI and vice versa.

3.2.3 Comparison Between QPSK and 16-QAM

As ive mentioned carlier, 1GQ-UI has a spectral efficiency that is two timcs higlier than

QPSIi. Since spectrum is scarce i r i wireless commuriication, we would like to know when

it is sensible to switch froin QPSK to 16-Q-AlSI. To answer this question, consider the

following scenario:

In our SS/TDhI system, we are transmitting data t o a mobile terminal iising QPSK.

Let us assume tha t we have a processing gain of 4 and we are using 2 IVCilsh codes. i-e.

I I I l i 1 l I 1 I I I I

+ K=l , FSCE : U K=l , RAKE . +- K=2, FSCE -x- K=2. RAKE .

-B- K=4. FSCE . 4- K 4 , RAKE

Figure 3.11 : Coin parison between the FSCE and Rake receivess ( N = 4. two-patli channel

witli 7 = 2T& IG-Q-AhI)

Figure 3.12: Effect of processirig gain, iV, on the performance of the FSCE receiver (two-

path channet with r = 2Tc, q = 2, A l = 15, 16-QXM)

Figure 3.13: Effect of ISI on the performance of the FSCE receiver (two-path channel,

q = 2. A/ = 15, 16-Q-Ah[)

iV = 4' = 2. Now consider that the channel condition improves. With the improved

channel condition. we can transmit more bits without sacrificing the probability of error.

There are two ways t o increase the bit rate. One is to keep the modulation scheme as it

is (Le. QPSK) and increase the number of Walsh codes. -4nother approach is to keep Ii-

the same and instead switch from QPSK to 16-QAM. The question is which method is

more efficient?

Figure 3.14 tries to answer this quest,ion. In this figure we have shown the BER curves

for QPSK and 16-Q,4R3. The dashed iine is the reference curve which corresponds to

QPSK witb N = 4 and = 2. It is seen frorn the figure that for t,he same overail bit

rate, usiiig QPSK is riiore efficient ttiari usirig 16-Q-4bI. For esarriple. to double the bit

rate arid keep the BER a t 4 x 1 0 - ~ , if we use QPSK aiid change Iil frorri 2 to -1: ive iieed

to increase the transmitted power by IdB. On the other hand. if we keep A- a t 2 and

switch to 16-QXhI? ive need to increase the power by about 9dB. This means that QPSK

is about 8dB more efficient than 16-Q.AhI. This can be explained as follows:

In the case of QPSK: when ive double K , we double the average transmitted power.

Howcvcr. whcn WC switch from QPSK to 16-QA-UvI: WC incrcasc thc ai-cragc powcr bi- a

factor of 5 . In othcr words. to kccp thc avcrapc transmittcd powcr tlic same. wc have

to diviclr thc arnplititdc of thc trnnsrnittcd 1 6 - Q U I signal by fi. This gives QPSK a

$ ( = 4 d ~ ) adrantage over 16-QAhI in terms of signal to iriterference power ratio [33]. In

addition. effect of fading is much niore severe on 16-QAhl tlian on QPSK [34].

Bascd on thc abovc discussion. switching from QPSK to 16-QUI makcs scnsc only

mhcn WC have rcaclicd thc maxiinum spcctral cfficicncy achicvablc bj. QPSK (i.c. h- = iV).

This means that 16-Q-4hl slioiild be used only after we have reached the 2 bps/Hz ~p~ic t ï i l l

cfficiency possible with QPSK. At this point if we still want to increase the bit rate. \ire

cannot do it with QPSK and ive have to switch to a liighcr order modulation.

1 J I 1 1 1 I 1 L , I i 1 l

4 N=4, K=4. QPSK + N=4, K=2, 16-QAM 1

1 - - N=4. K=2, QPSK (Ref.) I f

Figure 3.14: Cornparison t~etween QPSK and 16-Q-AM (two-path channel with T = lTc,

3.2.4 Correlated Fading

In ordcr to motivatc the antcnna diversity schcmc introduccd in the ncst chaptcr. WC show

the pcrformancc of thc FSCE for a channel with vcry short dclay spread (i.c. smallcr than

onc chip) and cornparc it with that of a channcl with a longer del- sprcad. To do this. WC

consider two channels: one is a two-path channel with eqiial path strengths and dehy of

O.lTc. The other is a two-path channel with eqiial path strengths and delay of 1.1 Tc. The

FSCE has 1.5 taps and a t ap spacing of i.e. AI = 15. q = 2. Figure 3.15 shows the BER

curves for these two channels. From the figure, it is observed that the BER is higher in

the case of short delay spread. This is because a delay of O.lTc results in a high correlation

between the two paths at the receiver. This will reduce the diversity gain significantly.

_At high SNR levels. the effect of diversity becomes more pronounced and the gap between

the two BER curves widens. It should be noted that although the difference betweeii the

average probabilities of error shown in the figure may not be considered significant, the

fluctuation around the average BER value is rnuch larger in the case of the channel with

0. lTc delay spread.

3.2.5 Decision-Feed back Equalizer

We mentioned in the previous chapter that a multipath channel can have spectral nulls. I t

is known that a linear equalizer results in noise enhancement when the channel spectrum

has nulls. To rectify this problem a Decision-Feedback Equalizer (DFE) can be iised [25].

However: since we are implementing a chip equalizer, using a DFE is not feasible because

the chip values are not known to the receiver. However, just to demonstrate the effect of

iising a DFE instead of a linear equalizer we perform the followirig simulation:

We assume a two-patii channel with equal path strengths and delay of WC. We ilse one

data streani. i.e. II' = 1. This way the in-phase and quadrature chip values can be either

+l or -1. We compare the performance of the receiver for tliree cases: a linear FSCE

Figure 3-15: Effect of correlateci fading (two-path ctiannel? N = 1. li = 1 , q = 2: dl = 15)

with q = 2 and 11.1 = 15, a DFE with perfect knowledge of chip values (ideal DFE)? and

a decision-directed DFE. Both DFE equalizers have a feedforward lengt,h of 11 taps and

a feedback length of 4 taps. In ideal DFE? we assume that we have perfect knowledge of

chip values a t the receiver. For the decision-directed DFE, Ive use two threshold detectors

to detect the in-phase and quadrature compone~its of th2 chips before feeding them back

into the equalizer. The simulation results are shown in Figure 3.16. -4s espected the

ideal DFE outperforms the other two. The performance of the decision-directed DFE

is worse than the linear equalizer for low SNR values. This is because chip detection

does ilot benefit frorn the processing gaiii. Hence, the resulting chip decisions are not

accurate whe~i the SNR is not high. At high SNR levels. the decision-directed DFE starts

to outperform the linear FSCE equalizer.

3.3 Chapter Summary

I n this diapter, ive presented a compreherisive study of the performance of the FSCE

receiver for the downlink of SS/TDM systerns. i v e used chiplevel simulations to show

the effect of different parameters on the performance of the equalizer. It \vas çhown that

processing gain and ISI do not have significant effects on the FSCE performance. We

also investigated the performance of the chip equalizer under different channel profiles.

In addition, we cornpared the performance of the FSCE receiver for QPSK and 16-Q.Ah4

modulation scherncs. WC concludcd that QPSK shouki be iiscd instcad of 16-4.-1'11 until

wc rcach the maximum spcctral cficicncy uchicvablc by QPSK (i.e. 2 bps/Hz). \\iC

also demonstrated t.he effect of correlated fading on the performance of the eqiializer.

It was observed that becaiise correlatecl fading rediices the diversity gain: it resiilts in

degradation in performance. In the nest cliapter, we combine transmit antenna diversity

with chip equalization to mitigate this problem.

loO r 1 1 4 1 1 I 1 I t L I I l

4 K=l , FSCE -N- K=1, DFE (ideal) -e- K=1, DFE (decision-direct&) 1

Figure 3.16: Cornparison betweeii FSCE and DFE (two-path cfianncl witli r = -Tc,

= 4, A- = 1: QPSIi)

Chapter 4

Combined Transmit Antenna

Diversity and Chip Equalization

Alultipath fading makes reliable wireless communications very difficult . .At the receiver,

multiple copies of the transrnitted signal are superimposecl. This superposition could he

constructive or destructive depending on the relative phase of the multipath components.

Destructive superposition results in deep fades in the signal amplitude. This, in turn, will

cause error bursts in the received bits. To combat fading. diversity techniques arc used.

In a11 of these techniques. multiple copies of the signal are sent in such a way tha.t these

copies undergo independent fading. This way? the probability t hat al1 of them fade at the

same time is reduced considerably.

-4s we nlentioned in the previous chapters, spread spectrum provicles pat h di\-ersity

if the bandwidth of the signal is larger ttian the coherence bandwidth of the channel

(frequency-selective fading). On the other hand, in environments siich as indoors where

the clelay spread is short. al1 multipath components ma- arrive within one chip period (flat

fading). In this case, the energy of the received signal fluctuates considerably depending

on tlie relative phase of the multipath components. One approach for mitigating the

flat fading problem is t o spreacl the signal over a larger bandwidth such that the fading

becomes frequency-selective. However, in many cases, this solution may not be practical.

For esample, to achieve frequency-selective fading: it may be required t o spread the signal

over a bandwidth larger than the allocated bandwidth for the syst.em. Even if we have the

freedom of increasing the system bandwidth, it mal- require costly hardware modifications.

-An alternative approach is to use other sources of diversity to mitigate fading. It should

be noted that even in the case of frequency-selective fading: in many real-life scenarios,

there is a strong correlation between adjacent resolvable multipath components [35]. This

means that even in frequency-selective channels, t here may still be a need for additional

sources of diversity.

,\riterina diversity is an effective way to combat fading. Due to size and conipiexity

limitations of the mobile terrriinal, placing multiple aritennas a t the mobile is not very

practical. -4s a result, for the downlink, transmit diversity is preferred over receive diver-

situ. Alost transmit diversity methods are either bandwidt,h inefficient or require feedback.

Alamouti in [4] and DaSilva and Sousa in [5] have proposed two different transmit diversity

techniques for flat fading channels. A1amout.i uses a special case of orthogonal space-time

coding (361 to achim-c divcrsity whcrcas DaSilva and Sousa rotatc the constellation to

obtain rcsistancc against fading. Both mcthods arc bandwidth efficient and do not rc-

qiiirr fccdback. A modificd version of Alamouti's schcmc lias becn proposcd in [ï] for ISI

channcls and narrowband niodiilation.

In this &aptes: we first clescrihe Alamoiiti's diversity schenie for flat fading channels.

After that. we apply t h e modified version of this schenic proposed in [î] to spread spectriirii

ancl combine it with chip equalization to achieve both di\;ersity gain and interference

suppression in channels with short delay spread. At the end, we show simulation results

for the combined scheme.

4.1 Alamouti's Diversity Scheme

In [Il. .-\lamouti presented a two-branch transmit diversity scherne for channels with no

intersyrnbol interference (ISI). This scheme uses two antennas at the transmitter and one

antenna at the receiver and achieves the same diversity gain as maximal ratio combining

(MRC) with one transmit antenna and two receive antennas. Furtherrnore, this scheme,

while simple to implemeat, does not require ariy bandnidth expansion and feedback from

the receiver to the transmitter. Here, we give a brief surnmary of .~lamouti 's transmit

diversity scheme.

Let us assume that ure have two antennas a t the transmitter. tVe cal1 the antennas A

and B. At a given symbol period, T l , two indeperident symbols are transmitted sirnulta-

neously froni the two antennas, d.4 from -4ntenna -4 and dB froni Antenna B. During the

nest synibol period! T2, we transmit -d, from -4ntenna .4 and d i from Antenna B. So,

the received signals during Tl and S2 are

and

respectivcly. 111 tlie above equatioiis, ha-\ = ry.4ej0'\ aiid hs = uee~'n regreserit the cfiariiiels

frorn .4riteriria -4 and Aritenria B to the receive aiitenna. d', arid d, are the corriples

coiijugates ~ f ' t l . ~ arid d B , respectively. Iri additiori. 711 arid na are ttic additive rioise wtrich

is assiimed to bc white and Gaussian.

A A Let x 1 = 1-1 and x2 = r.5. Now, (-4.1) and (4.2) can be written in matris forni as

.= [n:]

and

To retrieve the transmitteci symbols. we combine rl and r2 as follotvs

and

d B = h é r , - h,ir; .

After a few simple steps, the above equations become

4 4 = (a2! + a;) d.4 + qi ,

and

whcre i l l ancl are white Gaussian noise. Combining rl and r2 according to (4.4) and (4.5)

is equivalent to niultiplying x by the transpose conjugate of H. Sincc H is an orthogonal

matris, rnultiplying H witli its transpose conjugate resiilts iii a diagonal matris. Hence,

ive Cali ret rieve d.

Equatio~is (4.6) arid (4.7) are similar to the m e s obtairied usirig hIRC witti oiie trans-

mit antenna and two receive antennas. Figure 4.1 shows the transmitter and receiver

for -Ll1amoutits diversity method. The above scheme assumes that the chaniiel does not

67

TI:

Figure 4.1: Transmit ter and receiver structures for -41amouti7s diversity scheme

cause any ISI. In addition? the channel is assurned to be known to the receiver and to be

invariant during Ti and TL. In this scheme: two antennas transmit independent symbols

during Tl. Herice, there is no bandwidth expansion.

4.2 Transmit Antenna Diversity with Chip Equaliza-

tion for SS/TDM Systems

In the previous section. te describecl Alamoutios transmit diversity scheme. \F'e saw tliat

this scheme does not result in bandwidth expansion and does not require any feedback. It

also fits wry m l 1 with the time-division nature of the SS/TDM system. In this section.

ive apply a inodificd version of Alamouti's scherne to the downlink of SS/TDh,I systems

and combine it with the Fractionally Spaced Chip Equalizer (FSCE) receiver proposed in

the previous chapters.

Consider the SS/TDM scheme ive described in Chapter 2 for the downlink of a data-

oriented wireless system. In this scheme, we divide the time into frames. During each

frame, Ive transmit to onIy one user using spread spectrum with orthogonal W'alsh codes.

The channel can be rnodeled as

whcrc 4 = criejol is thc complcs channcl coefficient corrcsponding to thc Ph path and T[

is the corresponding path delay. If the channel is frequency-selective? a Rake receiver c m

be iised to esploit thc path diversity. In Chapter 2, we claimed that an FSCE rcceiver

not only exploits this diversity but also cancels interpath ancl interchannel interference

and hence is superior in performance to the Rake receiver. Our simulations in Chapter 3

confirmed tliis claim. In addition: we showed that if the relative path delays are smaller

than one chip period, the performance of the FSCE receiver degrades because of correlated

fading. Our goal in this section is to combine chip equalization with transmit cliversity.

This will not only kecp the advantages that the chip equalizer had over the conventional

Rake receiver but also provide additional diversity for combating fading.

We use two antennas at the transmitter (base station) and one antenna at the rccei~ver

(mobile terminal). The transmit antenrias are placed far enough so tliat thcir signals

undergo independent fading. After the data symbols are divided into i< streams? they are

spread using orthogonal 1Valsh codes. The resulting Ii- seyuences are summcd together

and are multiplied by a scrambling code. The resuiting comples-valueci cliip sequcnce is

clfQ(rz) as descrihed in Chapter 3. The job of the FSCE at the receiwr is to estimate the

transmitted chip sequence. The estimated chip sequence at the output of the equalizer

can then be despread to retrieve the corresponding data bits. Let us for noir- ignore the

spi-eading and despreading operations at the traiismit.ter and receiver. By cloirig so. oilr

system can be viewed a s a non-spread-spectrum system in which transmitted symbols

are chip values (d1Q 's) and the channel has ISI. However: ISI in oiir case is actually

interchip interference (ICI). For the rest of the section. we concentrate on transmission of

chips (instead of bits) but i t is understood that a chip sequence is sum of K data streams

spread by orthogonal codes. Also. for simplicity, we drop the IQ superscript keeping in

rnind that the cliip values are complex in general. tVe now follow a procedure similar to

the one descri bed in [il. We divide each frame into two halves. In the first half, we transmit d,\ (n) from the first

antenna and de(*rt) froni the second antenna, where da4(n) and dB(n) are two independent

chip sequerices. The resultirig received sequence will be

wliere hdl(n) ancl h,*(n) are the cliscrete miiltipath channels from the first and second

transmit antennas to the receive antenna. They are obtained in the same \vit? that

h(n) was obtâined in Section 3.1. In the second half of the frarne, Ive transmit negative

conjugate of dB(n) in reverse order, i.e. -dB(-n) , from the first antenna and con.jugate of

d,l (n) in reverse orde- i-e. df, ( - n ) , from the second antenna. The corresporiding receiveci

sequence is

In above equations. and q2 are Gaussian noise. It should be noted that because we use

a sampling rate higher than the chip rate. and 772 are not white in general.

Let xi (n ) r l (n) and x2(n) r; (-n). This rneans tha t ~ ~ ( 7 2 ) is the reverse-ordcred

conjugate of ~ ( 7 2 ) . At the receiver we combine xl (n) and x2(n) as follows

and

The combining operation can be viewed as a Multiple Input Multiple Output (klIMO)

system where the inputs are xl(n) and ~ ( n ) and the 0utput.s are y,(n) and yB(n) . We

take the z-transform of (4.11) and (4.12) to get

and

We now combine (4.13) and (4.14) with the 2-transforms of (4.9) and (4.10): making use

of the facts that ,Y1 ( 2 ) = Ri ( 2 ) and X2(z) = R;(&), to obtain

ivhere Da-,(,.) and D B ( z ) are the z-transforms of d 4 n ) and d ~ ( n ) : respectively. Further-

more:

Ici (4.15) arid (4. l û ) , rA (2) arid r B ( z ) are z-transforrns of yA(n) aiid yB(r1) wllidi are liiiear

combinations of q1 and q 2 and hence are Gaussian. The abow equations can equivalentlx

New: if we pass y.., (T L ) anci y B ( n ) ttirough two chip equalizers, we can obtain est i~iiates

of claA1 (TL) and dB(n) as sfiow~i in Figure 4.3. The z-tra~isforrri of the MMSE chip equalizer

1 MIMO

r X 1 1 - ?i 2

z-

Figure 4.2: Block diagram of the receiver for the combined çcheme

d iere S,(z) is the power spectrurn of -,,\(n) and ys(n). But Qls(&) = Q - i B ( ~ ) . There-

chip equalizer

y~ d

= chip equalizer . B >

fore,

A >

X 2 > '

r 2 )

The operation of chip ecpalization can be included as part of the MI110 filters. This

rime reverse and conjugale

will give us four filters:

and

Based on above equations, the overall receiver including diversity cornbining and chip

cqualization c m bc writtcn as

Figure 4.3: The overall receiver for the combined transmit diversity and chip equalization

scheme

and

where u ~ ~ . ~ ( n ) , waii(n), wiB(n) and wpB(n) are four FIR filters as shown in Figure 4.3.

IVe can represent these filters in vector form as W ~ A . w p ~ ? W ~ B and W ~ B . In (4.27)

and (4.28), da4 (n) and d B (n) are estimates of the transmitted chip sequences. These chip

sequences are then despread to retrieve the corresponding data bits.

-4s s!iown in Figure 4.3, w l ~ and W ~ A can be concatenated to make a larger filter,

WA. Similarly, w . 1 ~ and w z ~ can be put together to make a larger filter. WB. NOW, W A

and WB can be irnplemented as two Fractionally Spaced Chip Equalizers (FSCE). They

perform cliip matched filtering, path and space diversity combining as well as interference

suppressiori. It slioiild be rloted that based ori (4.18) f 4.20) : the equivalerit cliaririel for

these equalizers has a ierigth wfiich is approsirnately equal to 1riax(2L.~, 2LB) . wliere L,\

and L are lengt hs of he4 ( r r ) arid ilB (n), respectively. This means that to achieve the

same level of interference suppression, w~ and WB must have a larger length compared

to an equalizer used in the case of no transmit diversity. While this increases the receiver

cornplesity. the corribined scheme provides robustness against fading even when the chan-

ne1 delay spread is short. Simple chip ecpalization will not have this robiistness if the

arriving paths are correlated.

Similar to the FSCE described in the previous section, a training sequence is trans-

mitted a t the beginning of each frame. .ln adaptive algorithm such as the one in [XI

can be used to train the filters. In the next section, ive illustrate the performance of this

receiver using chiplevel simulations.

4.3 Simulation Results and Discussions

In this section. ive perform chip-level simulations to demonstrate the performance of the

combined equalization and transmit diversity scheme. Ive consider a channel with two

paths of equal average powers and delay of O.lTc- The RLS algorithm is used for training.

For the case of simple chip equalization. Ive use an FSCE as described in the previous

cliapters with q = 2 and -11 = 15.

For the case of cotribiried trarisrriit diversity arid ctiip equalizatiori, ive use two trarisriiit

anterinas and orle receive ariterina. To rriake a fair cornparisori, we norrnaiize tlie transmit

power so that the total transmitted power in this case is the same as the case of one

transmit antenna. The two channels froni the transmit antennas to the receive antenna

are assumed to fade independently and to have identical delay spread. Here, we also use

two sarriples per chip and 15 taps for each of the four filters on the left side of Figure 4.3.

To initigate the eclge effect caused by the miiltipath channel, we insert training syrnbols

bot11 at thc bcginning and in the middlc of each framc bcforo dividing it into two halves.

-4s shown in Figiirc 4.4, tiic combincd schcinc rcsrilts in considcrablc improvciiicnt in

the BER. The improvement becomes rnore significarit as SKR increases. This is because

tlie diversitu gain rcsiiltcd froni iising two transmit antennas is highcr at high SNR levels.

l o O I l 4 1 1 I I I 1 I - 1 1 I

f + equalization oniy '

- * combined scheme

Figure 4.4: Cornparison between simple equalization and combinecl chip equalizstion witli

transmit diversity (two-patli channel with r = O.lTc, .V = 4: IC = 1)

-- ILI

4.4 Chapter Summary

Spread spectrum can provide path diversity if the signal bandwidth is larger than the

coherence bandwidth of the channel. On the other hand, if the delay spread of the channel

is less than the chip duration. the arriving paths beconie correlated at the receiver. This

will result in reduction in diversity gain and degradation in performance. The same will

happen in frequency-selective channels if the arriving paths are correlated.

To mitigate this problem: we proposed a scheme for cornbining chip equalization with

transmit antenna diversity for the downlink of SS/TDhI systems. The combined scheme,

while being more cornplex, pro\-ides both interference suppression and robustness against

fading. \Ve used transmit diversity because receive diversity is not very practical for the

downlink due to size limitation of mobile terminais. A modified version of -Alamouti's

cliversity scheme was used because this scheme is bandwidth efficient and does not re-

quire any feeclback. The performarice of the conibined receiver was dernonstrated usiug

sirr~u1atioris.

Chapter 5

Conclusions

In tliis chapter, we summarize the results and discussions presented in the previous c h a p

ters. We also suggest a feu- areas for future research.

5.1 Thesis Summary

The traffic of future wireless systerns ndl be mainly data rather than voice. Since the

cliaracteristics of data traffic are quite different from those of voice traffic, there will be

a need for rietworks that are particularly optimized for data rather than for voice. -4

pro~iiising sclleriie for the air interface of tlie downlink of liigh-speed wireless data systeiiis

is the 11)-brid Spread Spectrurri/Tiirie Division h,lultiples (SS/TDM). 1x1 SS/TDI,l. tiriie

is dividec! irito slots. Duririg eadi tirrie slot, data is serit to orily one user usirig spread

spectruni rnodulatiori. Tlierefore. users receive data i r i biirsts. Tlie tirrie division iiatiire

of SS/TDhl facilitates scheduling of different users with different bit-rate requirements

vith ho ut degrading the system performance. It also allows for the traiismission to be

optiiiiized for the user of interest during each time slot. The spread spectrum nature

of the SS/TDhlI scheme provides robustness against interference and allows a frequency

reusc factor of one to he used.

In this thesis, we described a SS/TDM scheme for the downlink of packet-based wire-

less systems. In this scheme: orthogonal (IValsh) codes are used to spread the data signal.

However. multipath propagation destroys the orthogonaiity and causes intracell interfer-

ence. We proposed a novel receiver for the downlink of SS/TDhI sÿstems. This receiver,

which consists of a Fractionally Spaced Chip EquaIizer (FSCE) and a despreader, was

shown to perform significantly better than the conventionai Rake receiver. The chip

equalizer riot orily performs masimal ratio combining to exploit the path diversity but

also suppresses the intracell interference caused by the multipath channel. The FSCE

receiver has rnoderate coniplexity and can be used in systems with long spreading codes.

The fractiorially spaced equalizer provides robustriess agaiiist timing inaccuracies arid

cari haridle spectral nulls bet ter. In addition, sirice FSCE irriplicitly performs matched

filtering, a simple and inexpensive front-end filter can be used at the receiver.

We presented an adaptive implementation of the FSCE receiver and studied its per-

formance using chipleve: simulations. We investigated the effect of different parameters

such as processing gain. constellation size and channel profile on the performance of this

rccci ver.

If al1 multipath components arrivc a t thc rcccivcr within one chip pcriod. sprcad spcc-

trtim cannot proviclc rohiistncss against fading. Thc silrnc will happcn in a frcqiicncy-

sclcctivc channcl if thcrr! is high corrclation betwccn adjacent rcsolvablc psths. To rniti-

gate t his problern, we proposed a scheme thnt combines transmit antenna diversity with

chip equalizatiori. This combined scheme provides bot h robustness against fading and

inter ference suppression in the downlin k of SS/TDN systems. We presented a n aclap-

tivc i~iiplenientation of sucli a receiver and demonstrated its perforniance using chip-le\-el

simulations.

5.2 Future Work

This work can be estended a t a few fronts:

-4 muitipath channel in general has spectral nulis. I t is known that a nonlinear equal-

izer such as the Decision Feedback Equalizer (DFE) is able to handle spectral nulls better

than a linear equalizer. In the case of chip equalization, we need accurate estimation of

chip values in order for the DFE to work properly. But, chip detection is not easy to do

because of the multi-level nature of chip values and because of the fact that chip detection

does not benefit from the processing gain. -4 rnethod for accurately detecting the cliip

values needs to be developed before a DFE can be used effectively.

Another area for further investigation is equalizer training. Given the structure of

the receiver, one can investigate the effect of different training patterns on the equalizer

perforniaiice. For esample: is it better to use K data streams for training or one data

streani with K times the power? What happens if the power of transmittecl signal is

iricreased duririg training to facilitate convergence:' -4lso: effect of different adaptive

algorit hms on the receiver performance needs to be investigated.

For the conibined chip equalization and transmit diversity scheme, one can study the

effect of different system parameters on the performance of the receiver. For esample. the

effect of processing gain, constellation size and channel profile on the receiver performance

can be investigated. In addition, the case of frequency-selective channels with correlated

fading cari IIC studicrl and cornparcd with the casc of flat fading.

Appendix A

The Recursive Least Squares (RLS)

Algorit hm

Here, we briefly describe the RLS algoritlim used to train the Fractionally Spaced Chip

EquaIizer (FSCE).

Let r = [ r ( 0 ) r(1) ... r ( n - 1) r ( n ) r ( n + 1) ... 1'' be the received signal which is

a noisy version of the convolution between the trarismitted chip sequcnce. d, and the

channel, h. Né denote the signal input to the equalizer during tlie nth iteratioa tq-

xj;';' = [ r ( n ) r ( n - 1 ) ... ~ ( 7 2 - iC[ + 1) IT. ivhere AI is tlie nuniber of equalizer taps. The

equalizer output is lience equal t o

wliere u = [ ir(0) ~ ( 1 ) ... u ( d l - 1) IT is the equalizer coefficients. The error is then

where dnJ is the corresponding chip value in the training sequence. MTe tlien obtain tlie

gain vector? Knl , using

1 KY) = p(n- l j x(n)* ( n ) " p c - ~ ) (n)* "' AI :

,w + x,, 'bl

where O < w < 1 is a weighting factor and P,ll is the estimate of the inverse of the

au tocorrelation matrix of the received signal. l i e now update P.il to get

The equalizer coefficients are also updated using

For initialization. we set do) = O and PEI = $ In[, where III is the AI x AI identity

matris and 6 is a small positive constant.

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