Multi-user Interference Cancellat ion in DS-CDMA with Forward Error Correction

b~

Kitw Kar Yan Wong

-4 thesis submitted to the Department of Electrical and Computer Engineering

in conformity nit h the requirements for the degree of Master of Science (Engineering)

Queen's University Kingston? Ontario, Canada

September 2000

Copyright @ Kitty Kar Yan Wang: 2000

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Abstract

In a code division multiple access (CDM-4) system, the presence of the multiple access

interference (LI-41) limits the number of users that can simultaneously communicate

over the channel. To overcome the detrimental effects of the M-41, the use of a multi-

user detection (MUD) algorithm is needed. Many MUD algorithms proposed in the

literature involve the use of complex maximum-a-posteriori (&lAP) decoders that

prohibits their use in many practical applications. The goal of this research project

is to design a lou- complexity algorithm that is targeted at the 384 kbps application

in t hird-generation wideband CDMA (WCDMA).

In this thesis, the use of multi-user interference cancellation in a F~rward Error

Correction (FEC) coded CDMA system is studied. The proposed algorithm combines

linear MUD and iterative interference cancellation. It involves iterative decoding and

soft interference cancellation that is based on FEC decoder decision feedback. The

investigation of the iterative algorithm uses a full CDMA system mode1 which involves

three types of commonly used spreading sequences: GoId. Kasami, and extended S(2)

sequences. Computer simulations are used in this thesis to obtain the performance

of the proposed algorithm using each of the spreading sequences.

For an AWGN channel, the classical CDM-4 detector with no MUD supports 5

high-bit-rate users in WCDMA a t a bit-error-rate of for the constraint length 7,

rate-; convolutionally coded system. The iterative algorithm proposed in this thesis

doubles the number of users in the targeted application.

Acknowledgement s

I would like to thank Dr. Peter McLane, my supervisor, for his support, guidance.

and patience. Without his help, the completion of this thesis would not be possible.

He is also a great addition t o Our softball team.

Special thanks for Dr. Mohsen Hossenian from Harris Corporation, Canada, who

suggested the use of the extended S ( 2 ) code in our simulations. This made Our work

much more meaningful, and gave some insight as why the es~ended S(2) code was

chosen by 3GPP.

Thanks to al1 members in Peter's lab for making it a great place to work. Specif-

ically: Jean .Au, for his help a t the early stage of this project on clarifj4ng some key

concepts; Frederick Lee, for his efforts in proof-reading my thesis; Chan-Tong Lam,

for his knowledge in LaSex: Elvis Chen. for his expertise in programming language,

LaTex, his effort in proof-reading my thesis? and his patience; Pawel Dmochowski and

JValaa Hamouda, for making the lab a friendly place.

Xlso, thanks to Dr. Fady -4lajaji: Dr. Steven Blostein, and Dr. Naraig Majikian for

their comments on this thesis. The quality of this thesis write-up n7as much improved.

Finallyv, thank you to my family and friends for their care and support.

iii

Table of Contents

Table of Contents iv

List of Abbreviations xiii

List of Symbols xiv

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Performance Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Literature Sun-ey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Thesis Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 -

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Thesis Outline 1

2 General Background 9

2.1 Oven-ien- of a CDhl-4 system . . . . . . . . . . . . . . . . . . . . . . 9

2.2 User capacity of a C D X 4 system . . . . . . . . . . . . . . . . . . . . 12

2 -3 On hl ultiple Access Interference Cancellation . . . . . . . . . . . . . . 14

2.3.1 Parallel Interference Cancellation . . . . . . . . . . . . . . . . 15

2.3.2 Serial Interference Cancellation . . . . . . . . . . . . . . . . . 16

2.4 Convolutional Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

. 2.4.1 Convolutional Encoder [l 2: 31 . . . . . . . . . . . . . . . . . 18

. . 2.1.2 Convolutional Decoder[l 2 31 . . . . . . . . . . . . . . . . . . 20

2 . 4 3 The ITiterbi Algorithm (1 . . . . . . . . . . . . . . . . . . . 21

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.44 Interleaving 23

2.5 CDMA with FEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

The Discrete Mode1 28

. . . . . . . . . . . . . . . . . . . . 3.1 Iterative Interference Cancellation 29

3.1.1 Brute Force Interference Cancellation . . . . . . . . . . . . . . 3C

3.1.2 Partial Interference Cancellation . . . . . . . . . . . . . . . . . 36

3.1.3 Soft Interference Cancellation . . . . . . . . . . . . . . . . . . 40

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Pre-processing 43

3.2.1 The Decorrelating detector . . . . . . . . . . . . . . . . . . . . 44

3.2.2 The Minimum Mean-Squared-Error Detector . . . . . . . . . . 45

3.2.3 Iterative Interference Cancellation with Pre-processor . . . . . 45

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Chapter Surnmal 49

4 The Signature Sequences 52

. . . . . . . . . . . . . . . . 4.1 Maximal Length Shift Register Sequences 53

. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Gold Sequences 58

. . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 The Kasami Sequences 59

. . . . . . . . . . . . . . . . . . . . . . 4.4 The extended S(2) Sequences 60

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Chapter Summary 62

5 Iterative Interference Canceilation for High Data Rate Users in

WCDMA 63

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 System parameters 63

5.2 Iterative Interference Cancellation with different spreading sequences 64

. . . . . . . . . . . . . . . . . 5.2.1 Spreading a i th Gold sequences 64 c. C . . . . . . . . . . . . . . . . 5.2.2 Spreading with Kasami sequences (a

. . . . . . . . . . . . 5.2.3 Spreading with extended S(2) sequences 82

3 Multi-user interference Cancellation with Increased Processing Gain . 87

5.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . SS

6 Conclusions 91

6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.2 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . . 92

Bibliography 94

A Approximating the cross-correlation p 98

B Simulations and the Confidence Intervals 100

Vita 101

List of Tables

A list of m-sequences generated using primitive polynomial f (D) =

I t D + D 2 . . . . . . . . . . . . . . . . . . . * . . . . . . , . . . . .

Mapping from quantery S(2) sequences to extended S(2) sequences . .

Number of available sequences of each spreading code family - - - . .

Error Profile for the Brute Force IIC algorithm using tdegree Gold

code at an SXR of 5dB . . . . . . . . . . . . . . . . . . . . . . . . . -

The number of bits required to achieve different confidence inten-als -

List of Figures

2.1 -4 general ~V...user CDh1.A transmit ter . . . . . . . . . . . . . . . . . . 10

2.2 Conventional ikL-user CDM-4 receiver . . . . . . . . . . . . . . . . . . 11

. . . . . 2.3 .A general ;',.user parallel interference cancellation algorithm 15

. . . . . . 2.4 -4 general user serial interference cancellation algorithm 11

. . . . . . . . . . . . . 2.5 -4 general convolutional encoder of rate.k,/n, 19

. . . . . . . . . . 2.6 -4 rate-$. constraint length 3' convolutional encoder 40

2.7 State diagram for the rate-;: constraint length 3. encoder shown in

Figure2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

. . . . . . . 33 2.8 Trellis diagram for the rate-!' constraint length 3 encoder -- . . . . . . . 2.9 The add-compare-select process of the I'iterbi -Ilgorithm 23

2.10 .A typical interference cancellation procedure . . . . . . . . . . . . . . 24

. . . . . . . 2.11 The error propagation diagram for the Viterbi Algorithm 25

2.12 -AA%-u~erCDhI~4systemn-ithFEC . . . . . . . . . . . . . . . . . . 25

2.13 Conventional CDh4-A receiver with FEC . . . . . . . . . . . . . . . . 2s

. . . . . . . . 3.1 -4 general Iterative Interference Cancellation Algorithm 29

3.2 .A 2-user Iterative Brute Force Interference Cancellation .A lgorithm . . 30

3.3 Performance of the Brute Force IIC Algorithm on a 9-user system with

crosçcorrelation p = 0.20 . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4 Performance of the Brute Force IIC -ilgorithm on a 9-user system with

. . . . . . . . . . . . . . . . . . . . . . . . . cross-correlation p = (3.35 33

viii

Performance of the Brute Force IIC Algoritiim on a 9-user system with

cross-correlation p = 0.30 . . . . . . . . . . . . . . . . . . . . . . . . . Performance of the Brute Force IIC Algorithm on a l e u s e r system

with cross-correlation p = 0.25 . . . . . . . . . . . . . . . . . . . . . . Performance of the Brute Force IIC Algorithm on a Il-user system

with cross-correlation p = 0.25 . . . . . . . . . . . . . . . . . . . . . . Performance of the Brute Force IIC Algorithm on a 12-user p t e m

with cross-correlation p = 0.25 . . . . . . . . . . . . . . . . . . . . . .

-4 2-user Partial Iterative Interference Cancellation Algorithm . . . .

Cornparison on different values of the cancellation fractions on a 9-user

system wit h cross-correlation p = 0.25 . . . . . . . . . . . . . . . . . .

Performance of Partial IIC Algorithm with cancellation fraction y' =

60% on a 9-user system with cross-correlation p = 0.30 . . . . . . . .

Performance of Partial IIC Algorithm with cancellation fractions y l =

50%, y* = 5O%, y3 = 60% and y4 = 60% on a 9-user system with

cross-correlation p = 0.30 . . - . . . . . . . . . . . . . . . . . . . . . . The merging branches . . . . . . . . . . . . . . . . . . . . . . . . . .

Performance of the Soft IIC .Algorithm on a 9-user system with cross-

correlation p = 0.30 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Performance of the decorrelôting detector and MMSE detector on a

9-user system with cross-correlation p = 0.25 . . . . . . . . . . . . . .

Performance of the pre-processor-aided Brute Force IIC -4lgorithm on

a 10-user system with cross-correlation p = 0.25 . . . . . . . . . . . .

Performance of the pre-processor-aided Brute Force IIC -4igorithm on

a 10-user system with cross-correlation p = 0.35 . . . . . . . . . . . .

Performance of the pre-processor-aided Brute Force IIC Algorit hm on

a 10-user system with cross-correlat ion p = 0.45 . . . . . . . . . . . .

3.19 Performance of the pre-processor-aided Brute Force IIC Algorit hm on

a 13-user system with crosçcorrelation p = 0.45 . . . . . . . . . . . .

The structure for a r-degree Linear Feedback Shift Register . . - . . .

-4 2-stage m-sequence generator . . . . . . . . . . . . . . . . . . . . .

-Autocorrelation function for an m-sequence with chip duration Tc and

period :t'Tc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Generating a Gold sequence of period K=7 . . . . . . . . . . . . . . .

Generating a Kasami sequence of penod N=4 . . . . - - . . . . . . .

The S (2) sequence generator . . . . . . . . . . . . . . . . . . . . . . .

Performance of the Brute Force IIC .Ilgorithm on a 9-user system with

processing gain of 7, spreading with Gold sequences. . . . . . . . . . .

The ,Yu-stage Preliminary Interference Cancellation -Algorithm . . . .

Performance of the Bmte Force IIC ,Ilgorit hm nvit h a %stage prelim-

inary IC on a 9-user system ni th processing gain of ï 1 spreading with

Gold sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance of the Brute Force IIC .ilgorithm combined with a 2-stage

Partial Preliminary IC on a 9-user system with processing gain of 7.

spreading with Gold sequences. . . . . . . . . . . . . . . . . . . . . . Performance of the Brute Force IIC ,Ilgorithm combined with a 2-

stage Soj? Preliminary IC on a 9-user system with processing gain of

7. spreading with Gold sequences. . . . . . . . . . . . . . . . . . . . .

Performance of the 3.IMSE pre-processor on a 9-user system with pro-

cessing gain of 7, spreading with Gold sequences. . . . . . . . . . . .

Performance of the Brute Force IIC algorithm on a 9-user systern with

processing gain of 7: spreading with Kasami sequences. . . . . . . . . Performance of the Partial IIC .Algorithm on a 9-user system with

processing gain of 7, spreading with Kasami sequences. . . . . . . . .

5.9 Performance of the Soft IIC Algorithm on a 9-user q t e m 11-ith pro- -- cessing gain of 7. spreading n-ith Iiasami sequences. . . . . . . . . . . t t

5-10 Performance of the Pre-processor-aided Brute Force IIC algorithm on

a %user system mlth processing gain of 7. spreading n-ith Iiasami se-

quences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5-11 Performance of the Pre-processor-aided Partial IIC -ilgorithm on a 9-

user system with processing gain of 7: spreading with Kasami sequences. 79

5.12 Performance of the Pre-processor-aided Soft IIC Algorit hm on a 9-user

systern with processing gain of 7. spreading wïth Kasami sequences. . 79

5.13 -4 cornparison on average MMSE detector and optimal MMSE detector 80

5.14 Performance of the Pre-processor-aided Soft IIC -4lgorithm on a 10-

user system with processing gain of 7: spreading with Kasami sequences. 81

5.15 Performance of the Pm-processor-aided Soft IIC Algorithm on a 11-

user -tem with processing gain of 7. spreading with Iiasami sequences. 81

5.16 Performance of the Brute Force IIC Algorithm on a 9-user system 119th

processing gain of 7. spreading with extended S(2) sequences. . . . . .

5.17 Performance of the Partial IIC -Algorithm on a 9-user system with

processing gain of 7. spreading nith estended S(2) sequences. . . . . .

5.18 Performance of the Sofl IIC Algorithm on a 9-user system with pro-

cessing gain of 7. spreading with estended S(2) sequences. . . . . . .

5.19 Performance of the Pre-processor-aided Brute Force IIC Algorithm on

a 9-user system with processing gain of 7. spreading with estended

S (2) sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.20 Performance of the Soft IIC .Algorithm on a 10-user system with pro-

cessing gain of 7. spreading with estended S(2) sequences. . . . . . .

5.21 Performance of the Soft IIC algorithm on a Il-user system with pro-

cessing gain of 7. spreading with estended S(2) sequences. . . . . . ,

5.22 Performance of the Pre-processor-aided Soft IIC algorithm on a Il-

user -stem nith processing gain of 7. spreading nith estended S(2)

sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.23 Performance of the Pre-processor-aided Soft IIC aigorithm on a 12-

user system wlth processing gain of 7, spreading with estended S(2)

sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.24 Performance of the Brute Force IIC AIgorithm on a 18-user sj-stem

using rate-f convolutional code with uncoded processing gain of 30 - 89

5.25 Performance of the Brute Force IIC Algorithm on a 18-user system

using rate-$ convolutionai code with uncoded processing gain of 30 . 89

sii

List of Abbreviations

Third-Generation P artne~bip Project

Additive White Gaussian I\ioise

Bit-Enor-Rate

Base Station

Code Division Multiple -4tcess

Fonvard Error Correction

Int erference Cancellat ion

Linear Feedback Shift Register

Multiple -4ccess Interference

3Iaximurn -1 Posteriori

&Ia,uimurn Likelikhood

$1 inimurn Mean-Squared-&-or

Multi-User Detection

Wideband Code Division Plfultiple -4ccess

Pseudo-Xoise

\.'iterbi ,Algorit hm

Iterative Interference Cancellatiori

Soft-Input Soft-Output

Signal-to-Soise Ratio

Soft Output Viterbi -1lgoritfim

xiii

List of Symbols

- b;

b - -1

&k -1

- . I re f ined b;

bi

PK sequence assigneci to the jch user

for uncoded system: ith information sjmbol of the jth user for coded system: ih interleaver output q m b o l of the jth user

tentative bit decision made for b;

finai bit decision made for 6;

the tentative bit decision made for b; a t the kth iteration

interleaver output sequence of the jth user

the tentative decision made for b, at the kt" iteration

the bit decision made for 6; by the preliminary IC algorithm.

for uncoded system: ith information symbol vector of al1 users for coded system: i th interleaver output vector of al1 users

symbol bandwidth

branch metric from the transition from state S;' at time i - 1 to state Si at time 1

baseband signal of the jth user

unit delay

i units delay

characteristic polynomial of the LFSR

polynomial that captures the the initial load of the LFSR

kth feedback coefficient of the LFSR

the ich encoder generator

generating polynomial

the pre-processor matris

siv

the average pre-processor matrix

-Y,, x :Vu identity matr~x

average interference power spectral density seen by the receiver

total interference ponTer

number of input bits taken by the ccn~olutional encoder at each cycle

total iterations needed

constraint length of the convolutional encoder

length of information sequence

length of the encoded sequence

number of States of the encoder

MMSE filter

average 34MSE pre-processor

number of output bits produced by the convolutional encoder at each cycle

noise seen by the j th user during the ith interval

noise sequence for the j th user

noise vector for i th syrnbol intenal

period length of the LFSR sequence

number of primitive polynomial of degree r

number of users

power spectral density of the noise for .AWGX channel

rectangular pulse of duration Tc

processing gain of the CDh.1-4 systern

interference power after despreading

signal power

noise ponrer

Ph prime decomposition

path metric that ends at stâte S, at time 1 that includes the j th competing branch

the best path metric that ends at state S, at time Z

degree of the LFSR

degree of the ith shift register

mâ.\=imum number of aie ut^ tne shift register

baseband received signal

code rate

cross-correlation matris

average cross-correlation matrix

cross-correlation matris for the ith spreading i n t e m l

auto-correlation function

cross-correlation function

state z

the jth previous state of state S,

signature waveform for the jîh user

signature waveform for the ith symbol of the jth user

chip interval

SJ-rnbol inten-al

i th bit of the encoder input for shift register cycle 1

it" bit of the information sequence of the j'" user

tentative bit decision made for u; at the kth iteration

final bit decision made for u;

information sequence sent by the j th user

tentative decision sequence made for 2, a t the kîh iteration

final decision sequence made for gj

available channelbandwidth

encoder output for shift cycle Z

i th bit of the encoder output for shift register cycle Z

ith bit of the encoded sequence of the jth user

tentative bit decision made for x; at the kth iteration

encoded sequence of the j* user

tentative decision sequence made for z, at the kf"teration

final bit decision made for x;

final bit decision made for Z;

ith matched-filter output bit of the j th user

matched-filter output sequence of the jth user

ith matched-filter output vector

the reliability measure for &>k

the reliability rneasure sequence for 6: difference between the path metric for the ith merging path and the su-ivor path

cancellation fraction at kth iteration

cancellation fraction for the preliminary IC algorithm

decoding depth

3.1-41 seen by the j th user during the ith interval

estimation of I-,

tentative decision made for i9; at the kth iteration

SIAI sequence seen by the jth user

tentative decision made of z9, at the kth iteration

XIAI vector for ith symbol interval

cross-correlation between the sequence assigned to the nth and j th user for the ith interval

identical cross-correlation value in the discrete mode1

time offset of the j th user

svii

Chapter 1

Introduction

1.1 Motivation

The aim of the next-generation wireless network is to provide access to rnulti-media

services t hrough a universal persona1 communication device [4]. To achieve t his goal.

there is a need to improve both trafic capacity and service quality of esisting cellular

networks. Code Division Multiple -1ccess (CDM-4) is a spread-spectrum communica-

tien technique that offers solutions to the aforementioned problem [j]. Adopted by

the Telecornmunication Industry -i\ssociation. it is the standard platform for third-

generation persona1 cellular communication systems [6]. Unlike traditional multiple

access systems, CDM-4 allows al1 active users to transmit messages simultaneously

over the same channel bandtvidth. Alessages transmitted from each CDhll-1 user are

modulated a second time to a bandwidth much wider than necessary tvith a wide-

band noise-like signai called the pseudo-noise (PX) signal. This second modulation

is termed spreading. It alloms suppression of the multiple access interference (hl-41)

produced by other active users of the system provided that each user has a distinct

P N signzl. The amount of suppression depends on the cross-correlation properties

among the PN signals of al1 users as well as the ratio in bandwidth between the P N

signal and the information-bearing signal. This ratio. called the processing gain, is

crucial to the needed high spectral efficiency of CDM-4 systems. Due to the limited

wireless resources, the processing gain of a CDPVI-4 system is constrained by the avail-

able channel bandnidth. Hence. a typical CDbl-4 systern can only tolerate a fised

amount of 11-II. -4s a result. there exists a maximum number of active users that a

CDhl-4 system can support.

One way to expand user capacity is to rnodify the conventional CDlI-A detec-

tors [Tl. The conventional CDM-4 detector is composed of a bank of single-user

matched-filter receivers. each matched to the individual PX waveform assigned to

the corresponding user. This type of receiver structure performs independent data

detection for each user, neglects the presence of the other users. and is not optimal for

the non-Gaussian CDM-4 channel. Multi-user detection (MC'D) is a technique t hat

makes use of the MAI during the detection process to alleviate the disadvantages of

the conventional CDBIA detector [il. The optimal MUD algorithm derived by Verdu

[8, 91 is a maximum likelihood (ML) detection algorithm that performs joint detection

for al1 simultaneous users. This algorithm yields the minimum achievabie probability

of error in detecting CDM-4 signals and significantly improves the performance Gver

the conventional detectors. The improvement. however. is obtained at the espense

of a dramatic increase in computational complexity. n-hich grows esponentially with

the number of simultaneous users. Therefore. it is infeasible to implement the k r d u

algorit hm in practical applications.

,Mani sub-optimal hWD algorithms have been proposed that eshibit good perfor-

mance and complexity tradeoffs. Linear 11UD algorithms such as the decorrelating

detector [IO] and the minimum mean-squared-error (1IMSE) detector 111) are one

of the simpIer and earlier sub-optimum detectors proposed that give s a t i s f a c t o ~

performance by inverting the effect of the 11-41. The non-linear SICD scheme in-

volving interference cancellation (IC) is anot her popular approach t hat a t tempts to

remove the hi-41 from the received signal for each user before making data decisions

[12. 13. 14. 15. 16. 17. 18. 191.

The purpose of t his t hesis is to study various interference cancellation algorithms

for a CDM-JL system employing a fonvard error correction (FEC) scheme, and to

deveiop a low-complexiw suboptimal MUD scheme for the high-data-rate service

based on the Wideband-CDMA (WCDMA) [6] standard. In particular. this thesis

is focused on MUD schemes for the 384 kbps senlce in WCDhI.4. Homyever, the

additive white Gaussian noise (-4WGN) channel, a channel mode1 much simpler than

the models used in the WCDMA standard, is used. Combining both linear MUD and

iterative interference cancellation, a fairly low-complexity detection algorithm can be

designed to improve the user capacity of such systems, but at the cost of increased

delay.

1.2 Performance Measure

One of the most important performance measures in communications is the probabil-

ity of error or the bit-error-rate (BER). BER is defined as the probability of making

an error on an individual bit of information. It provides vital information conceming

the effectiveness of a given algorithm. In this thesis, the BER for a single-user system

in the absence of kL4I will be used as a benchmark for comparing the performance

of sub-optimal multi-user detectors. The particular MUD algorithm proposed in this

thesis has an iterative structure. Therefore, the nurnber of iterations needed for the

algorithm to converge to the single-user performance bound is also used as a figure of

merit. Since the system considered has a nonlinear structure due to both the FEC and

IC algorithms: a closed-form expression on the BER is very difficult to obtain. Thus,

cornputer simulations are used for determining the BER. For the research described

in this thesis, the goal is to achieve a BER of 10-~.

1.3 Literature Survey

The use of MUD to improve user capacity in CDMA communication systems is the

subject of much past and present research activity. In the early 198OYs, Verdu [20]

showed that the conventional matched-filter receiver is oniy individually optimum in

the sense that it gives optimal data detection for each individual user only when no

observation on the interfering users are allon-ed. 1;erdu [8. 91 Lias also derived and

analyzed the optimal detection algorithm that gives jointly optimal data decisions

based on the M L criterion. This algorithm searches through the set of al1 possible

input sequences and selects the one that yields the minimum achievable probabilit?.

of error. ,Ut hough the Verdu algorithm significantly improves the performance over

the conventional receiver, it suffers from a dramatic increase in the computational

complexity, which grows exponentially wïth the number of active users in the system.

This drawback has motivated researchers to seek low-complexi ty sub-optimal MUD

algorit hms.

The MUD algorithrns in the literature can be categorized into optimal. linear,

and nonlinear. Optimal MUD gives jointly optimal decisions on al1 user's bits based

on some optimality criterion. Recent work in this area combines MCID with FEC

schemes and makes use of the Turbo processing principle [21] to obtain an iterative

MUD algorithm that asymptotically achieves the optimal performance at the espense

of increasing delay [22' 23. 24: 25, 26. 271. In general. an iterative MGD algorithm

contains two soft-input soft-output (SISO) decoders. The first SISO decoder is a

multi-user rna.simum-a-posteriori (LLAP) decoder that reads the matched-filter output

of al1 the users and their a priori information to produce a set of soft measures on

the decoded bits. The second decoder consists of a bank of single-user decoders. each

uses the corresponding soft value produced by the first SISO decoder to generate the

a priori information for the particular user. -4 close loop through these two decoders

completes one iteration. The method of computing the soft values and the a priori

information depends on the particular opt imality criterion. In [22, 231 the optimal

iterative MGD algorithm based on the cross-eniropy minimization and its sub-optimal

implementation are derived by Moher. In [24]. an iterative MUD algorithm based on

the MAP criterion is proposed by Reed et al. In [25], Gamel and Geraniotis derived

their iterative receiver based on the MNSE criterion. Recently, Wang and Poor

[26, 271 derived their iterative hIUD algorithm based on an interference suppression

technique and M M E filtering. These iterative J K D algorithms generally give near-

optimal performance, but the use of the ven high complexity X 4 P decoders in these

algorithms prohibits their use in man'. practical applications.

Linear multi-user detection algorithms such as the decorrelating receiver [IO] and

the MMSE receiver [ll] make use of equalization techniques that perform linear trans-

formation on the receiver output to suppress the hl-AI. The decorrelating receivîr

completely eliminates the hl-41. but it also suffers from a channel noise enhancement

[il. The M'SE receiver, on the other hand. compromises between MAI rejection and

noise enhancement [7], but its linear structure limits its performance when compared

to other sub-optimal MUD algorithms. Xlthough these MUD algorithms do not pro-

vide near-optimal performance. their implementation sirnplicity makes them one of

the best candidates for practical multi-user detectors [28].

Nonlinear MUD such as interference cancellation attempts to rernove the 11-11 be-

fore making data decisions in order to improve the system performance with moderate

computational complexity [29]. Interference cancellation can be classified into serial

and parallel 1161. Serial cancellation ranks the users according to their received power

strengths and successively performs interference cancellation and data detection on

a user-by-user basis. ParalIel interference cancellation. on the other hand. at tempts

to remove interference from each user simultaneously. Serial cancellation generally

performs better when the users are received with different ponrer strengths. but it

also suffers from an extended delay compared to parallel cancellation (991. Many

serial-cancellation-based algorit hms (12. 13. l-l. 151 and parallel-cancellation-based

algorithms [16. 17, 18. 191 have been proposed. These algorithms focus mainly on

an uncoded system with no FEC. Less work on interference cancellation has been

conducted on a coded system.

The work in this thesis is focused on a convolutional coded CDMA system with

a sub-optimal MUD algorithm that combines Iinear MUD and parallel interference

cancellation. The main reference for the partial interference cancellation scheme used

in this thesis is the work by Simon and Divsalar [16]. The fundamental background

on XIUD can be found in the test by \>rd6 [il. It provides an estensive treatment

on different MUD algorithms including their performance as well as their cornplesit!-.

General communications texts used for reference include Proakis and Salehi [30].

Peterson et al (311. and Cooper and McGillum [32]. Information on the different

proposals submitted for the third generation mobile communications can be found

in the text by Ojanpera and Prasad [6] and the summary paper by Zeng et al [-Il.

References on the spreading sequences include texts by Golomb [33]. and Peterson

and Weldon [34]; a tutonal paper by Dinan and Jabbariin [35]: and the document by

the third generation partnership project group [36]. References on the convolut ional

code and its components can be found in Wilson [l], Wicker [2]. and \Ïterbi and

Omura [3]. The development of the soft output Viterbi algorithm can be found in a

paper by Hagenauer and Hoeher (371.

1.4 Thesis Contribution

1. Most of the literature on MUD with coding concentrates on a discrete mode1

which does not involve any particular class of spreading codes. This thesis uses

a full system mode1 and considers AICD performance for convolutional codes

with three types of spreading sequexxes: Gold. Kasami and estended S(2). The

thesis is focused on the 384 kbps third-generation \I'CDL.I,4 semice in a 5 hWiz

bandn-idth.

2. -4 novel MUD algorithm is considered for multi-user decoding. The decoding

algorithm is iterative and it has been found that the quality of the detected

data used in the first iteration is crucial for the convergence of the iterative

process. -4ccordingly: various pre-processors are applied to the matched-filter

outputs to improve the initial decoder decisions. In the following iterations, the

pre-processor is no longer used and the soft interference cancellation algorithm

is applied to the matched filter outputs until convergence is attained. In the

soft interference canceliation algorithm, the quality of the decoded outputs of

the previous iteration is used to aid the decoding process.

3. For an AWGN channel, it is found that the iterative decoder described abot-e can

double the number of users in the target application relative to the conventional

CDM-4 detector.

4. For the Gold codes, it is found that performance is limited by the fact that

the channel crosscorrelation matrix becomes singular. This fact has not been

found in the papers included in the literature survey.

5. In the case of using long codes, where only consecutive segments of the codes

are used in each transmissiont it was found that using the time average cross-

correlation matrix for the pre-processing step was inferior to using the instan-

taneous value of this matrix.

1.5 Thesis Outline

Chapter 2 of this thesis begins with an overview of a general CDMA system model.

The intuition behind the interference cancellation algorithm is discussed. The two

classical interference cancellation algorithms. parallel cancellation and serial cancella-

tion, are aIso introduced. The convolutional code and its components, including the

encoder and the Viterbi decoding algorithm? are summarized. The chapter concludes

with a discussion on the CDMA system mode1 employing the convolutional code.

Chapter 3 describes the iterative interference cancellation algorithm that is pro-

posed in this thesis and the intuition behind the different types of cancellation

schemes, including the brute force, partial, and soft cancellations. A simplified CDMA

channel is introduced for comparing the effectiveness of these algorithms. The perfor-

mance of each algorithm is studied and analyzed using the simpiified CDM.4 model.

Chapter 4 describes the linear feedback shift registers for generating spreading

sequences for the CD31-4 system. Practical sequences such as the Gold. Kasami. and

estended S (2) sequences are discussed.

Chapter 5 compares the performance of different iterative interference canceliation

schemes on a more refined CDh.1-4 model. The performance of these cancellation

schemes on common spreading sequences used in practice are also presented.

Finall_v. Chapter 6 provides the conclusions and addresses future work.

Chapter 2

General Background

In this chapter. a general CDMA system mode1 is presented followed by two classical

interference cancellation algorithrns. The background material on a convolutional

code and its components are discussed. This chapter then concludes with an outline

of a CDPV1-4 system that employs convolutional codes.

2.1 Overview of a CDMA system

The block diagram for a general CDlrLL sTstem with 1';, users communicating simul-

taneously over a common -4WGX channel is show-n in Figure 2.1. It consists of a bank

of :\; parallei transmitters, where each represents a single user in the system. In addi-

tion to the components of a conventional transmitter. a second modulator. called the

spreader, is incorporated for each user. Its function is to modulate the user's messages

by a wide-band noise-like time-varying waveform. the P N waveform. which is a pre-

assigned signature waveform for a particular user. It is assurned t hat binary antipodal

signals are used to transmit the information symbols from each user. Denote the ith

information symbol for the j th user as b;. where 6; E {Il}. During the i th symbol

interval, i = 0: 1. . . .. the input vector (for al1 users) is b' = [ b; 6 . . . b'vu lT. Each user symbol is spread by its orvn unit energ' signature waveform Sj ( t - iT') of

duration Ts, where Ts is the symbol interval. -4 signature waveform may be espressed

Figure 2.1: A general iL-user CDM-4 transmitter

S,(t - iT, )

where j denotes the j th

code sequence assigned

PG- 1

= a j ( l + iPG)p,(t - iTs - [Tc). O 5 t 5 T,: (2.1) 1 =O

user. i denotes the ith symbol interval. and { a j ( ( ) } is the PX

to the j th user that takes on values of {kl}. .Usa PG = 2 is the processing gain of the systern and p , ( t ) is a rectangular pulse of duration Tc-

The rectangular pulse p , ( t ) is usually called a chip. and its duration Tc is called the

chip intemai. In practice. the chip inten-al Tc is usually selected such that Ts is an

integer multiple of Tc. Hence. PG can be viewed as the number of chips of PX code

sequence per information bit.

The baseband signal for the jth user r n q be espressed as

where Ï, E [O7 Ts), j = 1:. . . . .\Tu. represents the spbol-epoch time offset for the jth

user with respect to an arbitrary time origin. -1 synchronous CDM-4 system has

identical offset for al1 users. Le.. r, = s V j ? while an asynchronous system has different

offsets for each user. For satellite and microcell applications, synchronous systerns

are of more practical interest since a quasi-synchronous approach has been proposed

[38,39]. Moreover, every asynchronous system can be generalized using a synchronous

Figure 2.2: Conventional Nu-user CD4IA receiver

system mode1 Mth more effective users [40]. Therefore. this thesis is focused on a

synchronous CDMA system. Without loss of generaliw. we should assume zero offset,

i-e.. r = 0. for al1 users.

The baseband received signal r ( t ) consists of the sum of antipodall-modulated

signature waveforms for al1 users embedded in additive white gaussian noise.

where n(t) represents the white gaussian noise.

Figure 2.2 depicts the block diagram of a conventional CDM.1 receiver. It is a

bank of matched-filter detectors. each consisting of a filter that is matched to the

individual P 3 signal assigned to the particular user followed by a sampler at time

instances iTs, i = 1 . 2 . . . .. It is easy to see that a decision for the jih user at the ith

symbol interval, 6: is a one-shot decision because it requires the obsen-ation of the

received signal only at its symbol time inten-al.

The ith matched-filter output symbol for the jth user is expressed as

where

(ii l)Ts n(t) Sj( t - iTs)dt'

It can be shonn that p L is the cross correlation between the PX sequences assigned

to the nth and j" users in the time-inten-al [iTs, ( 2 + l)Ts]. Le..

t PC-I

It is noted from Equation (2.4) that the matched-filter output. y:' is composed

of three terms: the desired information (b;): the .\LAI (9) and the noise (ni). If the

interference term can be subtracted from the matched-filter output. the performance

of the CDMA system can be enhanced. which results in a larger number of users being

simultaneously supported. This is the motivation behind the interference cancellation

scheme used in this thesis.

2.2 User capacity of a CDMA system

The interference suppression capability of a CDk1.4 system depends highly on its

processing gain. Denote II/' as the bandwidth of the transmitted signal and B as the

bandwidth of the information-bearing signal. where CC; = & » B = &. -Us0 denote

.J as the total ponTer of the interfering signal. .At the transmitter, the PX signal

spreads the information-bearing signal over a wider bandwidth I i.- for transmission.

-At the receiver, the received signal is multiplied with a synchronized replica of the

PX signal to despread the desired signal back to its original bandwidth B and to

spread the interference signal over a nrider bandwidth I.1-. The power spectrum of

the interference signal seen by the receiver has an average power-spectral density of

J ~ = J . ' ~ 5 - - After matched-filtering the total interfering power is reduced to

Therefore, the net effect of the spreading and despreading processes is to reduce the

interference power by a factor of g. This factor is termed the processing gain.

Theoretically, in the absence of &IUD. the maximum number of users a CDM-4

system can simultaneously support is proportional to the processing gain PG. Let P,

be the total power of each information symboi. If the CDM-4 system can support ivu

users, the total interference pow-er seen by a particular user prior to despreading is

Esing Equation (2.6). the amount of interference power seen after despreading is

Let SiV&eq,,,,d be the required signal-to-noise ratio (SXR) for the conventionai

CDh.1-A system to achieve a desired performance level in terms of the bit-error-rate.

The required signal-to-noise ratio is formulated by the ratio between signal power and

the surn of interfering power and noise power.

where P, denotes the white Gaussian noise power. In a typical mobile radio envi-

ronment. communication links are interference-limited and not noise-lirnited [41]: i.e.,

Pd >> P,. Hence. the noise term in Equation (2.9) can be omitted and thus

As observed from Equation (2.10): the number of users being simultaneously s u p

ported by a CDiçZ-4 system is proportional to its processing gain.

2.3 On Multiple Access Int erference Cancellat ion

Interference cancellation (IC) is a method that attempts to remove the hIAI before

making data decisions. Recail from Equation (2.4) that the basic idea of IC is to

estimate the MAI and later subtract it from the matched-filter output t o refine its

quality prior to data detection. In the literature. IC schemes are classified as either

parallel or seriai [16]. In a parallel IC algorithm. the MAI is removed from al1 of the

users simultaneously. In a serial IC algorithm. SIAI is cancelled on a user-by-user

basis. one after the other.

In this section. both parallel IC and serial IC algorithms are described. Note

that in order to perform IC or an' other l I G D algorithm. the knowledge of channel

parameters. as well as the PX sequences of al1 the active users are required. -2

sensitivity study on imperfect knowledge of there entities is left as a problem for

future s t u d . In a cellular system. a base station (BS) communicating with a number

of mobile usen has to detect al1 signals at any given instant while each mobile user is

concerned only a i t h its olr-n data detection. For this reason. hICD is currently being

envisioned for the BS only. that is for the reverse link from terminal to base station.

Figure 2.3: -4 general Nu-user parallel interference cancellation algorithm

2.3.1 Parallel Interference Cancellat ion

In the parallel IC algorithm. the MAI is estimated based on a rough evaluation on al1

users' messages. -4 final decision is made after the estimated M-41 is removed from

the received messages. Figure 2.3 illustrates the parallel IC algorithm.

Let 6; be the ith bit decision made for the jth user. One common way to estimate

received user bit is by the sign of the received amplitude, Le.,

where sgn(-) is a function that returns the sign of the variable in question.

With the knowledge of the cross-correlation values between al1 the P N sequences

and the initial decisions on al1 the users' bits. the MAI can be estimated. Let 8; be

the estimated M.41 seen by the jt" user at the ith syrnbol interval. 8; is estimated as

Let bi be the final decision on 6;. bi is formulated as

b; = q. (Y; - 8;)

= sgn (b; + ni - - 3;)

Su

= sgn (b; +ni + p;(6i -gi) n= 1 ,n#;

Xote chat an incorrect initial bit decision for a particular user doubles its contributed

3.1-41. The parallel IC algorithm improves performance if the initial bits decisions are

relatively reliable.

2.3.2 Serial Interference Cancellation

The idea behind serial IC arises from the observation that each mobile signal is re-

ceived n i th different power strength a t the BS (411. hIobile users closer to the BS tend

to have higher signal strengths than users who are further awa . Higher power u s e s

act as stronger interference sources to the weaker users but the' esperience relatively

less interference t han t hose users. Ltilizing the particular iriterference intensity a

user is esperiencing, the serial IC algorithm r a n k the mobile users according to their

received signal strengths and perfonns IC and data detection seriall. To illustrate

the serial IC algorithm. let us assume that al1 of the users in the system are ranked,

with a lower-indesed user indicating that the user \vas received with higher signal

strength (i.e.. this user may be considered to be more reiiable). Figure 2.4 illustrates

the serial IC algorithm. -At the first stage of the seria1 IC algorithm. the bit decision

for the first user (the user esperiencing the ieast 11-41) is detected as if there were no

m r ,

-At the second stage of the SIC algorithm, ,\LAI for second user is estimated based

solely on the decision made on the first user. i.e..

Figure 2.4: -4 general .Vu-user serial interference cancellation algorithm

At the kth stage. the kI-41 for the kth user is estimated based only on the bit decisions

made for the previous k - I users. The final bit decision is made neglecting the

presence of the remaining weaker users.

The above procedure is repeated until al1 of the mobile users are considered.

The serial IC algorithm improves the fidelity of the XL4I estimation at each suc-

cessive stage. Messages sent by the dominant users are detected only using an ap-

proximated M-41 estimation. Messages sent

M,41 are detected using a more refined MAI

Serial IC generally outperforms parallel

by users who suffered severely from the

estimation.

IC in a situation where al1 of the users

are received with different signal strengths. On the other hand. paraIlel IC performs

better when the received signal strengths are relatively equal [29]. For the same

CDk1.4 system, the serial algorithm suffers frorn an estended delay relative ro that

for the parallel algorithm [29]. It is easy to observe that an ,I; bit delay is required for

an ATu-user system with the serial cancellation but only 1 bit delay occurs for systems

\vit h the parallel algorit hm. In practical n-ireless systems. power-control algorithms

are often employed so that al1 mobile users are received with nearly identical signal

strengths at the BS. Therefore. this thesis focuses on a paraIlel IC-based algorithm.

2 -4 Convolut ional Codes

The noise introduced in communication channels corrupts transmit ted signals and

gives rise to channel transmission errors. One way to overcome this problem is to

employ a FEC scheme that adds controlled redundancy to the transrnitted signal.

Such an approach consists of two extra components. At the transmitter side. a channel

encoder is used to add information redundancy. At the receiving side. a decoder is

used to utilize such redundancy to detect and correct channel errors occurred during

transmission. Convolutional coding is one of the powerful FEC techniques that has

been widely used since its invention by Elias [U] in 1955. It is not only used in this

thesis to combat noise introduced by the channel. but it is also used to aid reliable

51-41 estimation for the IC algorithm.

2.4.1 Convolutional Encoder [l, 2, 31

Figure 2.5 demonstrates an encoder with a rate R, of k,/n,: where at each encoding

stage. k, is the number of input bits. n, is the number of output bits, and k, < n,.

The encoder. as a whole, consists of k, parallel shift registers. Each shift register

is composed of r, delay cells. where i denotes the ith shift register and r, may not

equal to r, for i # j. At shift cycle 1. the encoder reads in a binary Ir,-tuple u1 =

{ u ~ ~ ~ . uLJ . - . . Y U ' ~ ~ C - ~ ) and returns an output n-tuple xL = {xi". xLJ ..... X'+C-~} that

ul.I ..-, *S.. m.. I

Figure 2.5: -4 general convolutional encoder of rate-kc/nc

is produced by some Boolean functions operating on the entire set of inputs residing

in the various shift registers. For binaq convolutional codes, these Boolean functions

are modulo-2 sums.

-4s shown in Figure 2.5: the nc output bits are computed not only from the current

k,-tuple entering the encoder but are also computed from al1 other inputs stored

n-ithin the delay cells. Let r-,,, be the maximum number of delay cells of any shift

register. i.e.?

The nc output

T,, kc-tuples.

bits are constrained by the current input kc-tuple and the previous

Define KC as

&= mas r t + l . z=O ...., kc- 1

Hence h', is called the constraint length of the convolutional encoder. -A complete

convolutional encoder is specified by its code rate. constraint length. and its generators

that define the input-output relationship. For example. consider a rate-$_ constraint

length 3. convolutional encoder shown in Figure 2.6. The input-output relationship

is given by two generators. go and gl, that define the connection rules between the

Figure 2.6: -4 rate- $. constraint length 3: convolut ional encoder

delay line and the adders. The generators for this particular encoder are go = [101]

and g, = (1111; ahich correspond to the connection rules from the del- line to

the top and bottom adder, respectively, where the least significant bit corresponds

to the rightmost connection. Generally. a "1" represents a connection between the

corresponding position and the adder; whereas a "O" represents no connection is

presented. Generators are often espressed in octal form so that (go. gl) = (5.7) for

t his particular example.

-4 closed form espression for the encoder output in Figure 2.6 can be espressed as

where >: @ denotes modulo-2 sum and * denotes convolution. Note that the output

n,-tuple results from a convolution between the input sequence and the generator and

this is why the entire procedure is termed a convolutional encoder.

2.4.2 Convolutional Decoder(1, 2 , 31

-4 binary convolutional encoder with LV total delay cells can be viewed as a finite

state machine with 2h' States. each corresponding to the different contents in the

shift register. Figure 2.7 shows an alternative representation of the rate-$ encoder in

Figure 2.6. The output bits are determined according to the current input bit and the

state of the encoder. -1 state diagram can be transformed to a trellis diagram in order

Figure 2.7: State diagram for the rate-& constraint length 3. encoder shown in Figure 2.6

to incorporate time. Figure 2.8 shows the trellis diagram for the encoder in Figure 2.6.

Let Si: i = O?. . . : 2"' - 1, be the ith state of the encoder. It is assumed that the initial

and the ending States of the encoder are at state So, the all-zero state. Each branch

of the trellis diagram is labeled 114th the output bits corresponding to the associated

state transition. Eveq- codeword in a convolutional code is associated with a unique

path starting and ending a t state So through the associated trellis diagram. For a

rate-k,/n, code, there are 2'. branches leaving and entering each node. Giren an

input sequence of k,L bits' there are 2kL distinct paths through the general trellis,

each corresponding to a convolutional codeword of length n,(L t ICc - l), where

rie - 1 is the number of state transitions required for the encoder to return to state

So after the input sequence has been entered into the encoder. Therefore, the optimal

decoding algorithm. the ML decoder. involves searching through each of these 2 ' ~ ~

paths for the most probable sequence.

2.4.3 The Viterbi Algorithm (VA)

The Viterbi Algorithm (LT-4) [43]: named after its inventor, -4.J. Viterbi, is a ML

decoding algorithm that is widely used in practice. Instead of searching through al1

possible paths, the \.:A simplifies the ML decoder through the elimination of the non-

survivor paths a t each tirne instant by branch metric and path metric calculations.

Stae O (00)

Sotc 1 (01)

Satc 2 (10)

Sm= 3 (1 1)

L-2 - L-I L L-1 L-2

Figure 2.8: Trellis diagram for the rate-$, constraint length 3' encoder

The branch metric is a convenient value that represents the likelihood of a particular

branch n-hereas the path metne for a particular state at a particular time instant

represents the likelihood of the best path that originates from the initial state So and

ends at the state in question. The idea of the is to select the branch a t each time

instant for each state that results in a path with the best path metric. The selected

paths are cailed the sunrivors, while the others are called non-sumi\-ors.

For a binary rate-+ code, there are 2 branches leaving and entering each state S*

at each time instant i. Let Sp and SI be the 2 States that the 2 branches are entered

from. Let the branch metric for the transition from state S;'l j = 0. 1' at time 1 - 1

to state Si at time [ be denoted by BAfi-l(S:. Silyl-'). where y'-' is the received

n,-tuple at time instant i - 1. Let the path metric that ends a t state S;' at time

Z - 1 be PM:",. The path metric at time Z that includes the jth cornpeting branch is

calculated by

PM? ( j ) = P M ( - ~ ~ t B M [ - ~ (s:. S, I ~ I - ' ) . (2 -20)

The V-A compares the 2 cornpeting path rnetrics. PM,S' (0) and P1\fI1 (l), and selects

the better one. The non-sun-king path is discarded and the winning path and its

corresponding path metric are stored. This add-compare-select process (see Figure

2.9) is repeated for each state at each time instant until the end of the received

codeword is reached. At that time. the path with the best path metric is the M L

tirne f - f time f

Figure 2.9: The add-compare-select process of the Viterbi -Algorithm

path which represents the decoder output.

The VA can be further modified to make data decisions on the Z t h k,-tuple upon

receiving the (1 + I')th symbol where r is called the decoding depth. Instead of

choosing one h4L path, the path with the best path metric is chosen at each time

instant 1 + l? + 1 for decoding the Ph k,-tuple. It was shown in [30] that choosing

r 3 5Kc gives negligible performance degradation relative to the optimum \'.4 in

terms of the BER-

2.4.4 Interleaving

Alost well-known FEC schemes: inciuding convolutional codes. are not capable of

correcting errors in bursts but only those errors that are statistically independent [l].

However, many practical situations such as communicating over a fading channel,

errors tend to occur in bursts. A particularly important technique that aids the

decoders to correct these errors is interleaving. It re-orders a sequence of bits or

symbols according to some deterministic patterns. Its counterpart. deinterleaving,

maps the re-ordered sequence back into its original order.

Interleaving is often done for the encoded sequence prior to transmission while

deinterleaving is done for the dernodulated sequence prior to decoding. Together, the

interleaving and deinterleaving pair scrambles the error sequences seen at the receiver

and may possibly break down burst errors into nearly independent errors and hence

enhances decoder performance.

&coder R e f d

Figure 2.10: -4 typical interference cancellation procedure

Interleaving aiso p lay a crucial role in communication systems employing decision

feedback algorit hms. The IC is one of t hese algorit hms and its performance is sensitive

to the error patterns produced both by the channel and the decoder. During an

IC process. the estimated MAI based on the decoder decision is removed from the

matched-filter output signal to provide a more reliable data decision through another

decoding procedure. Figure 2.10 demonstrates a general IC algorithm with FEC. To

maximize the performance of the decoders shonm in Figure 2.10' it is necessary to

preclude error bursts from entering the decoders. Unfortunately, the errors produced

by the VA tend to be in bursts. To illustrate this fact, let us consider the trellis

diagram s h o w in Figure 2.11. If the decoder makes an erroneous bit decision at

time te' then this error propagates such that it t a h s more than one symbol for the

erroneous path to merge back into the correct path. Thus. errors made by the CA are

not statistically independent. but occur in bursts. In this thesis. an interleaver with

a random pattern is used to scramble error bursts produced by the Val. It is noted

that no effort is made to optirnize the interleaver in this thesis.

& c d v

2.5 CDMA with FEC

, Wou<purI, vitchi decoda

w o u t p u r l

subtnction MFoutpur Nu

In a CDM.4 system where FEC is eniployed. messages sent by each user are first

encoded, intarleaved, and then spread by the user-specfic P': signal. as depicted in

Figure 2.12.

~ O w

, , Final decoder ourpirt l

~~ vi-i

-

R+eà

MAI Vi-i decoder

M F q t N , dec*

0utpvtI

ourp.1 N"

i Final Vitcrbi > decoder

Time Sate O (00)

Smte 1 (O 1)

S u 2 (10)

Sote 3 (1 1)

Figure 2.11: The error propagation diagram for the Viterbi .Ilgorithm

Infomϟon E, Xi souru for > Emod.rjr ) In t . rk ivn j

b, usefj

Figure 2.12:

s,;. 0 )

CDM-4 system with FEC

Figure 2.13: Conventional CD3.l-4 receiver with FEC

Let 2, = [ u; uj . . . u:-' ] be a vector representing the information sequence

sent by the jth user: zj = [ 21: . . - xic-' ] be a wctor representing the encoded

sequence for the j fh user: and !I, = [ b; b; . . . 15:-' ] be a wctor representing the

j th interleaved sequence. where L denotes the length of the information sequence and

L, denotes the length of the encoded sequence. These sequences are related by the

following espressions:

where encode(-) denotes an encoding procedure and Ii(-) denotes interleaving. -At the

receiving end (see Figure 2.13). let y = [ y; . . . -1

] be a vector represent-

ing the matched-filter output sequence for the jth user; let 2, = [ 20 I f . . . ifc-' ] be a vector representing the jth deinterleaved sequence and 3 = [ 6; ûf . . . fifi ] be a vector representing the decoded sequence. These sequences are reiated by:

where ll-'(.) denotes deinterleaving and decode(-) denotes a decoding procedure. -As

in the uncoded case. the ith matched-filter output bit for the jth user? y; ? is formulated

where nf is the noise seen by the j th user during the ith bit interval. is the cross-

correlation between the PX sequences assigned to the jth and the nth users a t the ith

symbol interval, and i = O , . . . ? L, - 1.

The matched-filter output vector for al1 of the users during the ith symbol interval

where R' is an !Vu x Nu cross-correlation matrix.

T b' = [ bf 6; . . . biru ] is a vector representing the ith interkaver output for al1 :V,

users; ni = [ nf n . . . nk lT is a vector representing the zerernean Gaussian

noise with covariance rnatrix given by

where y is the power spectral density of the noise for the .WGN channel.

Equation (2.26) can be rewritten as

where 1% is an Nu x Nu identity matrix and 9' = (Ri - INu)bi denotes the M.41

vector for the ith bit interval. The matched-filter output for a coded CDM4 system

is also composed of three terms: the interleaved encoder output bi; the M.41 di; and

the noise ni. M-41 estimation in a coded system is done through the use of decoder

decisions. The detailed algorithm wil1 be demonstrated in the next chapter.

Chapter 3

The Discrete Mode1

The CDM-4 system model with FEC introduced in the previous chapter (see Figures

2.12 and 2.13) is further simplified for simulation purposes. Instead of generating the

PX sequences for ail of the users. one rnay model the CDBIA system by speci-ing the

cross-correlation matrix Ri shown in Equation (2 .26) . where R is a symmetric matrix

\vit h each element [Ri], representing the cross-correlation between the signature

sequences assigned to the nth and the jth users during the ith bit interval. In the

literature. XWD algorithms are generally studied and analyzed using a symmetric

channel. This channel is often modeled as a R matrix with identical cross-correlation

value between each PX sequence pair. i.e..

where L, is the length of the encoded sequence. This model is referred as the discrete

model in this thesis. -Although the discrete mode1 does not have much relevance in

practice, it does provide a means of rneasurement on the effectiveness of a MUD

algorithm. The typical value of p is about 0.22. The detailed calculation of p is given

in Appendi~ A at the end of this thesis. The rest of this chapter discusses the intuition

behind the different IC methods and presents the performance of each method through

the use of cornputer simulations. These simulations are aimed such that the simulated

BER is within 3~30% of the true BER with 95% confidence. Details on the confidence

MF ovrpwl

a MAI - F i ~ l subboctiori -

decirion 1

MF o u ~ t - MAI > Deciskm

wbbactiori mJgng '

decision N, -

Figure 3.1: -4 general Iterative Interference Cancellation -Ilgorithm

interval and the required number of trials to achieve the desired level of confidence

can be found in -1ppendiu B a t the end of this thesis. The FEC code used is the

rate-$. constraint length 7. convdutional code with generators {13, li}. Based on the

constraint length of the convolutional code. a decision depth of 36 (r 2 5Kc) is used

in the VA for near->IL decoding. To cope mith burst errors produced by each Viterbi

decoder, different block interleavers of size 1000 for each user are also used in the

simulations. These interleavers are randomly generated at run-time and no attempt

is made to optimize them. Since a block structure is needed for the interleavers: the

blocked data of length 2000 synbols that is appended with 36 dummy symbols to

give a block length of 2036 symbols is used in the simulations throughout the thesis.

3.1 Iterative Interference Cancellation

The iterative processing technique has received an enormous amount of attention

since the discovery of Turbo codes [21]. The idea behind an iterative algorithm is to

repeatedly improve the fidelity of the information being sought until no further prac-

tical improvement is attained. Figure 3.1 illustrates the block diagram for a general

iterative interference cancellation (IIC) algorithm. .At each stage of the IIC algorithm,

the MAI is being re-estimated using the decoder decisions from the previous stage of

- k + -hi

ZI =XI -91 ri, -' I * El Zl

Figure 3.2: -4 2-user Iterative Brute Force Interference Cancellation ,LUgorit hm

decoding. -4s the algorithm proceeds, the MU estimate becomes more accurate and

hence improves the quality of the decoded decisions at the end of the IIC aigorithm.

The number of iterations needed to achieve the desired performance level. Le.. the

single-user performance bound, is highly dependent on the channel characteristics

such as the signal-to-noise ratio (SNR) as well as the signal-to-interference ratio. The

criterion for convergence requires reliable decoder decisions at the initial stage.

In the following sections, the algorithms of three different kinds of IL41 cancella-

tion schernes are discussed. The three schemes are brute force cancellation, partial

caiicellation, and sofr cancellation. To demomtrate the capability of these IC tech-

niques, the performance of these schemes on a system with various cross-correlation

values and with different numbers of users are presented. The number of users \vas

chosen so that the simulation results in this Chapter can be cornpared with results in

Chapter 5 of this thesis.

3.1.1 Brute Force Interference Cancellation

In brute force cancellation. an attempt is made for each user to completely remove

the MAI at each stage of the iterating algorithm [16]. Figure 3.2 illustrates the block

diagram for such algorithm on a 2-user system.

Recall from the previous chapter that the matched-filter output sequences of the

2 users are given by:

where y . = [ y: . . . ] denotes the vector representing the j th rnatched- -1

filter output sequence. 9, = [ 9; 19: . . . ] is the wctor representing the j th

MAI sequence and 2, = [ n; nf . . . RF-' ] denotes the vector representing noise

sequence seen by the j th user.

Let the superscript k denotes the kth iteration of the IIC algorithm. Let ü:." be

the tentative decoder decision made a t the kth iteration on the i th information symbol

sent by the jth user. .Also, let 9;' be the estimation made at the kth iteration on the

MAI seen at the ith bit interval by the jch user. The >,LAI seen by the first and the

second user are estimated as

-k = p II (encode@:)) . (3-4)

-k = p - n (encode@:)) . (3.5)

- k where ej = Q?.* d i s k [ 1 I - - - dLc-l" ] denotes the M-AI sequence estimated a t the kih 1

-L-1,k iteration for the jth user‘iif = [ 69' citk . . . 111 ] denotes the j th information

sequence decoded at the kth iteration. Ii(-) denotes an interleaving procedure and

encode(-) denotes an encoding procedure.

At the (k + l)th iteration. the jch matched-filter output sequence is refined by

subtracting the h4.41. 3:' estirnated based on the decoder decisions frorn the previous

iteration:

-k - y1 -21, iktl - - 1 (3-6)

-k - y 2 - 4 - ykfl - -2 (3. '7)

The refined sequence. i jki '. is then deinterleaved and decoded to produce a new -3

decision sequence, ii?":

-"l = decode (Il-' (zjti')). gr -

31

where decode(-) denotes a decoding procedure and n-'(.) denotes a deinterleaving

procedure.

This estimate-subtract-decode procedure is repeated until the desired system per-

formance is achieved. Assuming h' iterations are needed for the IC algorithm to

achieve a desired performance level, the final decisions on the information sequences

The Nu-user iterative brute force cancellation algorithm is formulated as the foi-

Step(1) Initialization:

S tep(2) Recursive algorit hm:

S tep(3) Final decisions:

Figures 3.3. 3.4. and 3.5 demonstrate the simulation results using the brute force

IIC algorithm on a 9-user system with cross-correlation value of 0.20, 0.25: and 0.30,

respectively For comparison purposes, the BER for both the conventional receiver

and the single-user s ~ s t e m with no 31.41 are also plotted. The BER is plotted against

Figure 3.3: Performance of the Brute Force IIC -ilgorithm on a 9-user systern with cross-correlation p = 0.20

+ 4 rteralions

2 2.5 3 3.5 4 4 -5 S SNR (dB)

Figure 3.4: Performance of the Brute Force IIC -4Igorithrn on a 9-user system with cross-correlation p = 0.23

-- 2 3 3 5 4 4 5 5 SNR (dB)

Figure 3.5: Performance of the Brute Force IIC Algorithm on a 9-user system with cross-correlation p = 0.30

the SNR. which is defined as the signal energ'- per information bits. Eh. dil-ided

by No, where 9 is the power spectral density of the noise for the ;\CIGX channel.

This definition of SSR is used on al1 future plots in this thesis. For a particular

plot, the performance of the iterative algorit hm converges rapidly to the single-user

performance bound at the high-SNR region. .At the low-SXR region. the algorithm

converges either with many iterations or it does not converge at ali. Figure 3.5

shows that the operating SKR has to be above a threshold value in order to obtain

performance gain through the use of the cancellation algorithm. The IIC algorithm

converges to the single-user performance bound only at an SNR above the threshold.

Mrhen operating at an SNR below the threshold? no performance gain can be obtained.

Comparing the three figures, increasing the cross-correlation value requires a Iarger

number of iterations for the algorithm to converge to the single-user bound. The

threshold SNR value is also increased as the cross-correlation value increased.

The effect of increasing the nurnber of users is shown through Figures 3.6 to 3.8.

SNR (dB)

Figure 3.6: Performance of the Brute Force IIC Algorithm on a 10-user s p t e m with cross-correlation p = 0.25

, + convenbonal rccscver

: 6 3 iteraùons + 4 iterabons . + 5 itembons - ungie-user

I I 1

25 3 3.5 4 625 5 SNR (dB)

Figure 3.7: Performance of the Brute Force IIC -4lgorithm on a Il-user system with cross-correlation p = 0.23

Figure 3.8: Performance of the Brute Force IIC -4lgorithm on a 13-user sxstem with cross-correlation p = 0.23

-kt a cross-correlation value of 0.25, the performance of a IO-: a II-. and a 12-user

system are demonstrated in Figure 3.6, 3.7: and 3.8. respectively. Increasing the

number of users requires a larger number of iterations for the aigorithm to converge

to the single-user bound. The threshold SNR also increases as the number of users

increases. For example. the threshold SNR increases from 2.5dB to 4dB for the 10-user

case to the 12-user case.

3.1.2 Partial Interference Cancellation

The M.41 estimated a t the earIier stages of the IIC may not be as reliabie as the

latter stages. For this reason. it is not desirable to completely cancel the hl-41 at

early stages [16]. The partial cancellation algorithm is a modification to the brute

force algorithm that removes only a fraction of the hl-AI at a particular stage of the

IIC algorithm. Let 0 5 T' 5 1, be the desired fraction of the MAI to be removed

at the kth iteration. Figure 3.9 illustrates a 2-user IIC algorithm using the partial

Figure 3.9: -4 2-user Partid Iterative Interference Cancellation -Aigorithm

cancellation algorithm. The structure of the partial-IIC algorithm is almost identical

to the brute force case except for the M-41 estimation in Equations (3.4) and (3.5) are

The :Vu-user iterative partial cancellation algorithm is formulated as follow:

S tep(1) Initialization:

for 1 5 n 5 -Yu

a-' = 0 -n - S t ep (2) Recursive algorit,hrn:

for O 5 k 5 h'

Y; = decode (II-' (6")) -n

-k b, = l2 (encode (ci))

for 15 n 5 .rV,

sk = -,k =-y" -k -n j=i.j+n P - bj

S tep(3) Final decisions:

Figure system

3.10: with

t

5 toa: m .

los:--- c o m n O ~ - l ~ l + @am

1 +- . 4 a= a - * f) @- - eniuFora(@i=)

Cornparison on different values of the cancellation fractions cross-correlation p = 0.25

Figure 3.10 compares the performance of a 1-iteration partial cancellation algo-

rithm using different cancellation fractions on a 9-user system with cross-correlation

p = 0.25. NÏhen cancellation fraction. il. is above 50%. the partial cancellation algo-

rithm outperforms the brute force cancellation a!gorithm in the case shown. IVhen

the fraction is belon. 50%. the performance gain is obtained only at the low-SNR

region. For al1 SSR values. the fractions with values above 50% are superior than

those below 50%. Sotice that when the initial decoder decisions are relatively re-

liable, a larger cancellation fraction. i.e. = 80%. gives more performance gain

than the smaller one. Le.. = 60%. IVhen the initial BER is not reliable, a smaller

cancellation fraction. i.e. = 60%. results in better performance.

Figure 3.11 shows the performance of the partial IIC algorithm on a 9-user CDlc.1-4

system with cross-correlation p = 0.30. The cancellation fractions are 60% for the

first iteration 100% for the remaining iterations. Comparing to the brute force case

shomn in Figure 3.5. removing a fraction of the hIAI at only the first iteration signifi-

cantly enhances the performance of the IIC algorithm. The system employing partial

SNR (a)

Figure 3.11: Performance of Partial IIC Algorithm with cancellation fraction 7' = 60% on a 9-user system with cross-correlation p = 0.30

cancellation at iteration one iowered the threshold SNR value frorn about 3.75dB to

about 2.5dE3.

It is also possible to further improve the performance at the low-SNR region by

employing partial cancellation for more than 1 iteration. Figure 3.12 demonstrates the

performance of using partial cancellation for the first 4 iterations. The cancellation

fractions are 7' = 50%. î2 = 50%. 7 d 3 = 60%. 74 = 60%. respectiwly. Comparing

Figure 3.11 and 3.11. the 4-iteration partial IIC algorit hm significantly decreases the

threshold SKR and enhances the performance for the low-SXR region, but it does

not perform as well as the single-iteration case for the high-SNR region. -At higher

SNR, a relatively large canceilation fraction is required to obtain improvement over

the brute force algorithm. Whereas at lower-SXR. a smalIer fraction results in better

performance. Therefore. one should select these cancellation fractions according to

the desired operating S-iR. For operating at high-SNR. employing partial cancellation

a t only the first iteration wouid be sufficient to enhance system performance. For

- ungit-uscr 1 1 1 I 1

2 25 3 3.5 4 4.5 5 SNR (dB)

Figure 3.12: Performance of Partial IIC Algorithm with cancellation fractions -y1 = 5O%, y2 = 50%: -y3 = 60% and -t4 = 60% on a 9-user -tem with cross-correlation p = 0.30

operating at low-SNR region. several iterations of partial IC are required instead. The

optimal choice of these cancellation fractions depends highly on the system parameters

such as the number of users. the cross-correlation values. and the SSR. Yo effort is

made in this thesis to optimize these cancellation fractions.

3.1.3 Soft Interference Cancellation

The idea behind soft interference cancellation originates from partial interference

cancellation. During each symbol intemal. the decoded symbol of some users ma?; be

more accurate than others. Therefore. it is not optimal to use the same cancellation

fraction for al1 of the users. instead. cancellation can be done based on a reliability

rneasure for each decoded symbol of each user at each stage. This reliability measure

can be obtained by modifying the l ï te rb i algorithm.

ML p.th for tbe iOL symbol

Figure 3.13: The merging branches

Soft Output Viterbi Algorithm

The modified V-4 is called the Soft Output Viterbi Algorithm (SOV-4) [37]. It pro-

duces not only the decoded information bit, but also a soft-value that indicates the

reliability of each decoded bit. In addition to choosing the path. the S0\-.4 h a to

produce a soft reliability value for the each selected path. Recall that an information

symbol at time t = 2 . the ith s ~ m b o l . is decoded a t time t = i + r + 1 where r is

the decoding depth. Mhen an ML path is chosen for the ith symbol, there is one

non-sunriving path rhat could merge with the ML path at each time instant between

t = i to t = i + I' + 1. Figure 3.13 illustrates the typical M L path and its merging

branches. There are exactly r + 1 merging branches which leads to r + 1 different

merging paths. Denote Ar as the difference between the path metric for the Ph merg-

ing path and survivor path. Let Amin be the smallest 0 5 1 5 i'. which leads to

a different bit decision. The probability of selecting the wrong survit-or path is given

Thus- the reliability value for the ith decoded symbol is

Let the reliability measure for the jch user a t the kch iteration be denoted by 6: =

[ #?Y* 6;qk 6Lc-l .k 3 ... I 1: where b ; l k represents the reliability rneasure for &;* and

h;lk denotes the tentative bit decision made a t the kth iteration for the ith interleaver

output bit of the jth user.

For a Nu-user system using soft cancellation algorithm. the estimated IIAI at the

6'2.k Ph iteration of the jth user for the ith symbol interval is 6jiVk = x;kLJÉn - t k - p - 6 ; .

The Nu-user soft IIC algorithm is fomulated as follows:

S tep(1) Initialization:

for 1 5 n 5 -rV,

8-L = 0 -n -

Step(2) Recursive algorithm:

where multi(a, 6) denotes element by element multiplication of vector a and vector 6 .

Figure 3.14 shows the performance of such an algorithm on a 9-user system with

cross-correlation value of 0.30. Comparing to the brute force algorithm in Figure 3.5,

the soft cancellation algorithm significantly enhances the overall performance. Yotice

that the soft cancellation algorithm gives very similar performance as the partial

algorithm shown in Figure 3.1 1. The partial cancellation aigorithm has the advantage

that it is simpler to impiement. hotvevert the optimal sets of fractions changes with the

system parameters such as the cross-correlations and the operat ing SNR. Therefore,

Figure 3.14: Performance of the Soft IIC Algorithm on a 9-user system with cross- correlation p = 0.30

depending on the operating environment. these fractions are required to be computed

manually. On the other hand. the soft cancellation algorithm makes use of the decoder

structure and cornputes the reliability values automatically. However. ic requires an

extra amount of computational load for the decoders to compute these reliability

values.

It is observed that the performance of the iterative IC algorithm is very sensitive to

its initial decoder decisions. The convergence criteria depends on a reliable initial

tentative decisions.

One way to irnpro1.e the fidelity of the initial decoder decisions is to apply a Iinear

filter to the matched-filter outputs prior to the IIC algorithm to invert the effect of

the MAI. Linear filters such as the decorrelating receiwr (101 and the MUSE receiver

[Il] are widely used for XKD due to their implementation simplicity when compared

to the optimal MUD algorithm [il. They can be used in association a-ith the IIC

algorit hrns for furt her performance enhancement.

3.2.1 The Decorrelating detector

The decorrelating detector is one of the early MUD algorithms proposed [IO]. It

cancels the effect of MAI by decorrelating the matched-filter outputs. To demon-

strate the intuition behind the decorrelating detector, let us first consider a noise-free

environment. Recdl from Equation (2.26) that the matched-filter output vector is

where at the ith bit interval, R is the cross-correlation mat*, b' is the message vector

and ni is the noise vector.

In the absence of noise, the matched-filter output vector is simplified to

y' = Rbi

= bi+ (R- rNU)bi

= bi+9':

nhere IN, is a Nu x iK identity matrix, 19' is the M-41 vector, Nu is the number of

users, and i denotes the ith bit interval.

When the conventional receiver is employed, detection error occurs due to the

presence of the 34-41? 9'. To remove the effect of the MAI, the matched-filter output

vector y' is processed by rnultiplying it with the inverse of cross-correlation rnatrix

prior to data detection. Let z' be the resulting output vector,

where R-' is the inverse of R. If the cross-correlation matrui R is invertible, then

the decorrelating receiver exists, and hence the MAI can be successfully eliminated.

In the presence of noise. the processed matched-filter output can be espressed as

-4s observed from Equation (3.15)? the processed matched-filter output has only two

terms: the desired message vector b' and the noise vector R%'. The hIAI is com-

pletely eliminated by the decorrelating detector, however. the embedded noise. R-LnL.

is also enhanced [7]: which degrades the performance of the decorrelating detector rel-

ative to the optimal multi-user detector.

3.2.2 The Minimum Mean-Squared-Error Detector

The MMSE detector is another linear MUD algorithm proposed in the literarure [Il].

C'nlike the decorrelating detector. the MMSE detector takes into account the effect

of channel noise and gives appropriate tradeoff between AL41 rejection and noise

enhancement. The MIISE detector M. rninimizes the mean-squared error between

the matched-filter output and the resulting output zz. Its complete derivation can

be found in [î]. The MMSE detector is formulated as

where is the power spectral density of the noise for the .4M7GK channel. and IN,

is an iV, x !Vu Identity matris.

The MMSE detector M does not require the cross-correlation matris R to be

non-singular. It is also shown in [7] that the MMSE detector always e'ust.

3.2.3 Iterative Interference Cancellation with Pre-processor

Linear filtering can be applied to the matched-filter outputs prior to the IIC algo-

rithrns to aid reliable initial decoder decisions for accelerating the convergence rate

Figure 3.15: Performance of the decorrelating detector and XIPI4SE detector on a 9-user systern wit h cross-correlation p = 0.25

of the iterative IC aIgorithms. The use of a linear filter is referred to as the "pre-

processor" in this thesis.

Figure 3.15 compares the performance of the conventional receiver, the decorre-

Iating detector, and the 313ISE detector on a 9-user systern with cross-correlation

p = 0.25. The performance of the decorrelating detector and the hlMSE detector are

very sirnilar. Both detectors improve the BER by a significant amount when com-

pared to the conventional receiver. The performance of the decorrelating detector is

slightly better than the MMSE detector in the case shown. It is also less comples

to implement since it requires no knowledge about the channel noise. Therefore, the

decorrelating detector is always employed as the pre-processor in this thesis if it ex-

ists. Othenvise. the LIAISE detector is employed. In the cornputational results in

this Chapter, the decorrelating detector is always used as the pre-processor.

Let G be the pre-processor to be applied prior to the IIC algorithm. The pre-

processor-aided brute force IIC algorithm is formulated as follows:

Step(1) The initial stage:

for 1 5 n 5 ATu

2: = decode (II-' (gn))

S tep(2) Recursive algorithrn:

for 1s k 5 h'

for I 5 n 5 ATu

Step(3) Final decisions:

for the decorrelating detector where G = { 1 ) for the \,IMÇE detector

Figures 3.16, 3.17, and 3.18 show the performance of the decorrelator-aided brute

force IIC algorithm on a 10-user system mith cross-correlation p = 0.25. p = 0.35. and

p = 0.45, respectively. By pre-processing the matched-filter outputs, the initial BER

is significantly lowered. which accelerates the convergence rate for the brute force

IIC algorithm. Notice that with the aid of the decorrelating detector, the system

toIerates higher values of cross-correlation. However! t his improvement is obtained

Figure 3.16: Performance of the pre-processor-aided Brute Force IIC Xlgorithm on a 10-user system with cross-correlation p = 0.25

Figure 3.17: Performance of the pre-processor-aided Brute Force IIC Algorithm on a 10-user system with cross-correlation p = 0.35

SNR (dB)

Figure 3-18: Performance of the pre-processor-aided Brute Force IIC -ilgorit hm on a 10-user system tvith cross-correiation p = 0.45

a t the expense of extra computational load which involves matrix inverse calculation

and matrix multiplications.

With the aid of the pre-processor, the brute force IIC algorithm for a 13-user

system tolerates a cross-correlation value up to p = 0.45 (See Figure 3.19). Xotice

that a threshold SXR of 4dB is required to obtain any reasonable performance gain.

The use of the pre-processor results in a increase in complexity relative to the use

of the matched-filter receiver. The pre-processor in\*olves the inverse of a symmetric

mat ri^ that is only applied once on the initial rnatched-filter output before the itera-

tive detection algorithm is enabled. If the channel is knom-n. which is assumed in this

thesis, this matris inverse can be computed off-line.

Chapter Summary

Thsi chapter has introduced three iterative interference cancellation algorithms: brute

force cancellation, partial can~el la t ion~ and soft cancellation. The performance of

Figure 3.19: Performance of the pre-processor-aided Brute Force IIC -Algorithm on a 13-user system with cross-correlation p = 0.45

these algonthms are demonstrated and cornpared through the use of computer sim-

ulat ions. The brute force cancellation algorit hm seeks to corn plet el?. eliminates 31-41

at each iteration mithout taking into account the reliability of M.41 estimation. The

partial cancellation algorithm rnakes use of the reliability property of the iterative

algorithm and removes only a portion of the M-41 according to user-defined cancel-

lation fractions. The soft cancellation scheme uses the reliability measure provided

by the soft output Viterbi decoder and performs cancellation accordingly In general,

the soft cancellation scheme gives the best performance among the t hree algorithms.

It has the lowest threshold SXR. but it is also the most complex algorithm to im-

plement. The partial algorithm is less complex compared to the soft algorithni, but

i t gives similar performance to the soft algorithm a t high-SNRs. The brute force

algorithm has the worst performance arnong the three algorithms. It has the highest

t hreshold SNR and the slowest convergence rate.

The pre-processor-aided IIC algorithm is also introduced in this chapter. The two

pre-processors discussed are the decorrelating detector and the MNSE detector. \Vit h

the aid of a pre-processor. each IIC algorithm can support more users and tolerate a

higher cross-correlation value. In particular. a 13-user system using the pre-processor-

aided brute force IIC scheme can tolerate a cross-correlation value up to 0.45. The

improvement in performance is obtained at the expense of increased computational

complexity. which invoives matrix inversion and matrix multiplications.

Chapter 4

The Signature Sequences

The mathematical properties of the signature sequences used in CDhL4 communi-

cations are of fundamental importance in deterrnining the characteristics of such a

system. Recall from Equation (2.4) that when despreading is applied to the received

si,snaI, the arnount of the 34-11 contributed depends on the cross-correlation proper-

ties of the signature sequences. Good performance of such a system requires signature

sequences to have low cross-correlation values. Ideally, spreading codes are infinite

random sequences of equally likely binary digits. Ijnfortunately, the infinite memory

storage requiremeiit in both transmitter and receiver prohibits the use of such se-

quences, Therefore, mat hemat ically-generated periodic sequences t hat nearly satisfy

the randomness properties are generally employed [3 1). These sequences are called

the P N sequences. The randomness properties defined in Cooper and b1cGillem [32]

are re-stated as follo~vs:

1. In every period, the number of positive ones differs from the nurnber of negative

ones by exactly one. Hence the period A* is an odd number.

2. In e v e l period. half of the runs of the same sign have length 1. one fourth have

Iength 2, one eighth have length 3. and so forth. Also the number of positive

runs equals the number of negative runs.

3. The autocorrelation of a periodic sequence is tw-valued. That is, it can be

described by

7 = O. iv, 2 ~ ~ ~ . . . otherwise

where { a ( l ) ) represents the sequence in question.

Due to the nlde bandwidth of spreading sequences. the sequence generator is

required to operate at a veq- high speed. For this reason. shift-register-sequence

generatow are of most interest [31]. The PX sequences used most in practice (333 are

the Gold 144, 453. Kasami [46] and extended S(2) (361 sequences. Given the period

length, each code family chooses its member sequences over the entire set of available

codes according to mathematical d e s . Both the Gold and Kasami families have

very low cross-correlation member sequences [31]. They are binary sequences and are

obtained by combining two maximal length sequences. The estended S(2) codes are

complex-valued sequences that are obtained by estending the quaternaq S(2) code.

The extended S(2) codes are chosen by the Third Generation Partnership Project

(3GPP) Group [36] as one of their standard spreading sequences. In the folloaing

sections, the generation of the masimal length. Gold, Kasami. and estended S(2)

sequences are discussed.

4.1 Maximal Length Shift Register Sequence

The maximal length sequences (or m-sequences) are one of the most well-known

classes of P N sequences that satisfj- the randornness properties given in the previous

section. By definition. m-sequences have the masimum possible period that a Iinear

feedback shift register (LFSR) of a @\-en degree can generate. Figure 4.1 illustrates

the typical structure for a r-degree LFSR.

For a r-degree binary LFSR. there are 2' possible states, each corresponds to the

different contents that reside in the shift register. Since the riumber of states of the

Figure 4.1: The structure for a r-degree Linear Feedback Shift Register

LFSR is finite, the LFSR sequences are periodic 1331. To generate sequences with the

maximum possible period, the LFSR cycles through every possible state escept for

the all-zero state. as the subsequent states of the dl-zero state is always the all-zero

state. Therefore the maximum possible period .V for a r-degree LFSR is - 1 since

there are only 2' - I non-zero shift registers states.

Let {g17.. . ,g,},gi E {O. l}: 1 5 i 5 r, be the binary feedback coefficients of the

LFSR as s h o m in Figure 4.1. At each clock cycle, the LFSR shifts al1 contents to the

right and cornputes the feedback input. ai. The sequence { a * } is generated according

to the recursive formula

where gk, at E {O, 1}: 1 5 k 5 r and & denotes modulo-2 sum.

Define the output function of the LFSR as G(D),

where D is the delay operator. G ( D ) is called the generating polynomial of the shift

registers sequence. Combining Equations (4.2) and (4.3), the generating polynomial

becomes

Equation (4.4) gives:

where go(D) = zLz1 e9kDka-iD-' + . . . + a-lD-i and f (D) = 1 + EL,, @gkDk.

Therefore, the infinite generating polynomial G ( D ) can be espressed as a ratio of two

finite polynomials go(D) and f (D) . The denominator polynomial go(D) is dependent

on the initial load {a - , . . . . a- 1 } of the shift registers sh i ch determines the phase shift

of the sequence {a,}. The numerator polynomiai f ( D ) in Equation (4.5) is called the

characteristic polynomial for the LFSR sequence. This polynomial determines the

characteristics of the sequence {ai} such as the period length.

To generate an m-sequence. the characteristic polynomial f (D) of the LFSR must

be primitive. A polynomial of degree r is primitive if the following two conditions are

satisfied:

1. The smallest integer n for which f (D) divides Dn + 1 is n = 2' - 1 = N, and

2. f (D) is irreducible (non-factorable). i.e.. f ( D ) # f l ( D ) - f i (D) .

Figure 4.2: -4 %stage m-sequence generator

Table 4.1: A list of m-sequences generated using primitive polynomial f (D) = 1 +

.\nother restriction on generating m-sequences is that the initial state of the LFSR

D + D 2

has to be non-zero since a all-zero initial state generates only the all-zero sequence.

I n i t i a l l ~ a d { a - ~ , a - ~ ) { O : 11

Primitive polynomials exist for al1 values of the degree of the generating polpo-

mial T, r > 1. It is also showm in [33] that the number of primitive polynomials of

Statestransitions O 1 + 10 + 11 + O 1 + . . .

degree r is equal to

(ai 1 1~01l0110. - .

where {Pi, i = 1.2. . . - . k} is the prime decomposition of 2' - 1. That is.

where ni is an integer. -4 complete list of primitive polynomials with degree r 5 34

can be found in Peterson and Weldon [34].

Figure 4.2 illustrates a fi-stage m-sequence generater with primitive polynomial

f ( D ) = 1 + D + D2. The sequence { a i } is periodic with period N = 3. Table 4.1

lists the different m-sequences generated using the LFSR in Figure 4.2 with different

initial loads. The state transitions of each sequence are also shown in Table 4.1.

As observed from Table 4.1, using different initial loads resulted only with a

different phase shift of the same m-sequence. Without loss of generality, the initial

Figure 4.3: Autocorreiation function for an rn-sequence nith chip duration Tc and period NTc

- state of the shift registers is generally chosen to be a-1 = a-7 = . . . - al - , = O' a-, =

1. Therefore, the denominator of Equation (4.5) is simplified to go(D) = gr = 1 for a

r-degree m-sequence generator. The generating polynomial in Equation (4.5) is thus

reduced to 1

The normalized autocorrelation of any m-sequence is P-valued [33]. Denote Re&)

be the normalized autocorrelation funct ion?

where a( i ) = 1 -2a, is the ilh chip of the binary antipodal rn-sequence. 2 is any integer

and AT is the sequence period. Figure 4.3 illustrates the 2-valued autocorrelation

function for an m-sequence.

The cross-correlation functions of m-sequences are not well-behaved: they may be

many-valued functions. depending on the pair of sequences in question. The Iower

bound on the normalized cross-correlation between any pair of binary sequences of

period N in a set of m-sequences is [47]:

There exist composite code families t hat utilize- the ni-sequences to produce sets

of low cross-correlation codes. The Gold and Kasarni codes are among these and they

are widely used in practice as spreading sequences.

4.2 The Gold Sequences

The Gold code sets [44, 453 are generated by the summation of two distinct m-

sequences of the same period. Consider a binary m-sequence of penod N and let it

be represented by the vector a. Consider another sequence a' obtained by sampling

every qth symbol of a. The sequence a' is said to be a decimation of sequence a and is

denoted as a' = a[q]. It is proveo that the sequence a' is a m-sequence with penod N

if and only if gcd(N, q ) = 1, where "gcd(a, b)" denotes the greatest common divisor

of integer a and b [48]. Thus, any pair of m-sequences having the same period N

can be related by a' = a[q] for some q. The two m-sequences a and a' are called the

preferred pair if the following two conditions are satisfied:

1. r # O(mod4), where r is the degree of the shift register, and

2. q is odd and either q = 2' + 1 or q = 22k - 2k + 1 for some k

1 for r odd gcd(r, k) =

2 for r = 2(mod4)

If a and a' is a preferred pair, then the family of Gold codes

t hat sat isfies

(4.1 1)

for this preferred

pair of m-sequences is defined by {a, a'? a + a': a + Da', a + ~ ~ a ' , . . . , a t DN-la'}

where D is the delay element. The cross-correlation functions of the Gold farnily are

three-valued, where those three values are {-F, - k, k [t(r) - 211, and

for r odd for r even.

Tt is easily verified that the number of codes in the Gold farnily is N + 2 where N is

the sequence period.

Figure 4.4 illustrates the generation of a Gold sequence using two m-sequences

whose primitive polynomials are fi (D) = 1 + 0 + D3 and f2(D) = 1 + D2 + D3. The

Figure 4.4: Generating a Gold sequence of period N=7

different code sequences in the set can be generated using different initiai shift register

loads to obtain the desired sequence. The cross-correlation function of the above Gold

4.3 The Kasami Code

code set have values {-$. -$. q } . The correlation rnatrk for this particular code set

The Kasami family [46] is ariother class of important P N sequences that have low

is R = $

cross-correlation values between each sequence pair. Consider a m-sequence a of

- L

r 3 -1 -1 -1 -1 -1 -1 -1 - 3 7 -1 3 -1 -5 -1 3 -1

-1 -1 7 -1 -1 -1 -1 -1 -1 c. -1 3 -1 1 -1 -1 -1 -1 -1 - -1 -1 -1 -1 r -1 -1 -1 -1 - -1 -5 -1 -1 -1 r -1 -1 -1 - -1 -1 -1 -1 -1 -1 r -1 -1

-1 3 -1 -1 -1 -1 -1 T -1 - _ -1 -1 -1 -1 -1 -1 -1 -1 r _

period N = 2' - 1 where r is even. -Usa consider a second sequence a' which is obtain

by decimating a by 25 + 1. I t can be verified that a' is another m-sequence with

period 25 - 1 [35]- The family of Kasami sequences with M = 25 sequences is defined

by {a'a + a'. a + Da'. a + D'a'. . . . a t Di-2a'}. The auto-correlation and cross-

correlation of these sequences take on values from the set {-1: -(25 + l), 25 - 1).

Figure 4.5 illustrates the generator for a Kasami sequence of period !V equals 15.

Figure 4.5: Generating a Kasami sequence of period 3=4

The primitive p o l ~ o m i a l s for sequence a and a' are fi(D) = 1 + D3 + D4 and

f2 ( D ) = 1 + D +D2, respectively. The auto-correlation and cross-correlation functions

of the above Kasami code set have values {-&, -&, 5). The correlation matriu for r 13 -3 -5 -a 1

4.4 The extended S(2) sequences

this particular code set is R =

The extended S(2) sequences is chosen by the 3GPP group as the one of the standard

spreading sequences to be used in the third generation MiCDM.4 system [36]. At the

time of writing this thesis. there is no literature reference that gives the details on

the theory behind these codes. However. in Our simulation result (to be presented

in Chapter 5 of this thesis). it is demonstrated that the system spreading with the

extended S(2) sequences gives superior performance than those using other spreading

sequences.

The extended S(2) code family has 224 - 1 different code sequences, each with

period length ?V = 256. Each extended S(2) sequence is generated by extending

and mapping a length-255 quaternary S(2) sequence to a length-256 cornplex-valued

sequence. Hence, the code family is termed extended S(2).

-5 15 -5 -3 - - 15 -5

mod 2 1 ? I

@ multiplication

@ rnod n addition

Figure 4.6: The S(2) sequence generator

Each S(2) sequence is generated by modulo-4 addition of a quaternary sequence,

{ a r } : and 2 bina- sequences. {bi) and { d l ) These three sequences are 8-degree

LSFR sequences and are generated recursively according to the follon-ing generating

polynornials:

The generator for the S(2) code is shown in Figure 4.6. The initial loads for the

three LFSRs are determined froin the user number. Let jZ3 j2* . - . jO be the 24 bit

bina^ representation of the user number j, O 5 j 5 255. The initial loads are

a,l = 2 j o + 1 mod4,

a-i = 2ji,1 mod4, i = 2 . . . 8 .

b,i = jiCi mod 2, i = 1 . . .8.

Table 4.2: Mapping from quantery S ( 2 ) sequences to extended S(2) sequences

d-i = jlS+* mod 2, i = 1 . . -8.

The S(2) sequence for the j th user, {z,(i)}: of length 252 is generated according

to the folloning relationship:

~ ~ ( 1 ) = ai + 2br + 2dr mod 4 ,1 = 0: . . . .254. (1 .13)

This sequence is extended to length 236 by setting zj (255) = zj (O) -

The jth extended S(2) sequence. (C,(l)), is obtained by

a j ( l ) = n l ( l mod 236) ( 1 i j(-l) 'm2 ( L ( 1 mod 2 5 6 ) / 2 ] ) ) . ( 4 . 1 4 )

where m l ( l ) and m z ( l ) are mappings defined in Table 1.2: L-] denotes rounding to

the oearest lowest integer: and 1 = 0: 1:. . ..

4.5 Chapter Summary

This chapter stated the three commonly used spreading families for real applications.

These three code families are the Gold. Kasami and estended S(2) codes. Both

the Gold and Kasami codes are bina- sequences that have well-controiled cross-

correlation properties. In addition. the Kasami codes also have wll-controlled auto-

correlation properties. The estended S(2) codes are comples-valued codes nith the

advantage that they can supply a large number of code sequences mith good random-

ness properties. The performance of these codes for the IIC algorithm studied in tbis

thesis wïIl be given in the foilowing chapter.

Chapter 5

Iterat ive Interference Cancellat ion for High Data Rate Users in WCDMA

In contrast to Chapter 3, the performance of different IC schemes are verified in this

chapter using a more refined CDM-4 mode1 where actuai spreading takes place. This

chapter begins with the detail system parameters used in the cornputer simulations to

assess performance. The performance of different IC algorithms on common spreading

codes used in practice, such as the Gold, Kasami, and extended S(2) codes, are

presented. In the computational results to be given in this Chapter which involve

the use of a pre-processor. the MMSE case defined in Equation (3.16) was employed

as the pre-processing sub-system. This was done to avoid the possibility of having a

singular matrix to define the pre-processor which can occur for the decorrelator case.

5.1 System parameters

In this thesis, our system is targeted at the 384 kbps third-generation WCDMA

service. The available channel bandwidth, Wo for WCDMA is about 5MHz [4]. When

rate-; convolutional code is employed, the processing gain of the particular system is

given by

nhere B is the bandwidth of the encoded bit. To achieve the desired BER of

IO-'' the required SXR for a rate-?, constraint length 7, convolutional code is equal to

45dB [3]. Using Equation (2.10), only 5 users can be supported by such system a i t h

a processing gain of 7 when conventional CDMA detector without MUD is employed.

5.2 Iterative Interference Cancellation with differ- ent spreading sequences

Methods of spreading can be divided into 2 categories: spreading using sequences

with period larger than the bit period. i.e., N > PG. and spreading using sequences

with period equal to the bit period, i.e., N = PG. These two types of spreading

are referred as long and short spreading, respectively, in this thesis. The use of long

spreading complicates the task of MUD [?] since the code segments used for spreading

va- for each data syrnbol. On the other hand, the identical cross-correlation matrL~

in short spreading simplifies MUD, but a good spreading code family does not exist

for al1 period lengths N. Table 5.1 shows the number of available sequences of each

code family for a given period length N. Given a system with processing gain of 7,

the only code family with such a period length is the 3-degree Gold famil. Thus, the

3-degree gold code set is considered for short spreading, while the Kasami and the

estended S(2) codes are used for long spreading in this thesis.

5.2.1 Spreading with Gold sequences

The 3-degree Gold code set %th penod length AT = 7 is generated by using primitive

polynomials fi (D) = 1 + D2 + D3 and f2(D) = 1 + D + D3 (341. This code set has

only 9 available sequences and thus only 9 users can be supported. This Gold code

I number of seauences 1

Table 5.1: Number of available sequences of each spreading code family

set has normalized cross-correlation matLu

degree r

-4s observed from the cross-correlation matris. some spreading sequence pairs exhibit

larger cross-correlation than others. In particular. the sequence assigned to the sec-

ond user (the second column or row of the matr~x) has the worst cross-correlation

properties among the 9 users.

The performance of the brute force IIC algorithm on a 9-user system using Gold

spreading codes is demonstrated in Figure 5.1. It is observed that many iterations

are needed for this algorithm to converge CO the single-user performance bound. In

particular: at an SNR of 43dB. 7 iterations are needed. The reason for the slow

convergence is demonstrated by an esample shown telow.

Table 5.2 illustrates the number of errors each user has in a bit Stream of 0.2

million bits when using the iterative brute force IC algorithm at an SNR of 5 dB for

the first 4 iterations. It is noted that the user with the most errors alternates between

2 3

2 -

Period L\. i Gold Kasami

4 5 6 7 8 9 10

- -

ixtended S(2) 3 - 1

3 - 9

- - - -

z2' - 1 (X=226) - -

l a 31 63 127

255/256 511 1023

- 33

4 -

65 '

129 -

513 1025

8 -

16 (3=255) -

32

Figure 5.1: Performance of the Brute Force IIC Algorithm on a 9-user system n-ith processing gain of 7. spreading ~ l t h Gold sequences.

1 number of errors in 0.2 million bits at SNR=SdB 1

I I 1 I 1 1 1 I 1

2 iterations 1 8 1288101 O 1 O T 7 1 4 8 1 1 O 1 7 1 4 1 conventional receiver

1 iteration

1 I t 1 1 I 1 I r

3 iterations l 4 ? ! 6 1 O 1 4 4 1 2 1 7 3 5 0 1 O 1 6 4 1 6 1

Table 5.2: Error Profile for the Brute Force IIC algorithm using 3-degree Gold code at an SNR of 5dB

1

#3 84 3

#l 2038 797

#9 106 9

#a 81178 8978

#4 2120 830

#5 105 9

#6 34952

#7 88

#8 1944

53250 1 4 847

the second and the sixth user at each successive stage. This alternating phenomenon

is the key reason for the slow convergence. and the esplanation for this phenomenon

is as follows.

In order to obtain performance gain through the use of the parallel interference

cancellation algorithm, the A,I-kI estimation used must be relatively more reliable than

the received signal for the user in question. That is, the decoder decisions made for

the interfering users must be more reliable than the decoder decisions made for the

user in question. For the case shown in Table 5.2, performing IC on the second user

at the first iteration removes most of the MAI and resuits in fewer errors because

the estimated k1--1 is obtained from relatively reliable sources. On the other hand,

performing IC on the s ~ x t h user worsens its performance due to the unreliable 11-41

estimation caused bu the second user. Recail from Equation (2.13) that an incorrect

bit decision made for a particular user doubles its MAI contribution and further

degrades the quality of signal in question. Since the cross-correlation value between

the second user and the s h t h user is large. i.e., f i s = - k. I . the degradation caused

by an incorrect decision is detrimental. Therefore, at the end of the first iterative

IC stage. the sixth user resuits in more errors than its previous stage. Follo~ving the

same arguments, the sisth user results in fewer errors but the second user results in

more errors at the end of the second iteration. This situation keeps alternating until

the IC algorithm or the decoder makes no further improvement. Xotice that this

alternating phenomenon does not occur for users other than those mentioned above.

This is mainly due to the good crosçcorrelation properties between the other users

and the two aforementioned users. Therefore, the impact of performing IC using

incorrect estimates of both the second and the sixth users is not as detrimental.

-At a first glance. one might believe that serial caricellation is the best candidate

for solving the aforementioned problem. Serial cancellation works weli when the users

are received with unequal power strengths. In such a case. stronger users are usually

the reliable users and they contribute a larger percentage of the interference power

toward the nreaker users. Howevert in a case n-hen each user pair has its ou-n cross-

correlation. the reliable users are those who interfere other users the least 11-hile the

unreliable users are those who interfere others the most. Therefore. these two cases

are not equiwient. Fortunatelx a somewhat similar approach can be employed to

lower the initial BER for the two dominant interfering users to accelerate con\-ergence.

The algorithm used n-il1 be called the preliminary IC algorithm.

The preliminary IC algonthm is ernployed pnor to the regular IIC algorithm to

improve the initial XI,U estimation for a feu7 selected users. These users are usu-

ally the dominant interfering users and are determined by the cross-correlation ma-

trix. Starting with the most dominant interfering user. the preliminary IC algorithm

successively improves the fidelity of the estimated MAI for the user in question by

utilizing the result obtained from the previous stage of this algorithm. Figure 5.2

illustrates the procedures of a Su-user preliminary IC algorithm. Suppose the mobile

users are ranked with a lower index indicating a more unreliable user. The prelim-

inary IC is a simplified 4L-stage parallel IC algorithm where neither decoding nor

encoding procedures are involved. It uses the initial decoder decisions to improve

the estimation on the matched-filter outputs for the first ,Y, users on a user-by-user

b a i s and provides an improved -\LAI estimate at the end of the algorithm. Recall -0

that bj = [ bYl0 . . . &?-'*O ] denotes the estirnated received sequence for the j th -re f ined

user based on initial decoder decisions. Let b, = [ $.re fined 'L,- ivre fined ... b, 1 be the refinement of $ resulting from the preliminary IC algorithm. ;\t each stage

-re f ined x, 15 x 5 Xu, o, is obtained frorn an IC process for the user in question using

-re f ined -0 the refined received sequences 4, . I 5 n 5 rr - 1. and the original sequences on, x 5 n 5 1%. The algorithm continues for each user in succession until al1 -\-u users

are considered.

The procedure of the brute force IIC algorithm with a Su-stage preliminary IC

prior to its first iteration is formulated as follows:

Step(l) Initialization:

Figure 5.2: The &stage Preliminap Interference Cancellation .Algorithm

Step(2) Obtaining results from the initial decoding procedure

for 1 5 n 5 Nu -0 Y , = &

ü0 = decode (II-1 (2)) -n -0 on = n (e7zc.de (Q )

S tep (3) Preliminary IC algorit hm:

(i) Ini tialization:

for 1 5 n 5 AT,

iref incd - -0 -n - bn

(ii) Recursive algorit hm:

aref ined hr -re f ined

-x = EjZl Pjz bj bref incd -z = sgn (% - -r arefined)

(iii) Result Update:

for 1 < n 5 !Vu

Step(4) Proceed with regular Brute Force IIC algorit hm:

for 15 n < i& -k- 1

?jk = - gn -n

Ü" ddecode (II-1 (Q")) -n 4

-k on = il (encode (g:))

for l < n 5 1%

2 2 5 3 3.5 4 4.5 5 SNR (dB)

Figure 5.3: Performance of the Brute Force IC on a 9-user system with processing gain

IIC Algorithm with a 2-stage preliminary of 7, spreading with Gold sequences.

3' = p u -n ) = i j # n Pjn . bj

Step(5) Final decisions:

for 1 5 n 5 hYu

- -.ch' I n - -n

Figure 5.3 shows the performance of a 9-user CDMh srstem with a 2-stage prelimi-

nary IC algorithm prior to the first iterative stage of the regular IIC algorithm. The

two selected users are the second user and the sisth user gken in Table 5.2 according

to the cross-correlation matris in Equation (3.2). It is shown in Figure 5.2 that an

accelerated rate of convergence is pursuant which is attnbuted to the use of the pre-

liminary IC algorithm. Kote also that only 5 iterations are required for converging to

the single-user bound when the SXR is equal to 4.5dB. The improved performance

is obtained by an estra step that searches for the dominant interfering users. Notice

that the prelirninary IC algorithm does not require the decoding, encoding, interleav-

ing and deinterleaving procedures. Therefore. the delay incurred is minimal when

compared to the regular IIC aigorithm.

Partial interference cancellation or soft interference canceilation can also be a p

plied to the prelimina- IC algorithm as a further enhancement. Interference can-

cellation using the partiai preliminary IC algorithm is formulated by modifying the

third step from the ordinary p re i iminq IC algorithm as fol!ows:

Step(3)Preliminary IC algorithm:

(i) Initializat ion:

for 1 5 n 5 -Nu

iref lned -n = b0 -n

(ii) Recursive algorit hm:

f o r l ~ x < X ' ,

aref ined hU -r = YTe El=lj+r P ~ Z - -j irefined - te f ined k = sgn (& - -r arefined)

(iii) Result C'pdate:

where yPre denotes the fraction to cancel for the prelirnin ; IC dgorithm.

The soft preliminaq IC cancellation is formuiated by modifying the same step as

Step (3) Preliminary IC algorit hm:

(i) Initialization:

-re f ined -O - on - bn

(ii) Recursive algorithm:

(iii) Result Update:

,PO = pu -n j=ij+n P j n mdti

where 40, denotes the reliability sequence for the nth user gimn by the initial decoding

procedure and rnulti(at b) denotes element-by-element multiplication of vector a and

vector 6.

2 5 3 35 4 5 SNR (dB)

Figure 5.4: Performance of the Brute Force IIC Algorithm combined with a 2-stage Partial Pre l iminq IC on a 9-user system with processing gain of 7. spreading with Gold sequences.

Figures 5.4 and 5.5 demonstrate the performance of using partial preliminary

cancellation and soft preliminary cancellation, respectively. Both algorithms converge

to the single-user performance bound in 4 iterations at an SXR of 4.5dB. For the case

in Figure 5.5. the soft preliminary IC algorithm converges faster in the low-SNR

Figure 5.5: Performance of the Brute Force IIC AIgorithm combined with a 2-stage Soft Preliminary ZC on a 9-user system with processing gain of 7. spreading with Gold sequences.

Figure 5.6: Performance of the MMSE pre-processor on a 9-user system with pro-

I

Y

cessing gain of 7, spreading with Gold sequences.

1 o4

+ convenhonal recenier 4 MMSE Deimor

1 f 1

2 25 3 3.5 4 4 5 5 SNR (dB)

region.

-4 pre-processor can also be used in combination with the preliminary and the

i t erative IC algorit hm. However, the cross-correlation m a t r k given in Equat ion (3 2 )

is a singular matrix: therefore. only the MMSE pre-processor can be applied. Figure

5.6 demonstrates the performance of the bIbISE receiver. It shows that the gain

in performance in this particular case is v e l insignificant. Therefore. no work was

pursued in this direction. However: the use of the preliminary IC algorithm improves

the convergence by 3 iterations at an SNR of 4.5dB and ion-ers the threshold by O.5dB.

5 2 . 2 Spreading with Kasami sequences

Different Kasami code sets can be applied to a CDM-4 system for long spreading.

To ease irnplernentati~n~ the set with the smallest degree that gives sufficient code

sequences should be considered. Based on this criterion. the 8-degree Kasami set

of 16 available sequences each with period length of 255 is selected. The primitive

polj-nomial that generates the chosen Kasarni set is f ( D ) = 1 + D2 + D3 + D4 + Da. Since the period length of the spreading sequences esceeds the processing gain of the

system. consecutive segments of the Kasami sequences are used for spreading each

data symbol. The simulation result using a brute force IIC for a 9-user CDM-4 system

is shown in Figure 5.7.

Figure 5.7 shows that the brute force IIC algorithm requires a minimum SKR of

4dB to get some satisfactory performance gain. Jllso' a t an SNR of 4.5dB: 8 iterations

are needed for the algorithm to converge to the single-user performance bound. The

least satisfactory performance in this case is due to the Iarge cross-correlation d u e s

between the spreading sequences. Since only segments of the Kasami sequences are

used for spreading. the good cross-correlation properties of the Kasami familj. cannot

Figure 5.7: Performance of the Brute Force IIC algorithm on a 9-user system with processing gain of 7, spreading with Kasami sequences.

be maintained. -4 typical cross-correlation matris obtained from the simulation is

Figure 5.8 shows the simulation result of using a partial cancellation algorithm

with cancellation fractions of 60% for the first iteration and 100% for the remaining

iterations. Total convergence requires 4 iterations at an SNR of 4.5dB for this algo-

rithm. which is an improvement of 4 iterations n-hen compared to the brute force IIC

algorithm. Note that the threshold SNR is also lowered from 4dB to 3.5dB.

The performance of the soft IIC algorithm on Kasami sequences is shown in Figure

9 In the high-SNR region. the soft algorithm gives similar performance as the

Figure 5.8: Performance of the Partial IIC Algorithm on a 9-user system 111th pro- cessing gain of 7, spreading with Kasami sequences.

SNR (dB)

Figure 5.9: Performance of the Soft IIC -Algorithm on a 9-user system with processing gain of 7: spreading with Kasami sequences.

Figure 5.10: Performance of the Pre-processor-aided Brute Force IIC algorithm on a 9-user system nith processing gain of 7, spreading with Kasami sequences.

partial algorithm. In the lon-SNR region. the soft algonthm performs significantly

better. The threshold SNR is further lowered to 3dB by the soft IIC algorithm.

Pre-processing can also be applied to each IIC algorithm to achieve better per-

formance. Figure 5.10 shows the result of using a XISISE pre-processor in combi-

nation with the brute force IIC algorithm. Only 3 iterations are required for such

an algorithm to converge to the single-user bound at an SYR of 4.5dB. which is an

improvement of 1 iteration relative to the partial IIC case and 5 iterations relative

to the brute force case. Howec-er, the improvement is obtained at the espense of

increased computational complesity. In the case of Kasami codes ( N = 255) and the

estended S(2) codes ( N = 256) to follow. the matrix (R + 91~") in Equation (3.16)

must be computed and inverted on a symbol-by-symbol basis. The pre-processor mas

not used for the short Gold code. but if it is used. the MMSE matris is required to

be computed once.

Figures 5.1 1 and 5.12 show the performance of using a MMSE pre-processor in

Figure 5.1 1 : Performance of the Pre-pmcessor-aided Partial IIC Algorithm on a 9- user system with processing gain of 7: spreading nith Kasami sequences.

SNR (dB)

Figure 3.12: Performance of the Pre-processor-aided Soft IIC -4lgorithm on a 9-user system with processing gain of 7. spreading wit h Kasami sequences.

-e- average MMSE receiver

IO-= I I 1

2 25 3 3.5 4 4 5 5 SNR (dB)

Figure 5.13: A cornparison on average hISISE detector and optimal MMSE detector

combination with the partial cancellation and the soft cancellation algorithm. respec-

tivel. Both algorithms accelerate the convergence rate especially in the Ion-SNR

region. The threshold SSR is lowered to 3dB for the partial IIC case and 2.5dB for

the soft IIC case.

Instead of using a different 31MSE pre-processor for each symbol interval, the

performance of using an average &I.\ilSE pre-processor is studied. The average MXISE

pre-processor is obtained by

where R = EL, R' is the average cross-correlation matris. iV is the period length

of the spreading sequence. R' is given in Equation(2.27). 2 is power spectral density

of the noise in -4IVGX cchannel. and Inru is an ArK x i\i, identity matrix Figure 5.13

compares the performance of the conventional receiver: the average MMSE receiver

and the optimal MMSE receiver. The figure shows that the average MMSE receiver

is quite inferior to both the optimal MMSE receiver and the conventional receiver.

Figure 5.11: Performance of the Pre-processor-aided Soft IIC .Algorithm on a 10-user system with processing gain of 7. spreading with Kasami sequences.

Figure 5-15: Performance of the Pre-processor-aided Soft IIC Algorithm on a Il-user system \vit h processing gain of 7. spreading wi t h Kasami sequences.

With the optimal h1XfSE pre-processor. more than 9 users can be supported using

the soft IIC algorithm. Figure 5.14 and 5-15 show the simulation resuits for a 10- and

Il-user system, respectivel. At an SNR of 4.5dB, 4 iterations are required to achieve

the desired performance tevel for the 10-user -stem. However. many iterations are

required for the Il-user system to achieve the same performance level. Sote that

an SNR of at l e s t 3.5dB is needed to get an- reasonable performance gain for the

10-user system.

5.2.3 Spreading with extended S (2) sequences

The implementation i>f the estended S(2) code ntas presented in Chapter 1. Adopted

by the 3GPP group. this code family is designed to give a large number of sequences

with good cross-correlation properties (361.

The extended S(2) family with period length rV = 236 has 2*" - 1 available code

sequences. Each user selects its spreading sequence according to its user number.

Figure 5.16 demonstrates the performance of the brute force IIC algorithm on

a 9-user system spreading with extended S(2) sequences. -At an SYR of 4.5dB, 5

iterations are needed to converge to the single-user bound. Comparing to the case

when Kasami sequences are used (see Figure 5.7) . the estended S(Z) codes perform

relatively better. Fewer number of iterations are required for the system employing

the estended S(2) sequences to converge to the single-user bound at any given SXR.

Figures 5.17 and 5.18 demonstrate the performance of the partial and soft inter-

ference cancellation algorithms. respectivel. Total convergence requires 3 iterations

for the partial algorithm and 4 iterations for the soft algorithm a t an SXR of 4.SdB.

These 2 algorithms both lower the threshold SXR from 3.5dB to 2.5dB when com-

pared to the brute force case. Xotice that the partial IIC algorithm converges faster

in the high-SNR region for this case. When the decoder decisions on the interfering

users are reliable, a large cancellation fraction gives better performance than a small

one. Thus, soft IIC may not give better results when compared to the partial IIC in

2 2 5 3 3 5 4 5 SNR (dB)

Figure 5.16: Performance of the Brute Force IIC Algorithm on a 9-user system with processing gain of 7: spreading mith estended S(2) sequences.

4 1 ilerahon. oInb Parbal 1C 1 O* 4 2 flCrah0ftS

j -& 3 rterabons . +- 4 ~leralions . - 5 itemions

2 2.5 3 3.5 4 4 5 5

Figure 5.17: Performance of the Partial IIC -Algorithm on a 9-user system with processing gain of 7: spreading with extended S(2) sequences.

Figure 5.18: Performance of the Soft IIC Algorithm on a 9-user system with process- ing gain of 7, spreading with estended S(2) sequences.

the high-SNR region.

Figure 5-19 shows the performance of the pre-processor-aided brute force IIC

algorithm. Only 3 iterations are needed at an SNR of 4.5 dB to converge to the

single-user bound. which is an irnprovement of 2 iterations compared to the non pre-

processed case in Figure 3.16. Compared to the soft IIC case in Figure 5.18: the

pre-processor-aided brute force algorithm does not perform as me11 in the low-SNR

region. The t hreshold SXR for the pre-processor-aided brute force algorithm and the

soft IIC algorithm are about 3.5 and 2.5 dB. respectively.

\frithout the aid of the pre-processor, the systern that employs soft IIC can support

11 users. Figures 5.20 and 3.21 demonstrate the performance of a 10- and Il-user

system. respectively. For the IO-user system. 6 iterations are required at an SXR of

4.5dB to achieve a BER of IO-". For the Il-user system. T iterations arc required.

The threshold SKR for these 2 systems are 3dB and 3.5dB. respectively.

With the aid of the pre-processor, the Il-user system ernploying the soft IIC al-

Figure 5.19: Performance of the Pre-processor-aided Brute Force IIC -Aigorithm on a 9-user systern with processing gain of 7: spreading n-ith estended S(2) sequences.

SNR (dB)

Figure 5.20: Performance of the Soft IIC -Algorithm on a 10-user system cessing gain of 7, spreading with extended S(2) sequences.

with pro-

Figure cessing

5.21: Performance of the Soft IIC algorithm on a Il-user systern gain of 7. spreading with estended S(2) sequences.

with pro-

Figure 5.22: Performance of the Pre-processor-aided Safi IIC algorithm on a Il-user systern with processing gain of 7: spreading with extended S(2) sequences.

Figure 5.23: Performance of the Pre-pmcessor-aided Soft IIC algorithm on a 12-user system with processing gain of 7. spreading with extended S(2) sequences.

gorithm requires only 5 iterations to converge to the single-user performance bound

at a n SNR of 4.3dE. Figure 5.22 demonstrates the simulation result of such a sys-

tem. Note that the operating SXR has to be above 3.5dB to obtain any reasonable

performance gain. Csing the same algorithm. it is also possible to support 12 users.

The pre-processor-aided soft IIC algorithm requires T iterations at an SNR of 4.5dB

for the 12-user system to converge to the single-user bound.

5.3 Multi-user Interference Cancellation with In- creased Processing Gain

It is desirable to compare the performance of the IIC algorithm on a system with a

different code rate and a different processing gain. In this section. the performance of

the iterative interference cancellation algorithms with a larger processing gain using

both rate-$ and rate-f convolutional codes are esamined. The uncoded processing

gain considered is 30 such that the coded processing gain obtained from Equation (

5.1) are 15 and 10 for the rate-; and rate-$ code. respectively. The spreading code

farnily considered in this section is the extended S(2) code. It is shown in the previous

section that the systeïn using the estended S(2) sequences gkes superior performance

to those using the Gold or Kasami sequences.

To achieve a performance level of BER=10-'. the rate-?. constraint length 7. con-

volutional coded system employing conventional detector can support 6 simultaneous

users ulth a required SNR of 4.5dB.

Figure 5.24 demonstrates the performance of the brute force IIC algorithm on

a lbuser system using rate 4 convolutional code with coded processing gain of 15.

To achieve a BER of IO-': 4 iterations are needed for the brute force algorithm to

converge to the single-user performance at an SNR of 4.5dB. Sotice that the number

of user that can be simultaneously supported by the CDM-4 system employing IIC

algorithm is tripled when the uncoded processing gain is increased to 30.

Figure 5.25 demonstrates the performance of the brute force IIC algorithm on a

18-user system using rate-) code. The FEC code considered is the constraint length

9 convolutional code with generators (557.663.711) in octal. To achieve the desired

performance level. Le.. BER=10-'. 4 iterations. determined from Figure 5.25. are

required at an SKR of 3.5dB. Thus. the performance gain in terms of the convergence

rate obtained by using a lower rate code is insignificant. Hon-ever. the rate f code

requires a lower SXR to achieve the same performance level. This gain is obtained at

an increased computational complexity at the decoders.

5.4 Chapter Summary

The performance of the IIC algorithms with different spreading sequences are studied.

When the 3-degree Gold spreading sequences are used, the regular IIC algorithm fails

to provide a satisfactory performance. To solve this problem, a preliminary IC algo-

rithm is developed to accelerate the convergence rate. Using the partial preliminary

IC algorithm on a 9-user system. an improvement of 3 iterations is obtained at an

SNR (dB)

Figure 5.24: Performance of the Brute Force IIC Algorithm on a 18-user system using rate-; convolutional code with uncoded processing gain of 30

4 1 neratcon IO" 7 + 2 mations

I 4- 3 Rerarions + 4 ctara0ons

22 2 4 2.6 28 3 32 3.4 3.6 3.8 4 SNR (dB)

Figure 3.25: Performance of the Brute Force IIC Algorithm on a 18-user system using rate-+ convolutional code with uncoded processing gain of 30

SNR of 4.5dB.

IVhen the 8-degree Kasami spreading sequences are used. the best result is ob-

tained by using the pre-processor-aided soft IIC algorithm. The coefficients of the

pre-processor need to be updzted at every s-vmbol interval which increases the corn-

plesity of this algorithm significantly. For a 9-user system, the soft IIC algorithm

without pre-processing is only 1 iteration inferior to the one with pre-processing.

With the pre-processor-aided soft IIC algorithm, 10 users are possible at an SNR of

4.5dB with 4 iterations.

When the extended S(2) sequences are used. the soft IIC algorithm without the

aid of the pre-processor gives satisfactory performance on a 9-user system. Only 4

iterations are required for the ?stem to achieve the single-user performance at an

SXR of 4.5dB. To support 11 users, the pre-procesor-aided soft IIC algorithm is

needed for the system to converge in a reasonable number of iterations. In particuiar.

5 iterations are required at an SNR of 4.5dB.

For the system with uncoded processing gain of 30, the brute force IIC algonthm

on the rate-; coded system can support 18 users . When the rate-? code is employed.

a lower SNR can be used to obtain similar performance.

Chapter 6

Conclusions

6.1 Conclusions

The performance of muhi-user interference cancellation algorithms in a convolutional

coded CDM-4 system was evaluated in this thesis. The following points summarize

the major results:

1. For the AWGK channel, the use of an iterative interference cancellation algo-

rithm can double the number of high-bit-rate users in WCD3.I-1. In the case of

Gold codes, 9 users can be supported 11-hen the soft preliminary IC algorithm

is employed. in the case of Kasami codes. 10 users can be supported when the

pre-procesor-aided soft IIC algorithm is used. For the same algorithm, 11 users

can be supported in the case of extended S(2) codes.

2. The use of the 3-degree Gold spreading sequences demonstrates a phenornenon

where a particular user signature sequence esperiences much stronger interfer-

ence than other users in the system. In this case, the preliminary IC algorithm

is required to obtain satisfactory performance.

3. The performance of IIC on the estended S(2) codes is superior to that of the

Kasami codes. For each IC scheme. fewer number of iterations are required for

the system empIoying estended S(2) sequences to converge to the single-user

performance bound.

4. The amount of improvement obtained frorn the pre-processor-aided IIC varies

wit h the channel characteristics such as the cross-correlation values. In the

case of the Gold spreading sequences, the performance gain £rom using a pre-

processor is very insigdcant. On the other hand, improvements of a iterations

for the Kasami sequences and 2 iterations for the extended S(2) sequences are

O btained when compared to the non-pre-processed cases.

6.2 Suggestions for F'uture Work

The use of iterative interference cancellation algorithrns was shown to increase

user capacity of the CDMA system. Such results were obtained by cornputer

simulations that assumed perfect carrier and timing s~chronizat ion. One

should investigate the sensitivity of these algorithms without these assump

tions.

Perfect power control was also assumed in this thesis. One should consider

studying these algorithms with power control error.

In order to perform MUD: the knowledge of channel parameters are required. It

would be desirable to combine channel estimation with interference cancellation

and study the sensitivity of estimation error.

The work in this thesis was focused on the .4WGN channel. It would be desirable

to study the IIC algorithms under a channel model that includes shadow fading.

The CDM-4 model used in this thesis was idealized. I t would be desirable to

apply the IIC algorithm to a cellular structure with both inter-ce11 and intra-ce11

interference.

The performance of the soh IIC algorithm in this thesis was studied based on

the use of the SOV-4 decoding algorithm. It would be desirable to study the

same algorithm using the MAP decoder.

92

7. The spreading codes used in practice are designed without having hfUD in mind.

These spreading codes may not give the best performance under the LlLD

algorithms. For instance. the performance gain of using MMSE detector for a

system using Gold spreading sequences and a system using Kasami spreading

sequences are significantly different. This is due to the structural differences

in the crosscorrelation matrk- Therefore. it is desirable to design spreading

sequences that are optimized for MUD.

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Appendix A

Approximat ing the cross-correlat ion p

Based on the use of the Gaussian approximationo the average BER of a tj-pical CDM-4

system can be approximated by [dl]

(A. 1)

mhen the MAI is the dorninating noise.

Consider a discrete Nu-user CDbIA system nith identical cross-correlation value

p. The matched-filter output of the j th user is given by yj = bj + O j + nj. where 6,

is the desired information. 0, = x;ginw p - b, is the MAI. and nj is the Gaussian

noise. When AT, is large, dj can be modeled, based on the Central Limit Theorem.

by a zero-mean Gaussian random variable with variance od, shere

In the interference-limited case where the ILAI is dominating noise. the average

bit error probability of such system is approximated by

* -ta-/?

where Q ( x ) denotes 1: .%du.

The cross-correlation value p is appro-ximated bu equating (-4.1) and (-4.3).

In our typical CDM-4 system with processing gain of 7, the cross-correlation p is

approximately equal to 0.22.

Appendix B

Simulations and the Confidence Int ervals

The simulation results presented in this thesis are obtained based on the Monte-Carlo

method. To get an indication of the accuracy of the simulation results. the statistical

confidence intervals were used. The number of simulation trials (number of bits sent)

required to achieve a desired confidence level were derived in [49] using the Chernoff

bound. Table B.1 re-states the results obtained in [19].

The simulation results in this thesis are aimed such that the siniulated BER is

within 3~30% of the true BER with 95% confidence. To achieve the target confidence

level. a minimum of 8.98 x 106 trials are required for a BER of IO-'. Thus. the

simulations in this thesis use a bit Stream of 1 x 10' bits.

1 BER ( 95% certain / 95% certain 1 95% certain 1 99% certain 1 within 30% ( within 20% within 10% within 10%

10-' 8.00 x 102 1 1.755 x 103 6.833 x lo3 9.814 x 104 IO-' 8.88 x lo3 1 1.943 x 104 7.541 x 104 1.083 x 105

Table B.l: The number of bits required to achieve different confidence intervals