Intelligent receivers for

multi-user CDMA systems

By

Zhifeng Yun

SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF MSC

IN RADIO FREQUENCY COMMUNICATION SYSTEMS

AT

UNIVERSITY OF SOUTHAMPTON

SOUTHAMPTON, SO17 1BJ, UK

OCTOBER 2005

© Copyright by Zhifeng Yun, 2005

UNIVERSITY OF SOUTHAMPTON

SCHOOL OF

ELECTRONICS AND COMPUTER SCIENCE

The undersigned hereby certify that they have read and

recommend to the Faculty of Engineering and Applied Science for

acceptance a thesis entitled “Intelligent receivers for multi-user CDMA

systems” by Zhifeng Yun in partial fulfillment of the requirements for the

degree of MSc in Radio Frequency Communication Systems.

Dated: October 2005

Supervisor: Lajos Hanzo

ii

UNIVERSITY OF SOUTHAMPTON

Date: October 2005

Author: Zhifeng Yun

Title: Intelligent receivers for multi-user CDMA systems

School: Electronics and Computer Science

Degree: M.Sc. Convocation: July Year: 2006

Permission is herewith granted to University of Southampton to circulate and to

have copied for non-commercial purposes, at its discretion, the above title upon the

request of individuals or institutions.

Signature of Author THE AUTHOR RESERVES OTHER PUBLICATION RIGHTS, AND NEITHER THE THESIS NOR EXTENSIVE EXTRACTS FROM IT MAY BE PRINTED OR OTHERWISE REPRODUCED WITHOUT THE AUTHOR’S WRITTEN PERMISSION. THE AUTHOR ATTESTS THAT PERMISSION HAS BEEN OBTAINED FOR THE USE OF ANY COPYRIGHTED MATERIAL APPEARING IN THIS THESIS (OTHER THAN BRIEF EXCERPTS REQUIRING ONLY PROPER ACKNOWLEDGEMENT IN SCHOLARLY WRITING) AND THAT ALL SUCH USE IS CLEARLY ACKNOWLEDGED.

iii

Table of Contents Table of Contents ............................................................................................................. iv List of Figures................................................................................................................... vi Abstract.............................................................................................................................. x Acknowledgement ............................................................................................................ xi Introduction....................................................................................................................... 1 Chapter 1 ........................................................................................................................... 4 Overview of DS-CDMA System....................................................................................... 4 1.1 Description of the DS-CDMA System ......................................................................... 4 1.2 Multiple Access Interference ........................................................................................ 5 1.3 Different Methods to Combat the MAI ........................................................................ 7 1.4 Different Ways to Compensate Time Varying and Multi-path Fading ........................ 9 Chapter 2 Mobile Radio Channel Models .................................................................. 11 2.1 Additive White Gaussian Noise (AWGN) Channel ................................................... 11 2.2 Rayleigh Fading Channel............................................................................................ 13

2.2.1 Uncorrelated Rayleigh Fading Channel........................................................... 13 2.2.2 Correlated Rayleigh Fading Channel............................................................... 15

2.3 Summary ..................................................................................................................... 17 Chapter 3 ......................................................................................................................... 18 Successive Interference Cancellation and Parallel Interference Cancellation.......... 18 3.1 Successive Interference Cancellation ......................................................................... 18

3.1.1 Successive Interference Cancellation Algorithm and Implementation............ 18 3.1.2 Complexity Calculation of Successive Interference Cancellation................... 21 3.1.3 Simulation Results of Successive Interference Cancellation........................... 24

3.2 Parallel Interference Cancellation............................................................................... 26 3.2.1 Parallel Interference Cancellation Algorithm and Implementation ................. 26 3.2.2 Complexity Calculation of Parallel Interference Cancellation ........................ 30 3.2.3 Simulation Results of Parallel Interference Cancellation ................................ 33

3.3 Comparison of Different Multi-user detections.......................................................... 37 3.3.1 Simulation Results ........................................................................................... 37 3.3.2 Comparison of Different Detection Schemes .................................................. 40

3.4 Summary ..................................................................................................................... 41 Chapter 4 ......................................................................................................................... 42 Reduced multi-user channel estimation and detection algorithm.............................. 42 4.1 Introduction to Multi-user Channel Estimation and Detection................................... 42 4.2 System Model ............................................................................................................. 44

4.2.1 Received Signals Model .................................................................................. 45 4.2.2 Maximum Likelihood Multi-user Channel Estimation.................................... 46 4.2.3 Multi-user Detection ........................................................................................ 47

4.3 Iterative Implement of the ML Channel Estimation ................................................... 47

iv

4.3.1 Iterative Schemes for Channel Estimation ...................................................... 48 4.3.2 Simulation Results of the Iterative Schemes ................................................... 49

4.4 Pipelined Multi-user Detection ................................................................................... 51 4.4.1 Pipelined PIC Detector ................................................................................... 52 4.4.2 Simulation Results of the Pipelined PIC Detector........................................... 54

4.5 Summary ..................................................................................................................... 56 Chapter 5 Spatial Diversity Techniques ...................................................................... 57 5.1 Multiple Transmit and/or Receive Antennas .............................................................. 57

5.1.1 Single Transmit Antenna and Multiple Receive Antennas-Based System...... 57 5.1.2 Multiple Transmit Antennas and Single Receive Antenna-Based System...... 58 5.1.3 Multiple Transmit and Receive Antennas-Based System................................ 59

5.2 Multi-Relay System ................................................................................................... 61 5.2.1 Introduction to Multi-Relay System ................................................................ 61 5.2.2 System Model .................................................................................................. 63 5.2.3 Mathematical Analysis of the Multi-relay System .......................................... 65 5.2.4 Simulation Results ........................................................................................... 68 5.2.5 Extensions and Future Work............................................................................ 71

5.3 Summary ..................................................................................................................... 73 Conclusion ....................................................................................................................... 74 Bibliography .................................................................................................................... 76

v

List of Figures 1.1.1 Block diagram of a simple asynchronous DS-CDMA system over a Gaussian

channel…………………………………………………………………………….4

1.3.1 Matched filter bank……………………………………………………...…….......8

2.1.1 The PSD of AWGN noise (fs=2*106, t=0.1s)……………………………………..12

2.1.2 Normalized Gaussian amplitude PDF and CDF…………………………………..12

2.2.1 Baseband Uncorrelated Rayleigh-fading simulation model……………………...13

2.2.2 Simulated amplitude and the phase of the Uncrrelated Rayleigh fading channel

…………………………………………………………………………………….14

2.2.3 Simulated Uncorrelated Rayleigh PDF and CDF curve………………………....14

2.2.4 Simulated amplitude and phase of the Correlated Rayleigh channel……………15

2.2.5 Simulated amplitude of the Correlated Rayleigh channel when several paths

added together…………………………………………………………………..16

2.2.6 Envelope of correlated and uncorrelated Rayleigh channel with normalize

Doppler frequency shift 10-4…..………………………………………………...17

3.1.1 A schematic of the first three stage of the successive interference cancellation

(SIC) receiver for K users. The user’s signals r at the output of the former stage

which have been ranked, where the first user’s signal has the highest power. In

order to rank the signals, the data estimates of each user are obtained and the

received signal of each user is reconstructed and cancelled from the received

composite signal.………………………………………………………………...19

3.1.2 Simulation-based BER versus the SNR per bit, Eb/N0. performance of multi-stage

SIC detector for DS-CDMA system supporting 7 users using BPSK modulation

over AWGN channel, where using m-sequence and SF=7 is the length of

spreading sequence………………………………………………………………24

3.1.3 Simulation-based BER versus the SNR per bit, Eb/N0. performance of multi-stage

SIC detector for DS-CDMA system supporting 7 users using BPSK modulation

vi

over uncorrelated Rayleigh channel, where using m-sequence and SF=7 is the

length of spreading sequence…………………………………………...……….25

3.2.1 A scheme of the first two stages of the parallel interference cancellation (PIC)

receiver for K users. The data decision, d , , are the output of the

current stage and the input of the next stage. In each stage, the received signals of

all other users except the desired user’s are reconstructed and cancelled from the

received composite signals,

i (0) di (1) di (2)

r(t) ……………..…………………………………26

3.2.2 Comparison of the calculation complexity (in number of multiplications and

additions) of SIC, PIC and MMSE with the length of spreading sequence SF=31

and the number of bits of each user equals to 10^5……………………………..32

3.2.3 Simulation-based BER versus the SNR per bit, Eb/N0. performance of multi-stage

PIC detector for DS-CDMA system supporting 20 users using BPSK modulation

over AWGN channel, where using gold sequence and SF=31 is the length of

spreading sequence………………………………………………………………33

3.2.4 Simulation-based BER versus the SNR per bit, Eb/N0. performance of multi-stage

PIC detector for DS-CDMA system supporting 20 users using BPSK modulation

over uncorrelated Rayleigh channel, where using gold sequence and SF=31 is the

length of spreading sequence……………………………………………………34

3.2.5 Comparison of the performance of multi-stage PIC detector for DS-CDMA

system supporting 20 users using SF=31 gold sequence and BPSK modulation

over AWGN channel, while using correlation and MMSE as the stage 0………35

3.2.6 Comparison of the performance of multi-stage PIC detector for DS-CDMA

system supporting 20 users using SF=31 gold sequence and BPSK modulation

over uncorrelated Rayleigh channel, while using correlation and MMSE as the

stage 0……………………………………………………………………………36

3.3.1 Simulation-based BER versus the SNR per bit, Eb/N0. performance of different

MUD methods for DS-CDMA of 5 users using BPSK modulation over AWGN

channel, using the m-sequence where SF=7…………………………………….37

3.3.2 Simulation-based BER versus the SNR per bit, Eb/N0. performance of different

MUD methods for DS-CDMA of 5 users using BPSK modulation over

uncorrelated Rayleigh channel, using the m-sequence where SF=7…………….38

vii

3.3.3 Simulation-based BER versus the number of users performance of different MUD

methods for DS-CDMA at SNR=10dB using BPSK modulation over

uncorrelated Rayleigh channel, using the gold sequence where SF=15………...39

4.2.1 Block diagram of the system model of the multi-user channel estimation and

detection in the receiver. The training sequence (pilot) is used for channel

estimation and decision feedback is used to update the estimates in the absence of

a pilot…………………………………………………………………………….44

4.2.2 Block diagram of the decision feedback mode…………………………………..45

4.2.3 The received signal mode at the output of the multi-path channel………………46

4.3.1 Comparison of BER performance of different estimation schemes versus different

preamble length at the SNR=10dB, Walsh code, SF=16, 7 equal power users....50

4.3.2 Comparison of the BER performance of the proposed iterative scheme and the

matrix inversion scheme at the slow fading channel of 10km/h mobile velocity

with the carrier frequency 1.8GHz. The pilot length equals to 128……………..51

4.4.1 Block diagram of the pipelined implementation of multi-user channel estimation

and detection…………………………………………………………...………..53

4.4.2 Simulation-based BER versus the SNR per bit, Eb/N0. performance of this

combined iterative multi-user channel estimation and pipelined PIC detector for

DS-CDMA using BPSK modulation over AWGN channel with 3 different paths,

where SF=32 is the length of spreading sequence (Walsh code) and K=15 is the

number of users, u=1/256, L=128 is the preamble length…………………..….54

4.4.3 Comparison of the BER versus the SNR per bit, Eb/N0. performance of this

combined iterative multi-user channel estimation and pipelined PIC detector for

DS-CDMA using BPSK modulation over AWGN channel with 3 different paths,

while using the different preamble length at u=1/256, where SF=32 is the length

of spreading sequence (Walsh code) and K=15 is the number of users…………55

5.1.1 Simulation-based BER versus the SNR per bit, Eb/N0. performance of correlated

detector for DS-CDMA with multiple receivers and single transmitter using

BPSK modulation over uncorrelated Rayleigh channel, where SF =7 is the length

of spreading sequence and K is the number of users…………………..……….58

viii

5.1.2 Simulation-based BER versus the SNR per bit, Eb/N0. performance of correlated

detector for DS-CDMA with multiple transmitters and single receiver using

BPSK modulation over uncorrelated Rayleigh channel, where SF=7 is the length

of spreading sequence and K is the number of users…………..………………..59

5.1.3 Simulation-based BER versus the SNR per bit, Eb/N0. performance of correlated

detector for DS-CDMA with multiple receivers and transmitters using BPSK

modulation over uncorrelated Rayleigh channel, where SF=7 is the length of

spreading sequence and K is the number of users……………………………....60

5.2.1 Amplify and Forward Strategy……………………………………...…………..62

5.2.2 Detect and Forward Strategy………...………………………………………….62

5.2.3 Multi-relay system model………………...……………………………………..64

5.2.4. Simulation-based Average Symbol Error Rate (ASER) performance of different

number of relay stations in the multi-relay system, while K is the number of

relays...…………………………………………………………………………..69

5.2.5 Simulation-based Average Symbol Error Rate (ASER) performance of the multi-

relay system, while there is one single-hop and one two-hop transmissions

between the sender and the destination, to show how exactly the bounds of the

equations (9), (10) can work…………...………………………………………..70

5.2.6 Simulation-based Average Symbol Error Rate (ASER) performance with different

relay gains in the multi-relay system, while K is the number of relays……..….71

ix

Abstract In DS-CDMA system, overcoming the problem of multiple access interference (MAI)

and multi-path fading is imperative to improve the performance. A number of multi-user

detection (MUD) algorithms have been proposed to mitigate the MAI. This report

simulates the performance of two MUD schemes known as successive interference

cancellation (SIC) and parallel interference cancellation (PIC) and compares the

performance with some linear MUD algorithms such as correlating, decorrelator,

minimum mean-squared error (MMSE) and maximum likelihood detection (MLD). The

simulation results illustrate that SIC and PIC can achieve better performance but reduce

the computation complexity. Channel estimation and spatial diversity techniques are

investigated in this report to combat the multi-path fading. A reduced combined multi-

user channel estimation and detection algorithm has been explored, which shows to have

more efficient implementation meanwhile maintain the required performance. Spatial

diversity technique such as multiple transmit and/or receive antennas can be used to

mitigate the effects of the multi-path fading but it need several antennas. Multi-relay

system introduced in this report enables single antenna mobile to benefit from the MIMO

system and has been proofed to be able to achieve full diversity order. From our study we

can draw the conclusion that both these SIC and PIC algorithms, maximum likelihood-

based channel estimation scheme and the spatial diversity techniques are quite effective

in improving the system’s performance, which provide some innovative methods to break

through the limitation imposed by the system.

Index Terms—code-division multiple access (CDMA), parallel interference

cancellation (PIC), successive interference cancellation (SIC), minimum mean-squared

error (MMSE), maximum likelihood (ML), multi-relay system.

x

Acknowledgement I would like to sincerely thank Professor Lajos Hanzo, my personal tutor and my project

supervisor, who always gives me a lot of guidance during my project and plenty of

suggestions at this one-year’s study. I am also grateful for his support for my application.

I would like to express my gratitude to Dr. Lie-Liang Yang for his precious advice of my

project and his help for my application.

I also want to acknowledge my friend, Wei Fang for his help on my study.

At last I want to express my warm appreciation to my family for their support on my live

and study.

xi

Introduction In recent years, personal mobile communication has become as common as the wire line

telephone used to be, and it is able to provide reliable and affordable communications,

anywhere and anytime [1]. Direct-sequence code-division multiple access (DS-CDMA),

performed as a prevalent technique in the third-generation wireless cellular systems, has

got various applications such as optical and wireless communications [2]. In DS-CDMA

systems, each user is allocated a unique spreading code. By assigning different code

sequences to each user, it is possible to allow many users to share the same channel and

frequency simultaneously. DS-CDMA can provide a number of advantages compared to

other techniques. However, the capacity and performance of DS-CDMA systems can be

limited by the mobile channel characteristics and the multiple access interference (MAI)

[3]. The MAI is generated because the dispersion of the channel and the random time

offsets between the signals destroy the synchronization of the user’s signal, leading to

imperfect orthogonality between the spreading sequences of different users. The most

efficient method to combat the MAI is multi-user detection (MUD) [4].

Most of the multi-user detectors can be classified into two categories: linear multi-user

detectors and non-linear multi-user detectors [5]. Linear multi-user detectors, such as the

correlated, decorrelating and minimum mean squared error (MMSE), apply a linear

transformation to the outputs of the matched filter bank to reduce the MAI. Non-linear

multi-user detectors such as successive interference cancellation (SIC) and parallel

interference cancellation (PIC) try to suppress the effects of the MAI by reconstructing

the original transmitted signals of one or more users and then subtract the interference

contributed by these users from the composite received signals [6]. We implement the

SIC and PIC algorithms in this project and compare the performance of these interference

cancellation-based MUD algorithms with some linear MUD algorithms to see which

MUD algorithm can provide a better performance and can work more effectively.

Another factor which will degrade the performance of the system is the time varying and

multi-path fading of the mobile channel. Since the reflection of the signals with the line-

1

of-sight components, there are always multi-path in the channel. Each path will impose

its own delay, attenuation and phase shift to the transmitted signals [7]. The mobility of

the user will cause fading [8]. All these elements make the detection at the receiver

difficult. In order to mitigate these undesirable effects, multi-user channel estimation

should be implemented. Another more efficient way is to combine the multi-user channel

estimation and detection together. [9] and [10] have introduced some subspace-based

techniques which can be used in joint multi-user channel estimation and detection

situation. However, they are very complex in implementation and present a limitation to

the number of users they can deal with. In this project, we implement an iterative channel

estimation scheme based on the maximum likelihood technique and combine it with the

parallel interference cancellation to obtain a more efficient and more accurate way to

realize the channel estimation and multi-user detection.

Spatial diversity is also capable to combat the multi-path fading. Using multiple transmit

and/or receive antennas to achieve spatial diversity has already been acknowledged, and

certain transmit diversity methods have been incorporated into wireless standards [11].

Although spatial diversity is clearly advantageous to improve the capacity, it may not be

practical for other scenarios such as a small mobile which is not able to support multiple

transmit antennas [12]. A recent technique called cooperative communication explored in

the work of [13] and [14] introduces a novel way to enable single-antenna mobiles to

achieve transmit diversity by choosing some nearby idle mobile stations as the relays to

transfer their information signals to the destination. Transmit diversity is gained when the

selected stations retransmit the signals to the destination since the receiver can obtain

some independent versions of the transmitted signal from different locations. In this

project, we will investigate how the system can benefit from this kind of cooperation

based on the work of [15].

We arranged this report into the following chapters. Chapter 1 provides an overview of

the DS-CDMA system, lists the time varying characteristics of the mobile channel and

the MAI and several ways to combat these undesired effects. Chapter 2 presents some

properties of the mobile channels. In chapter 3, we implement the successive interference

cancellation and parallel interference cancellation algorithms and compare the

performance of these two algorithms with some linear multi-user detection algorithms.

2

Chapter 4 explores a reduced multi-user channel estimation and detection algorithm

while the channel estimation is implemented by an iterative scheme based on the

maximum likelihood technique and the multi-user detection is implemented in pipelined.

In chapter 5, we show some results to observe how can the system benefit from the

multiple transmit and/or receive antennas and explore a multi-relay system to verify how

the number of relays can affect the final BER performance.

3

Chapter 1

Overview of DS-CDMA System

1.1 Description of the DS-CDMA System Code division multiple access (CDMA) is a radio communication technique to allow

multiple users to share the same spectrum simultaneously. It is the most investigated

application of spread spectrum techniques [6]. In DS-CDMA (direct-sequence code

division multiple access), the narrowband message is multiplied by a large bandwidth

signal, which is called the spreading signal. The spreading signal is generated by

convolving a pseudo-noise (PN) code with a chip waveform whose duration is much

smaller than the symbol duration [6]. By assigning different code sequences to each user,

it is possible to allow many users to share the same channel and frequency

simultaneously [6].

⊗ ⊗User 1)cos()()()( 111 twtctAdts c=)()( 11 tctd

)(1 tc )cos( twA c

⊗ ⊗)cos()()()( 222 twtctAdts c=)()( 22 tctd

)(2 tc )cos( twA c

⊗ ⊗)cos()()()( twtctAdts cKKK =)()( tctd KK

)(tcK )cos( twA c

User 2

User K

)(1 td

)(tdK

)(2 td

∑ ⊕)(tn

)()()(1

tntstrK

kk +−=∑ τ

∫T

ctwtctr0

1 )cos()()(

∫T

0⊗)(1 td

)⊗

)cos()()( 1 twtctr c )()( 1 tctr

)cos( twc )(1 tc Figure 1.1.1 Block diagram of a simple asynchronous DS-CDMA

system over a Gaussian channel.

4

Figure 1.1.1 briefly explains the basic principle of the operations in a DS-CDMA scheme

in a noisy channel. This system supports K users, each of which transmits its own

information. The users are identified by k=1,2,…,K. The modulation scheme used is

BPSK. Each user’s data signal is denoted by dk(t) and each is assigned a unique pseudo-

random code known as the spreading code denoted by ck(t). There are two classes of

spreading codes in general, binary and complex. For simplicity, our simulation only

considers the binary codes. Each spreading code consists of Q pulses, commonly known

as chips. In the simulation, the wanted signal is the signal of user k=1 and all the other

(K-1) signals are referred to be interfering signals.

In DS-CDMA system the orthogonality constraint on the code sequence is employed to

guarantee acceptable performance. Since the dispersion of the channel and the random

time offsets between the signals, it is impossible to achieve perfect orthogonality between

the spreading sequences of different users, therefore, the signal of other users may appear

as noise in the desired user’s signal. This phenomenon is called the multiple access

interference (MAI) [6]. Although the MAI caused by each other user is generally small, it

will become substantial as the number of interferers or their power increases.

1.2 Multiple Access Interference

Based on the Figure 1.1.1, we can deduce the generation of the MAI from mathematics.

Consider the simplest situation in which we suppose all direct-sequence spreading-

spectrum transmitted signals are received synchronously. Then the received signal r(t)

will be

1

1

( ) ( ) ( )

2 ( ) ( ) cos( ) ( ),

K

jj

K

j j j c kj

r t s t n t

P d t c t t n t

τ

τ τ ω φ

=

=

= − +

= − − + +

∑

∑ (1)

where r(t)－ received signal;

K － total number of active users;

2Pj － amplitude of the user; j th

－ bit sequence of the user; d j (t) j th

5

－ spreading chip sequence of the user; cj (t) j th

－ Additive White Gaussian Noise (two sided power spectral density =

);

n(t)

N0 / 2

τ and φk － the time delay and phase of the user, which are assumed to be

known and uniform in this case, i.e., tracked accurately.

j th

Suppose we try to retrieve the signal of user , then i

( 1)

( 1)

1

( 1)2

1,

ˆ ( ) ( ) cos( )

[ 2 ( ) ( ) cos( ) ( )] ( ) cos( )

2 ( ) ( ) ( ) cos ( ) .

n T

i i c knT

n T K

j j j c k i c kjnT

n T K

i i i i c k jj j inT

d r t c t t dt

P d t c t t n t c t t dt

P d t c t c t t dt I

τ

τ

τ

τ

τ

τ

τ ω φ

τ τ ω φ τ ω φ

τ τ τ ω φ η

+ +

+

+ +

=+

+ +

= ≠+

= − +

= − − + + −

= − − − + + +

∫

∑∫

∑∫

+ (2)

Since ck (t − τ )ck (t − τ ) = 1 , ( 1)

1,

ˆ / 2 ( ) .n T K

i i i jj j inT

d P d t dt Iτ

τ

τ η+ +

= ≠+

= − + +∑∫ (3)

And ( 1)

22 ( ) ( ) ( ) cos ( )n T

j j j j i cnT

.kMAI I P d t c t c t t dtτ

τ

τ τ τ ω φ+ +

+

= = − − − +∫ (4)

If cj (t − τ )ci (t − τ ) = 0 , then MAI=0.

From the above deduction, we can draw the conclusion that if the PN sequence has zero

cross-correlation, then there will be no MAI and the signal can be retrieved more

accurately. But the thing is not that simple. Since the channel is always dispersive and

there is the effect of multi-path and fading during the transmission, every received signal

may have all kinds of delays, that introduces τ j and phase distortion of the carrier, φ j , to

each received signal. Because we can not design a code orthogonal to all kind of delays,

the MAI always exists.

MAI can cause dramatic degradation in bit error rate (BER) performance of the system.

This has leaded into a significant amount of researches dedicating to mitigating the effect

of MAI.

6

1.3 Different Methods to Combat the MAI Since MAI is the main factor to limit the capacity and performance of the DS-CDMA

system, in order to improve the performance, people have developed several ways to

combat the MAI , such as [5]:

i) Code Waveform Design which commits itself to design perfect spreading sequence

that the cross-correlation between these codes equals to zeros. However, since the mobile

channel is quite dispersive which leads to the asynchronism of the received signals, it is

impossible to design a code orthogonal to all possible delays, so it can only get a code has

as small cross-correlation value as possible instead.

ii) Use Power Control to make sure all the signals arrived with almost same power so

that no signal will be damaged by the stronger signal. It is an obbligato way to ensure the

success of the DS-CDMA system since the effect of near-far problem in the CDMA

system.

iii) Design more powerful Forward Error Correlation (FEC) codes to tolerate error rate

at lower signal-to-interference noise ratio level.

iv) Sectored/Adaptive Antennas are used to focus on receiving the signals over the

particular narrow angle ranges. The interfering signals arrive at other ranges can be

attenuated, therefore the decision circuits can get a more accurate decision at the end.

v) Use the Multi-user Detection to improve the performance.

Most of the multi-user detectors can be classified into two categories: linear multi-user

detectors and non-linear multi-user detector. Linear multi-user detectors, including the

correlated, decorrelating and minimum mean squared error (MMSE), apply a linear

transformation to the outputs of the matched filter bank to reduce the MAI seen by each

user.

7

Figure 1.3.1 Matched filter bank, © IEEE Commun. Mag., Moshavi [5], 1996.

The decorrelating detector applies the inverse of the correlation matrix ( ,where 1−= RLdec

R is the cross-correlated matrix) to the matched filter bank’s outputs, thereby decoupling

the signals. The MMSE detector applies a modified inverse of the correlation matrix

( 10 ])2([ −+= INRLMMSE ) to the matched filter bank’s outputs. It yields a better error

rate performance than the decorrelating detector, but requires estimation of the received

powers.

Interference cancellation based multi-user detection is a kind of non-linear MUD

methods to suppress the effects of the MAI and consequently improve the resulting

performance. IC receivers first reconstruct the original transmitted signals of one or more

users and then subtract the MAI contributed by these users from the composite received

signals [6]. The remaining signal is then processed with the same progress in order to get

the separate data estimates of the individual user and cancel the MAI imposed by each

user. The progress is going on until all users’ data has been detected. Such detector

always has multi-stage, with the first stage which is usually consisted of a bank of

matched filters or RAKE receivers to get the initial estimates. At the following stage, the

estimates from the former stage are used to reconstruct the signals and cancel the

interference. The outputs of the former stage are the inputs of the subsequent stage.

Interference cancellation techniques can be divided into two parts: successive

interference cancellation and parallel interference cancellation, which are the parts of this

project.

8

1.4 Different Ways to Compensate Time Varying and Multi-path Fading The performance of the DS-CDMA system is not only decided by the multiple access

interference but also the time varying characteristics of the channel. The signals received

at the receiver always pass through different paths in the channel, which will induce

different attenuations, delays and phase shifts and the mobility of the user will causes

fading [7]. Multi-user detection presents an effective way to combat the MAI, but if the

input to the receiver is a superposition of the signals of all the users attenuated and

delayed by an arbitrary amount [8], then the data bits can still not be retrieved correctly.

The goal of the channel parameter estimation is to detect these unknown and time varying

parameters and delays to facilitate recovery of the data bits [8]. However, since the near-

far effect of the CDMA system, the proposed technique should be near-far resistant.

Several techniques have been proposed but in order to meet the third generation wireless

system’s requirement which is to support extremely high data rate, highly efficient multi-

user algorithm for channel estimation need to be invented. Recently, the maximum-

likelihood (ML) technique emerged and a number of channel estimation algorithms based

on this ML technique has be implemented, such as in [16] and [17]. These ML-based

algorithms are computationally efficient and can also deal with a large number of users.

Evidence has proofed that combined the multi-user channel estimation and detection

together can work more efficient and provide better performance than implementing them

separately [8].

Another effective way to combat multi-path fading is to achieve spatial diversity.

Conventional technique to achieve spatial diversity is to use multiple transmit and/or

receive antennas. But when the multiple transmit antennas are not available, the single

antenna system can not benefit from the spatial diversity technique. A recent technique

called cooperative communication ([13] [14]) introduces a novel way to enable single-

antenna mobiles to achieve transmit diversity by choosing some nearby idle mobile

stations as the relays to transfer their information signals to the destination. This type of

co-operation makes the single antenna mobile look like a virtual multiple-antenna

transmitter because at the receiver, it seems there are signals transmitted from different

locations, thus receiving independently faded versions of the signals at the receiver.

9

Transmit diversity is gained when the selected stations retransmit the signals to the

destination. Full diversity order can be achieved by this kind of cooperation [15]. We will

discuss these combined multi-user channel estimation and detection and the cooperative

technique more deep in our project.

10

Chapter 2 Mobile Radio Channel Models All wireless systems transmit signals over the mobile radio channels. The mobile radio

channel is always deemed to be more hostile than other channels, because it induces

fading. A signal sent by the transmitter reaches the receiver via several paths of different

length, each of which results in a different phase shift. Unlike wired channels which are

stationary and predictable, radio channels are extremely random and do not offer easy

analysis.

2.1 Additive White Gaussian Noise (AWGN) Channel The simplest type of mobile radio channels is the Gaussian channel. It is often referred to

as the additive white Gaussian noise (AWGN) channel. Basically it is the noise generated

in the receiver while the transmission path is ideal. The noise is assumed to have a

constant power spectral density over the channel bandwidth, and a Gaussian amplitude

probability density function (PDF). In micro-cells it is possible to have a line-of-sight

(LOS) with essentially no multi-path, giving a Gaussian channel. Even when there is

multi-path fading, if the mobile is stationary and there are no other moving objects, such

as vehicles, in their vicinity, the mobile channel may be thought as Gaussian distributed

with the effects of fading represented by a local path loss. These below figures show the

PSD, PDF and CDF curves of AWGN.

11

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-120

-100

-80

-60

-40

-20

0

normalised frequency

Pow

er S

pect

rum

Mag

nitu

de (d

B)

the PSD of the white noise xw

Figure 2.1.1 The PSD of AWGN noise (fs=2*106, t=0.1s).

Figure 2.1.2 Normalized Gaussian amplitude PDF and CDF.

12

The Gaussian channel is important for providing an upper bound on system performance.

For a given modulation scheme, the BER performance is in the presence of Gaussian

channel. When multi-path fading occurs the BER will increase for a given channel SNR.

By using techniques to combat multi-path fading, such as diversity, equalization, channel

coding, data interleaving, we can observe how close the BER approaches to that of the

Gaussian channel.

2.2 Rayleigh Fading Channel Rayleigh channel model will always be encountered because it is approximate as the

urban (non-LOS) and suburban (LOS) environments. In practice, mobile communication

environments have characteristics to cause the transmitted/received signal to fade (drop

below a certain threshold) over time and distance. This characteristic is created because

there are several time-delayed versions of the input signals arrived at the receiver by

traveling through their own paths in the channel. We use the computer simulations to

approximate channel characteristics so that a general idea can be obtained about the

system performance (BER, SNR) at the input to the receiver.

2.2.1 Uncorrelated Rayleigh Fading Channel

Figure 2.2.1 Baseband Uncorrelated Rayleigh-fading simulation model.

Because of the effects of the fading over a distance, the Rayleigh channel model is

motivated and defined as a product of the transmitted signal with the complex fading

coefficients. Meanwhile the additive noise is the part of the model and is added after

13

fading. The complex fading coefficient’s magnitude is distributed as an exponential

random variable. The uncorrelated Rayleigh channel model can be represented by the

quadrature arrangement shown in the Figure 2.2.1 above, where both received quadrature

components are uncorrelated distributed AWGN sources.

0 10 20 30 40 50 60 70 80 90 100-40

-30

-20

-10

0

10UnCorrelated Rayleigh magnitude

samples

AM

P

0 20 40 60 80 100 120-200

-100

0

100

200UnCorrelated Rayleigh Phase

samples

PH

AS

E

Figure 2.2.2 Simulated amplitude and the phase of the Uncrrelated Rayleigh fading channel.

Figure2.2.3 Simulated Uncorrelated Rayleigh PDF and CDF curves.

14

2.2.2 Correlated Rayleigh Fading Channel In an urban environment where there is no direct line-of-sight (LOS) from the transmitter

to the receiver, the channel is referred to be of a “Rayleigh” distribution. The receiver

obtains several independent versions of the transmitted signals suffered from different

time and frequency shifts which depend on the particular path (reflection) they taken.

Because the propagation delay is based on reflection, the more objects that the signals

come in contact with, the longer the propagation delay will be for each component. The

frequency shift of each multi-path is derived from the Doppler shift that it encounters.

Because most mobile channels are in urban environments, the Rayleigh distribution is

frequently used to describe the statistical time varying nature of each multi-path signal.

Figure 2.2.4 shows the amplitude and the phase of the correlated Rayleigh fading

channel.

0 50 100 150 200 250 300 350 400 450 500-40

-30

-20

-10

0

10Correlated Rayleigh magnitude

samples

AM

P

0 100 200 300 400 500 600-200

-100

0

100

200Correlated Rayleigh Phase

samples

PH

AS

E

Figure 2.2.4 Simulated amplitude and phase of the Correlated Rayleigh channel.

15

0 50 100 150 200 250 300 350 400 450 500-40

-20

0

Correlated Rayleigh magnitude P=1

samplesA

MP

0 50 100 150 200 250 300 350 400 450 500-40-20

0

Correlated Rayleigh magnitude P=3

samples

AM

P

0 50 100 150 200 250 300 350 400 450 500-40

-20

0

Correlated Rayleigh magnitude P=7

samples

AM

P

Figure 2.2.5 Simulated amplitude of the Correlated Rayleigh channel when

several paths added together.

Figure 2.2.5 shows the result when there are 3 and 7 different paths added together. Every

path has its own amplitude and phase. Therefore, if the signals transmitted through the

multi-path channel, the received signal will have different delays, attenuations and phase

shifts, which lead to the error detection at the end. However, when these paths are

mathematically added together, the performance will be more likely as an AWGN

channel with almost flat amplitude.

Figure 2.2.6 shows the difference between the uncorrelated and correlated Rayleigh

channel. Because of the effect of Doppler shifts, the envelope of correlated Rayleigh

channel has slow variance compared with the one of uncorrelated Rayleigh channel.

16

Figure 2.2.6 Envelope of correlated and uncorrelated Rayleigh channel with normalize Doppler frequency shift 10-4.

2.3 Summary In this section, the channel models have been built, and the properties of channel have

been reviewed. The AWGN channel is considered as an ideal one with a flat amplitude

spectrum and linear phase spectrum over the frequency range. The slow fading Rayleigh

channel is modeled by the complex Gaussian noise with or without the Doppler shift.

Because of the different attenuations, delays, phase shifts and fading induced by the

multi-path channel, the performance of the receiver will degrade. These undesirable

influences imposed by the channel lead to our project on multi-user channel estimation in

order to mitigate these effects and spatial diversity techniques to combat the multi-path

fading.

17

Chapter 3

Successive Interference Cancellation and Parallel Interference Cancellation Interference cancellation based multi-user detection is a kind of non-linear MUD

methods to suppress the effects of the MAI and therefore improve the system

performance. It usually consists of multi-stage with the first stage as a bank of matched

filter or RAKE receivers to provide the initial estimates of the transmitted signals and the

following stages use the outputs of the former stage to reconstruct the signals and cancel

the MAI imposed by these users from the composite received signals to isolate the

desired users. Then hard decision is made to retrieve the data bits. These progresses can

be repeated until the system has reached the desired performance or the convergence of

the Bit Error Rate (BER) has been found [1]. Interference cancellation techniques can be

divided into two parts: successive interference cancellation and parallel interference

cancellation, which will be discussed as follows.

3.1 Successive Interference Cancellation In the algorithm of successive interference cancellation, the detector cancels the MAI of

different users by a serial approach. In each stage of the SIC detector, a decision for the

symbol of the user with the strongest strength or largest cross-correlation value is made,

which depends on the principle of the SIC receiver, and the MAI of this user is

regenerated, cancelled out from the received composite signals, so that the remained

signals will have less MAI when pass to the next stage. This progress goes on until a

desired performance has been reached.

3.1.1 Successive Interference Cancellation Algorithm and Implementation SIC receiver needs some criterions to rank the users’ signals at every stage. Two different

ways to rank the signals can be implemented in successive interference cancellation

18

algorithm. One way is to serially regenerate the signal of the strongest user and cancel the

MAI imposed by it from the received signal at every stage, which will be performed in

this project. Another way to execute SIC is to calculate the auto-correlation value and

using this obtained auto-correlation information to renew the output of the correlator.

Therefore, this method is operating at the bit level but both these two ways require the

same number of operations [18].

Based on the definition of the SIC stage from [5], the SIC assisted receiver model can be

drew as Figure 3.1.1, which simply presents the first three stages of this kind of detectors,

where a hard decision approach is employed.

Figure 3.1.1 A schematic of the first three stage of the successive interference cancellation (SIC)

receiver for K users. The user’s signals r at the output of the former stage which have been ranked, where the first user’s signal has the highest power. In order to rank the signals, the data estimates of each user are obtained and the received signal of each user is reconstructed and cancelled from the received composite signal.

The stage 0 is a matched filter or RAKE receiver exports a group of ranked signals by the

descending order of the received powers, with the strongest user being labelled 1. Then at

19

the stage 1, the initial data estimate of user 1 is obtained by processing the received

composite signal through a matched filter or RAKE receiver. Then by using the estimate

and the relative spreading sequence of this user and the relative CIR, the received signal

of this user is reconstructed and subtracted from the composite received signal to get the

signal without the MAI caused by this user. While at stage 2, the remaining signal is

processed through the matched filter bank or RAKE receiver in order to obtain the data

estimate of user 2. Implementing the estimate of the transmitted data, as well as the CIR

and spreading sequence of this second user, the corresponding received signal is

reconstructed and subtracted again from the remaining composite multi-user signal which

has already had the strongest user’s signal been cancelled from it. This progress is

repeated until the required BER performance has be obtained. Specifically, the stage 1

employs the follow steps [5]:

1) Detect the strongest user data, 1d , from the outputs of the matched filter or RAKE

receiver.

2) Make a hard decision on 1d to get the data estimate . d1

3) Regenerate the estimate of the received signal of this user, , by using: e1

• data decision from the step 2, d1

• the corresponding PN sequence of this user, c1

• the relative CIR, h1

4) Subtract from the received composite signal e1 r to get a partially cleaned version

of the received signal, . r1(t)

Two signals yielded at the stage 1, they are the data decision of the strongest user, ,

and the partially cleaned signal, r , which contains no MAI caused by the strongest

user.

d1

1(t)

The progress can be reduplicated into multi-stage, until the required BER performance

has been reached or can be afforded by the system. The s th stage takes the partially

cleaned outputs of the former stage, , as its input, and exports one more data

decision, , of the user

rs−1(t)

ds s and a composite signal, , which additionally cancels the

MAI from user

rs (t)

s .

20

The whole system can benefit from cancelling the MAI according to the signal strength

of the users in descending order. Such as in the situation of the near-far effect, the

strongest user will inflict plumbeous influence to the other users’ signal, even more, it

can float the data of some weaker users. Removing the strongest user first can benefit the

remaining users. It gains more chance to get a correct answer to demodulate the strongest

user’s data while the remained signal can also achieve more chance to be demodulated

correctly since it suffers less MAI. The weakest user will potentially get all the MAI from

the other users be reduced.

Compared with other linear multi-user detectors, the SIC detector can provide a much

better BER performance but only needs less hardware to implement. More detailed

results can be seen in the Section 3.2.2 and 3.3. However, it does pose some

disadvantages. Since the serial property of the SIC detector, one more bit delay will be

added at each stage of cancellation. Therefore, there exists a balance between the delay

can be tolerated and the BER performance. Much better performance can be achieved by

using more stages but more delays will occur. Another problem is that, if the initial data

estimates from the matched filter or RAKE receiver are not reliable, then even the timing,

phase estimate, and CIR estimate are perfect, the BER performance at the receiver will

dramatically degrade. So it is crucial to get more reliable data estimations from the

headmost stage [5].

3.1.2 Complexity Calculation of Successive Interference Cancellation

In this section we will discuss the calculation complexity of the SIC detector scheme

described above. The complexity can be represented by the number of multiplications

and the number of additions needed to accomplish the multi-user detection. Suppose in

each time, we cancel the MAI from the stronger users until the last user.

Usually, to accomplish the multiplication of a (M × N ) matrix with a (N × P) matrix we

need to do MNP times of multiplications and MNP times of additions. To finish the

Cholesky decomposition of a Hermitian matrix with the dimensions of (N × N ) we need

to do N 3 / 6 times of multiplications and N 3 / 6 times of additions.

21

Assuming in our case there are a total of K users in the system where the transmission is

in burst. Each user transmits N data symbols per burst. Q represents the length of the

spreading code for each user, and W is the complex matrix which contains the elements

describe the channel impulse response. Then for each user, it will need NQ times of

multiplications and NQ times of additions for every path ( (Q × N ) × (N ×1) ).

Multiplying with which represents the multi-path components, the RAKE receiver will

require

L

NQL times of additions and multiplications. To combine the N symbols

transmitted from the dispersive paths, it will need other L NL times of multiplications

and additions. Therefore, to get the data estimates from the RAKE receiver, NQL + NL

times of multiplications and additions are required. At the signal reconstruction part, the

detected data should be multiplied with the spreading code first, which results in NQ

times of multiplications, and then convolves with the corresponding CIR, which leads to

NQL times of multiplications and (NQ +W −1) times of additions. To carry out the

interference cancellation on the composite signal, it will require (NQ +W −1) times of

subtractions. Therefore, the total number of operations for detecting one user’s data as

well as signal reconstruction and MAI cancellation from the composite signal will be [6]

2 ( ) ( 1) ( 1)3 2 2( 1).

S NQL NL NQ NQL NQ W NQ WNQL NL NQ NQ W= × + + + + + − + + −

= + + + + −

For the system supporting K users, the total mathematic operation required for the SIC

algorithm will be (K −1) × S . Thus, the number of operations needed by the SIC detector

for every symbol is Ssymbol =(K −1)S

KN.

While in MMSE, the detector implements the linear mapping which minimizes the mean-

squared error between the actual data and the soft output of the correlated detector. The

operation is: , and the soft estimate of the MMSE detector is

.

LMMSE = [R + (N0 / 2)I ]−1

dMMSE = LMMSE y

Assume there is only one path from the transmitter to the receiver, then using the

parameters defined above, we can get the result that to calculate the cross-correlated

matrix R , it will need times of multiplications and times of additions. K 2Q K 2Q

22

Multiplying the diagonal matrix I with will lead to N0 / 2 K 2 multiplications and added

with the cross-correlated matrix R will require K 2 additions. To do the inversion of the

matrix will result in LMMSE K 3 / 6 multiplications and K 3 / 6 additions. At last to get the

soft estimate, it will need K 2 times of multiplications and K 2 additions. So if each user

transmits N data symbols per burst, the total number of mathematic operations will be 2 2 3

2 2 3

[2 2 2( / 6) 2 ](2 4 / 3)

S N K Q K K KN K Q K K= + + +

= + +

2

for single path. Therefore, the number of operations needed by the MMSE detector for

every symbol is Ssymbol =S

KN= 2KQ + 4K + K 2 / 3 .

For a system containing only one path and supporting K = 9 users, N = 20 symbols and

chips, we can get the result that for SIC detector, the number of operations

needed is

Q = 31

( 1)(3 2 2 ) ( 1)(6 2

8 (6 20 31 2 20) 30080.SICS K NQ N NQ NQ K NQ N= − + + + = − +

= × × × + × =)

Therefore, the number of operations needed by the SIC detector for every symbol is

/30080 167.9 20

SICSIC symbol

SSKN

= = ≈×

For MMSE detector, the number of operations needed is

2 2 3

2 2 3

(2 4 / 3)

20 (2 9 31 4 9 9 / 3) 111780.MMSES N K Q K K= + +

= × × × + × + =

And the number of operations needed by the MMSE detector for every symbol is

/111780 621.9 20

MMSEMMSE symbol

SSKN

= = =×

From the results above, it can be seen that the complexity of the SIC detector is much less

than that needed by the MMSE detector. In SIC receiver, the complexity increases

linearly with the number of users K . While in MMSE receiver, the complexity is defined

by the length of the spreading code Q and the cube of the number of users K .

23

3.1.3 Simulation Results of Successive Interference Cancellation

Figure 3.1.2 Simulation-based BER versus the SNR per bit, Eb/N0. performance of multi-stage SIC

detector for DS-CDMA system supporting 7 users using BPSK modulation over AWGN channel, where using m-sequence and SF=7 is the length of spreading sequence.

Figure 3.1.2 gives the result of the successive interference cancellation with multi-stage

over AWGN channel while using m-sequence with the spreading factor equals to 7 and

supporting 7 users in the system. The data bits from the matched filter give the initial

estimates of the transmitted signals and present the highest BER overall. The SIC at the

following stage can enhance the BER performance as the number of the stage increases.

In the th stage, we recover the th stronger user data and subtract the interference by

this user from the remained composite signal. To calculate the BER at the th stage, we

add together the BER of the first users’ data which have been recovered and subtracted

from the composite signals and the remained signals which are retrieved by the hard

decision. So in this case when supporting 7 users, the system with 6 stages presents the

best performance because all the 6 stronger user’ data has been recovered successively at

n n

n

n

24

each stage and leaves the last user’s data which will have no MAI imposed by other users

at all. This figure illustrates that when the system supporting users, then the

performance can quite reach the single user bound if the SIC detector can be repeated for

stages. However, when the number of users is large, we can just repeat the SIC

detector for several stages to cancel the several strongest users’ data so that removing the

MAI imposed by these users to obtain the desired performance but reduce the complexity

at the same time.

n

n −1

Figure 3.1.3 Simulation-based BER versus the SNR per bit, Eb/N0. performance of multi-stage

SIC detector for DS-CDMA system supporting 7 users using BPSK modulation over uncorrelated Rayleigh channel, where using m-sequence and SF=7 is the length of spreading sequence.

Figure 3.1.3 shows the result of the SIC system supporting 7 users and using SF=7 m-

sequence over uncorrelated Rayleigh fading channel. It is clear that when the number of

stage increases, the performance goes better. Because the MAI and the error floor in the

Rayleigh channel, the performance has slightly improvement at high SNR. But if all the

users’ data are retrieved by the different SIC stages, the performance can still reach the

25

single user bound. So SIC is a quite powerful algorithm to combat MAI, besides, it is

near-far resistant.

3.2 Parallel Interference Cancellation Comparing with the SIC detector, the parallel interference cancellation (PIC) receiver

works in a totally different way. For a desired user, the PIC detector regenerates the MAI

from all other users and subtracts them from the received composite signals to isolate the

user of interest. The data decision is made in parallel. This kind of detector can also be

extended into multi-stage, such as the SIC detector, to reach the BER performance

required or the limitation of the system’s capacity.

3.2.1 Parallel Interference Cancellation Algorithm and Implementation

Figure 3.2.1 A scheme of the first two stages of the parallel interference cancellation (PIC) receiver

for K users. The data decision, , , … , are the output of the

current stage and the input of the next stage. In each stage, the received signals of

all other users except the desired user’s are reconstructed and cancelled from the

received composite signals,

d1(n) d2 (n) dK (n)

n

r(t) .

Parallel interference cancellation (PIC) detector usually repeats the interference

cancellation for several stages to reach the convergence of the BER. Figure 3.2.1 shows

the first two cancellation stages of the PIC detector. At the end of each stage, hard

decision approach is investigated to get the data decisions. Stage 0 is consisted by a bank

of matched filters or RAKE receivers which are used to get the initial bit estimates. In

each cancellation stage, these data decisions are used to reconstruct the data estimates of

26

each user by invoking the corresponding spreading code and the relative CIR. Then, for

each user, the partial sum obtained by the summer which sums up the reconstructed

signals of all the other users, which represents the complete MAI estimates imposed for

each user, is subtracted from the received composite signal, and the resulting signal is

passed through a matched filter or RAKE receiver to get a new set of data for this

desired user. This process is implemented in parallel for each user as illustrated in the

Figure 3.2.1. This estimate, reconstruction and cancellation stage can be repeated for

multiple stages. Each stage takes the decisions from the previous stage as its input and

produces a new set of decisions at its output.

It can be seen that the main difference between SIC and PIC is that in each stage, SIC

only produce the estimate of the strongest user, while the PIC detector will produce the

estimates of all the users in every stage. Thus, the parallel cancellation appears to be

more complicated to analyze. The follow step will deduce the equations of the partial

sum and the data decisions of each stage.

The received signal at the base band can be given by

1

1( ) ( ) ( ) (2 2

k

Kjk

k k k k Zk

Pr t d t c t e n tφτ τ −

=

= − − +∑ ). (5)

The parameters are the same as these defined in the Section 1.2. Then at the output of the

matched filter or RAKE receiver, the decision of the user is ith

( 1)

,1

1(0) Re[ ( ) ( ) ]

1 ,2 2 2

i

i

i

n Tj

i inT

Ki k

i k i ikk i

d r t c tT

P Pd I N

τφ

τ

τ+ +

−

+

=≠

= −

= + +

∫

∑

i e dt

(6)

where is defined as the equation (4). Ik ,i

These decisions are used to regenerate the signal estimates of each user. Then at the stage

1, the modified signal of the i user which is obtained by cancelling the estimates of all

the other users from the received composite signals is given by

th

27

ri(1) (t) = r(t) − dm (0)cm (t − τm )e jφm

m=1m≠ i

K

∑

=Pi

2di (t − τ i )ci (t − τ i )e

jφi +12

nZ (t)

−Pk

2k=1k≠m

K

∑m=1m≠ i

K

∑ Ik ,mcm (t − τm )e jφm −12

Nicm (t − τm )e jφm

m=1m≠ i

K

∑ .

(7)

The decision of the user at the stage 1 is ith

( 1)(1)

, , ,1 1 1

1(1) Re[ ( ) ( ) ]

1 1 .2 2 2 2

i

i

i

n Tj

i i i inT

K K Ki k

i i k m i m i im k mm i k m m i

d r t c t e dT

P Pd N I I N I

τφ

τ

τ+ +

−

+

= = =≠ ≠ ≠

= −

= + − −

∫

∑∑ ∑ m

t

n

(8)

These consist of the outputs of the stage 1. If more stages are performed to get a more

accurately result, the output is used to regenerate the estimate of each user and

cancel from the composite signal. The modified signal at the stage 2 is

di (k)

(2)

1

( ) ( ) (1) ( ) .n

Kj

i n nnn i

r t r t d c t e φτ=≠

= − −∑ (9)

Then we can get the decisions from stage 2 as

( 1)(2)

, , ,1 1 1

, , ,1 1 1

1(2) Re[ ( ) ( ) ]

12 2 2

1 1 .2 2

i

i

i

n Tj

i i i inT

K K Ki k

i i k m n m n in m kn i m n k m

K K K

i i n i n m n in n mn i n i m n

d r t c tT

P Pd N I I I

N I N I I

τφ

τ

τ+ +

−

+

= = =≠ ≠ ≠

= = =≠ ≠ ≠

= −

= + +

+

∫

∑∑∑

∑ ∑∑

e dt

− (10)

Further analysis will be more complicate. [20] introduces a way to express the output of

the stage l + 1 of the PIC detector for all the N bits of all the K users in matrix as

(11) ˆ ˆ( 1) ( )

ˆ( ( ))

d l r QPd l

Pd QP d d l n

+ = −

= + − + ,

where P is a matrix represents the amplitude of each user, is the modulation bit of the d

28

user and is the noise. Q contains the off-diagonal elements represent the cross-

correlations. Combined well data estimates with perfect channel estimation, the MAI can

be completely eliminated.

n

An obvious advantage of PIC when compared with SIC is that PIC does not need any

user ranking, and will not induct different delays for different users. But PIC needs more

number of multiplications and additions, which will be verified at the Section 3.2.2,

because in order to retrieve the signal for each user, the signals of all the other users need

to be reconstructed and cancelled from the received signal.

Several other techniques have been used on PIC to improve the performance. These

include [5]:

1) Using more reliable detector as the first stage [20]

The correctness of the initial data estimates can heavily influent the performance of the

PIC detector. The matched filter or RAKE receiver plays a more important role in PIC

than in SIC, because in PIC, all the initial estimates will be produced at one time. If these

estimates are wrong, then the reconstructed estimates will be wrong, poor cancellation

will be posed at last. Even no cancellation will be better than poor cancellation since it

will cause some correct bits to be incorrect. Thus the performance will be degraded

tempestuously, although the phenomenon will be mitigated by the convergence behavior

of the iterations. Simulation results by using different ways of detections as the stage 0

will be exhibited in the Section 3.2.3.

2) Using the already detected bits of the current output to improve detection of the

remaining bits in the same stage [21]

The most up-to-date bit decisions are used to improve the capacity. This detector is

referred to as a multi-stage decision feedback detector [21].

3) Combining the output of the different stages of the parallel interference cancellation

detector linearly [22]

The aim of this kind of combining is to deal with the correlations of the extensive noises

which exist between the outputs of the different stages and to cause cancellation among

noise terms.

29

4) Doing a partial cancellation at each stage [23]

The principle behind is that the tentative decisions of the earlier stages are less reliable

than those of the later stages. Thus, scaling the MAI estimates first at the early stage may

lead to a better performance. A great many gains in performance are reported compared

to the standard PIC detector.

3.2.2 Complexity Calculation of Parallel Interference Cancellation As the complexity calculation discussed in the Section 3.1.2, in this section, we will

discuss the complexity of the PIC receiver based on the number of multiplications and

additions.

Using the conclusion and parameters given above, that is, K , the users; N , data symbols

per user; Q , the length of the spreading codes; , the number of paths and L W ,

represents the CIR, we can conduct the complexity equation as follows:

To obtain the data estimates from the RAKE receiver, NQL + NL times of

multiplications and additions are required. While to do the signal reconstruction, the

detected data should be multiplied with the spreading code first, which results in NQ

times of multiplications, and then convolves with the corresponding CIR, which leads to

NQL times of multiplications and (NQ +W −1) times of additions. Then goes to the

interference cancellation part, which is the different part from the SIC algorithm. In PIC,

to get the estimate for each user, all the other users’ influences should be subtracted. To

cancel one user’s MAI, it will need (NQ +W −1) times of subtraction. Therefore, for

each user, (K −1)(NQ +W −1) times of subtractions are needed. For a system supporting

K users, the total number of mathematic operations is [6]

[ 1

[3 2 ( 1)].

PICnumberofuser RAKEreceiver reconstruction InterferenceCancellation

S K NQL NL NQL NL NQ NQL NQ W K NQ W

K NQL NL NQ K NQ W

= × + + + + + + + − + − + −

= × + + + + −

14444244443 14444244443 144424443( 1)( 1)]

Therefore, the number of operations needed by the PIC detector for every symbol is

/( 13 2PIC

PIC symbolS K NQ WS QL L Q ) .KN N

+ −= = + + +

30

Using the same parameters as in Section 3.1.2 to calculate the complexity, that is,

containing only one path and supporting K = 9 users, N = 20 symbols and Q chips

for a system, we can get the number of operations needed for PIC detector is

= 31

(3 2 ) [( 4) 2 ]9 (13 20 31 2 20) 72900.

PICS K NQ N NQ KNQ K K NQ N= × + + + = + += × × × + × =

And the number of operations needed by the PIC detector for every symbol is

/72900 405.9 20

PICPIC symbol

SSKN

= = =×

Comparing with the number of operations needed for SIC, which is S ,

, and for MMSE, which is

SIC = 30080

SSIC /symbol ≈ 167 SMMSE = 111780 , in the same

system example, we can draw the conclusion that SIC has the lowest complexity. The

complexity of the PIC is more than SIC because, to get the data decision of one user, all

the other users’ signals should be reconstructed and cancelled, which increases the

number of calculations. MMSE has the highest complexity, especially when the number

of users and the length of the spreading code is large, the complexity will increase

exponentially. Collecting all the equations for the single path system together, as

SMMSE /symbol = 621

SSIC = (K −1) × N × (6Q + 2);SPIC = NQK 2 + 4NQK + 2NK;

SMMSE = N × (K 3

3+ 2QK 2 + 4K 2 );

⎧

⎨

⎪⎪

⎩

⎪⎪⎪

we can see the complexity of SIC proportion with the number of users; while in PIC, it is

of the order of O ; in MMSE, the complexity is of the order of O . (K 2 ) (K 3 )

31

0 5 10 15 20 25 300

1

2

3

4

5

6

7x 109 Comparison of the calculation complexity of the SIC,PIC and MMSE

Number of users

Num

ber o

f mul

tiplic

atio

ns a

nd a

dditi

ons

SICPICMMSE

Figure 3.2.2 Comparison of the calculation complexity (in number of multiplications and additions)

of SIC, PIC and MMSE with the length of spreading sequence SF=31 and the number

of bits of each user equals to 10^5.

32

3.2.3 Simulation Results of Parallel Interference Cancellation

0 5 10 15 20 25 3010-5

10-4

10-3

10-2

10-1

Comparison of multi-stage PIC for BPSK modulated signals over AWGN channelgold sequence, SF=31, 20 users

Eb/No(dB)

BE

R0 stage1 stage2 stages4 stagessingle user bound

Figure 3.2.3 Simulation-based BER versus the SNR per bit, Eb/N0. performance of multi-stage PIC

detector for DS-CDMA system supporting 20 users using BPSK modulation over AWGN channel, where using gold sequence and SF=31 is the length of spreading sequence.

Figure 3.2.3 shows the result of the parallel interference cancellation algorithm

implemented in the system using the gold sequence with the spreading factor equals to 31

and supporting 20 users over AWGN channel. The number of stage increases from 1 to 4.

In each cancellation stage, the PIC uses the estimation from the former stage to

reconstruct the signals and cancel the MAI from all the other users for each user

simultaneously. From the result we can observe that the initial estimate from the matched

filter has a higher bit error rate but at the output of the first stage of the PIC detector, the

BER has been reduced greatly. As the number of stage increases, the BER performance

improves. But as the number of stage increases to 4, the performance is not quite

different from the one with 2 stages because if there is no sign change of the detected

33

data bits, there will be no significant improvement at the succeeding stage. So we can

reduce the complexity by using 2 stages PIC detector at the end.

0 5 10 15 20 25 3010-4

10-3

10-2

10-1

100

Comparison of multi-stage PIC for BPSK modulated signals over uncorrelatedRayleigh channel, gold sequence, SF=31, 20 users

Eb/No(dB)

BE

R

0 stage1 stage2 stages4 stagessingle user bound

Figure 3.2.4 Simulation-based BER versus the SNR per bit, Eb/N0. performance of multi-stage PIC

detector for DS-CDMA system supporting 20 users using BPSK modulation over uncorrelated Rayleigh channel, where using gold sequence and SF=31 is the length of spreading sequence.

Figure 3.2.4 gives the BER performance of different PIC stages of the BPSK modulated

DS-CDMA system supporting 20 users over uncorrelated Rayleigh fading channel. As

the number of stage increases, the BER performance can be enhanced significantly. But

when the system extends to 4 stages, the performance does not change dramatically. In

flat Rayleigh fading channel, the MAI has a Gaussian first order distribution assuming

synchronous transmission and has less limitation on the performance. Therefore, when

the number of stage increases to more than 2, the BER performance will quite reach the

single user bound.

34

0 5 10 15 20 25 3010-5

10-4

10-3

10-2

10-1

100

Comparison of PIC with the correlation and MMSE as the stage 0 over AWGN channelgold sequence, SF=31,20 users

Eb/No(dB)

BE

R

correlation 0 stagecorrelation 1 stagecorrelation 2 stagesMMSE 0 stageMMSE 1 stageMMSE 2 stages

Figure 3.2.5 Comparison of the performance of multi-stage PIC detector for DS-CDMA system

supporting 20 users using SF=31 gold sequence and BPSK modulation over AWGN channel, while using correlation and MMSE as the stage 0.

As discussed above, the performance of the PIC detector relies heavily on the initial data

estimates. The matched filter or RAKE receiver plays a more important role in the

performance of the PIC detector than in the SIC. If these estimates are wrong, then the

reconstructed will be wrong, poor cancellation will be posed at last. Even no cancellation

will be better than poor cancellation since it will cause some correct bits to be incorrect.

Figure 3.2.5 shows how the correctness of the initial estimates from the stage 0 can affect

the whole system’s performance. In this figure, we support 20 users in the system to

transmit data bits through AWGN channel while using gold sequence with SF=31 as the

spreading sequence. At the receiver, we present two different ways, correlating and

MMSE as the first stage to obtain the initial estimates. From the Figure 3.2.5 we can see

that using MMSE as the first stage can greatly improve the performance. Even the

performance of the output of stage 1 of PIC while using MMSE can almost reach the

performance of the output of 2 stages PIC when using correlating detector. When

35

increasing to more than 2 stages, the performance will become very identical since the

convergence property of the iterations. So we can say using a more reliable detector as

the first stage can significantly improve the performance of the PIC detector at the first

several stages.

0 5 10 15 20 25 3010-4

10-3

10-2

10-1

100Comparison of PIC with the correlation and MMSE as the stage 0

gold sequence,SF=31,20 users

Eb/No(dB)

BE

R

correlation 0 stagecorrelation 1 stagecorrelation 2 stagesMMSE 0 stageMMSE 1 stageMMSE 2 stages

Figure 3.2.6 Comparison of the performance of multi-stage PIC detector for DS-CDMA system

supporting 20 users using SF=31 gold sequence and BPSK modulation over uncorrelated Rayleigh channel, while using correlation and MMSE as the stage 0.

The performance of the system using the MMSE as the first stage when the signals

transmitted through uncorrelated Rayleigh fading channel is presented in Figure 3.2.6.

Since MMSE detector is very powerful, the output of the MMSE will have a very low bit

error rate. When the signals pass through the PIC detector, the BER is reduced again to

reach the single user bound. Compared with MMSE, the correlating detector provides

less reliable estimates, so that the PIC detector can still improve the performance.

36

3.3 Comparison of Different Multi-user detections Since the multiple access interference significantly limits the performance of the DS-

CDMA system, many multi-user detection methods have been invented and

implemented. In this part, we will compare the performance of some prevalent multi-user

detection algorithms, such as correlating, decorrelating, minimum mean-squared error

(MMSE) and maximum likelihood detection (MLD), with our SIC and PIC detectors.

3.3.1 Simulation Results

Figure 3.3.1 Simulation-based BER versus the SNR per bit, Eb/N0. performance of different MUD

methods for DS-CDMA of 5 users using BPSK modulation over AWGN channel, using the m-sequence where SF=7.

Figure 3.3.1 shows the performance of different multi-user detection algorithms of the

system supporting 5 users and using the m-sequence with the spreading factor equals to

7. From the Figure 3.3.1 we can see that the MMSE detector trends to have the same

performance as the decorrelating detector at low noise level (high SNR). Because MMSE

detector takes the background noise into account, it usually provides better probability of

37

error performance than the decorrelating detector. As the background noise goes to zero,

the performance of the MMSE detector converges to the performance of the decorrelating

detector. Since the decorrelating detector pays a noise enhancement penalty for

eliminating the MAI, if the MAI is relatively low and the background noise power is

relatively high, by ignoring the MAI, it will provide a better performance. Maximum

likelihood detection (MLD) can provide excellent performance, but it is not practical

since the complexity of MLD is of the order of O , where (2K ) K is the number of the

users. When the system supports a large of users, the complexity will be extremely high.

Successive interference cancellation and parallel interference cancellation can both

achieve good performance in this situation. Since there are only 5 users in the system, the

MAI is relatively low. The SIC and PIC can almost reach the single user bound. Because

the SIC and PIC have lower complexity than the other MUD algorithms such as MMSE

and MLD, we can see these interference cancellation based algorithms perform superior

to the linear detectors.

0 2 4 6 8 10 12 14 16 18 2010-3

10-2

10-1

100Comparison of different MUD of BPSK modulated signals over uncorrelated

Rayleigh channel

Eb/No(dB)

BE

R

correlationdecorrelationMMSEMLDSICPIC-1 stagePIC-2 stagesingle user bound

Figure 3.3.2 Simulation-based BER versus the SNR per bit, Eb/N0 performance of different MUD

methods for DS-CDMA of 5 users using BPSK modulation over uncorrelated Rayleigh channel, using the m-sequence where SF=7.

38

The performance of different multi-user detectors over uncorrelated Rayleigh channel is

shown in Figure 3.3.2. Here the interferers act like additional independent Gaussian

background noise. This is because the MAI on the flat Rayleigh fading channel has a

Gaussian first order distribution assuming synchronous transmission. And the MAI over

uncorrelated Rayleigh channel has less limitation on the performance. Since the MAI is

relatively low in this kind of system, the difference between the performance of different

PIC stage is not quite obvious. All the multi-user detection algorithms work well in this

situation, and the SIC and PIC perform almost the same as the MMSE and MLD, which

have already reached the single user bound.

1 2 3 4 5 6

0.024

0.026

0.028

0.03

0.032

0.034

0.036

0.038

0.04

0.042

0.044

Number of users

BE

R

Comparison of different MUD of BPSK modulated signals over uncorrelatedRayleigh channel at SNR=10dB

correlationdecorrelationMMSEMLDSICPIC-2 stages

Figure 3.3.3 Simulation-based BER versus the number of users performance of different MUD

methods for DS-CDMA at SNR=10dB using BPSK modulation over uncorrelated Rayleigh channel, using the gold sequence where SF=15.

Figure 3.3.3 shows the result of the different MUD algorithms over uncorrelated

Rayleigh channel at the SNR=10dB. From the result we can see that the SIC and PIC

perform better than other MUD algorithms. The PIC almost keeps a flat BER although

39

the number of users is increasing. The performance of SIC and MLD accelerate a little

more at high number of users. While decorrelation and MMSE accelerate faster as the

number of user increases.

3.3.2 Comparison of Different Detection Schemes The main criterion to measure if a certain multi-user detection is a suitable way in some

particular situations is the system capacity and performance improvability. However, the

conclusion from [24, 25, 26] which compare the implementation complexity and

performance of MUD methods is that by appropriately designed, all MUD methods will

have similar performances. So the complexity is the main standard.

In decorrelating or MMSE detector, it needs to do the matrix inversion in every symbol

period, because the matrix elements depend on the cross-correlations of the spreading

codes. If a long code is used to support the users, it will be a hard work to do the

inversion since the complexity is cubic with the matrix size. Although some iterative

algorithms such as the conjugate gradient and the preconditioned conjugate gradient can

be used to reduce the complexity, the workload can not be substantially cut down.

IC methods cancel the MAI in a totally different way. To remove the MAI when a long

code exists, IC methods regenerate the signal of each interferer, using the CIR and the

spreading code for each user to reconstruct the initial data and subtract them from the

received signal, instead of doing matrix inversion, thus only require less implementation

complexity while provide even better performance. Although the complexity of the IC

methods is much less than conventional methods, it will increase linearly with the

number of users. Table 1 presents some advantages and disadvantages of different MUD

methods.

Table 1 Comparison of Detection Schemes

Detection Scheme Advantage Disadvantage

Correlated Detector Simplicity Low capacity

Decorrelating

Detector

Near-Far resistance

Substantial capacity gain

Linear computational complexity

Worse BER in low SNR

MMSE Detector Better BER than Decorrelatin

Detector in low SNR

Required estimation of amplitudes

Required matrix inversion

40

MLD High capacity Exponential computationa

complexity

Decorrelating

Decision-Feedback

Detector

High capacity gain ove

multistage detector

Need to estimate amplitude

Required Cholesky factorizatio

and matrix inversion

Successive

interference

cancellation

Near-far resistance A bit delay per stage of cancellatio

Quite complex when supportin

large users

Parallel Interferenc

Cancellation

Near-far resistance Quite complex when supportin

large users

3.4 Summary In the DS-CDMA system, multiple access interference (MAI) is a main problem to limit

the capacity. The most efficient way to combat the MAI is using multi-user detection

(MUD). Most of the detectors can be set into two categories: linear and subtractive

(nonlinear) MUD. In this part of the project, we implement the successive interference

cancellation and parallel interference cancellation which are the two main categories of

the nonlinear MUD, calculate the implement complexity and compare the performance of

these detectors with some other detectors such as correlating, decorrelating, MMSE and

MLD. From the comparison results, it is clear that both successive and parallel

interference cancellation schemes have good performance but can be achieved much

simpler. From the comparison between PIC and SIC we can see that the PIC detector

needs more hardware to implement but the SIC needs to deal with the power

rearrangement and large delays. Several ways [23] for improving the SIC and PIC

performance have been proposed, which can be studied later.

41

Chapter 4

Reduced multi-user channel estimation and detection algorithm

The results presented at the last chapter are based on the assumption that we can get the

perfect channel estimation. While in the real situation, the receiver will receive the

signals came from the different paths caused by the ground-reflected of the transmitted

signals and the direct line-of-sight path in the channel. These different paths in the

channel will induce arbitrary factors to the transmitted signals such as various delays,

attenuations and phase shifts and will induce fading because of the mobility of the users

[7]. All these elements added together present an impediment to prevent the receiver

decoding the data bits correctly. The aim of multi-user channel estimation is to jointly

detect these unknown factors for all users to mitigate the influence posed by the channel,

thus leading to a more correct detection at the receiver. While multi-user detection which

has been discussed in the former chapter refers to detect the exact data bits of different

users accurately and cancel the interference inflicted by all the other users. The work of

[8] has confirmed that by combining channel estimation and multi-user detection we can

get lower calculation complexity and better bit error rate (BER) performance than

employing them separately thus to meet the real-time requirements. We will discuss these

in this chapter.

4.1 Introduction to Multi-user Channel Estimation and Detection

In the third-generation wireless cellular systems DS-CDMA becomes a dominative

technique since it has many prerogatives when compared with other techniques. The

main constraint which limits the capacity and the performance of DS-CDMA system is

the time varying characteristic of the mobile radio channel and the MAI [3]. Multi-user

detection plays an important role in the DS-CDMA system since it is the most efficient

technique to combat the MAI so that the data bits of different users can be retrieved

exactly. However, the signals received by the receiver suffered from multi-path fading

which imposes the different amount of attenuations and delays to the transmitted signals

42

will be not easy to be recovered. The aim of channel estimation is to detect these

unknown time varying parameters of the channel to make the recovery of the data bits

more reliable [8].

Moreover, near-far effect is a serious problem in the CDMA system. Even a small

amount of the near-far effect can affect the performance of the whole system drastically.

So the efficient multi-user channel estimation and detection algorithm must be near-far

resistant.

The work of [27] and [28] investigates techniques to detect the demanded parameters for

all the users jointly. Although these algorithms can provide good performance, they are

not easy to be implemented because there are so many parameters in this multi-

dimensional situation that it is difficult to get an optimum decision. [29]-[32] present a

technique to decompose the multi-dimensional optimization problem into single

dimensional. These techniques are near-far resistant and efficient in dealing with the

multi-path fading situation. The work of [9] and [10] introduces a way to combine these

subspace-based channel estimation techniques with the efficient multi-user detection.

However, these algorithms still have fatal disadvantages. The main problem is that such

algorithms need to estimate signals or noise in the progress which increases the

calculation complexity. Another problem is that it presents a limitation on the number of

users it can deal with.

Since the third-generation wireless system is aimed to support high data rate [33], highly

efficient multi-user algorithm for channel estimation and detection need to be invented.

Fortunately, the maximum-likelihood (ML) technique emerged and people invented a lot

of channel estimation algorithms based on this ML technique, such as in [16] and [17].

These ML-based algorithms are efficient in realization and can deal with a large number

of users, which can also provide an excellent performance.

In this chapter we will present another way to achieve efficient channel estimation

through an iterative scheme based on the ML principle and extend to joint channel

estimation and detection based on [7] to see how the system can benefit from this

algorithm.

43

4.2 System Model

Figure 4.2.1 shows the block diagram of this kind of combined multi-user channel

estimation and detection algorithm at the receiver. By transmitting the training sequence

through the channel, the ML channel estimate can be obtained. When the training

symbols are not allowed, we use the decision feedback algorithm to gain the knowledge

of the time-varying channel.

Figure 4.2

In the tra

training p

locally. T

at the rec

While in

receiver.

update th

the equal

response.

MultipleUsers

.1 Block diagram of the system model of the multi-user channel estimation and detection in the receiver. The training sequence (pilot) is used for channel estimation and decision feedback is used to update the estimates in the absence of a pilot.

ining mode, the transmitter transmits a prefixed sequence (pilot) during the

eriod. Since the receiver knows the sequence, it can generate this pilot sequence

hus, during the training period, the equaliser produces the transmitted symbols

eiver and can use them as the desired response to adapt the coefficients.

the decision feedback mode, there is no pilot sequence transmitted to the

In order to track the time varying channel, the equaliser must continuously

e coefficients of the equalizer by using the decisions at the output of

izer which are assumed to be correct to substitute for as the desired

The decision feedback mode can be illustrated by the Figure 4.2.2.

s(k − d)

s(k − d)

44

Figure 4.2.2 Block diagram of the decision feedback mode.

4.2.1 Received Signals Model Suppose the whole system is DS-CDMA system and the data bits are BPSK modulated,

where each user uses a unique spreading sequence to modulate the symbol bits . The

input to the receiver is a summation of the signals from all the users, attenuated by the

different delays and phase shifts. Although the multi-user detection can combat the MAI,

but if the data bits suffered from deep fading, the transmitted bits can not be retrieved

accurately. So when the system consists of multi-path fading, that is, each user’s bits are

transmitted to the receiver from separate propagation path, then the multi-user channel

estimation will present a more important role in the detection part since the performance

of the multi-user detection will depend heavily on the correctness of the channel

estimation. The signals received after multi-path channel can be written as [7]

(±1)

ˆ ,i ir Ad ni= + (12)

where Nir C∈ is the matrix of the received signals, N is the length of the PN sequence.

K is the number of users. di ∈ −1,+1 2K = [d1,i−1,d1,i ⋅ ⋅⋅,dK ,i−1,dK ,i ]T are the bits of

different users need to be detected while i is the time index. The size of is di 2K since

we assume that all the user data bits are coarse synchronized during one symbol period,

as illustrated in the Figure 4.2.3. Therefore only two successive symbols of every user

may overlap. n is the AWGN imposed in the channel. i2N KA C ×∈ is the matrix containing

45

the mixed information of the PN sequence of each user and the channel effect including

the delays, attenuations and phase shifts of each path. So our channel estimation is aimed

to detect these unknown parameters jointly for all the users to mitigate the effects and

provide an accurate estimation to detect the received bits of each user.

Figure 4.2.3 The received signal mode at the output of the multi-path channel.

4.2.2 Maximum Likelihood Multi-user Channel Estimation [8] presents a good channel estimation technique, maximum likelihood technique, to

provide an accurate estimation of the multi-path channels. Consider the training mode

situation, while the training bits b1,b2 ,⋅ ⋅ ⋅,bL are known and the corresponding received

signals are where is length of the observation window. The received signal

vector is conditionally independent with the training bits and each of them is Gaussian

distributed. Therefore we can write the joint conditional probability density function of

the training bits and the corresponding received bits as [8]

r1,r2 ,⋅ ⋅ ⋅,rL L

1 2 1 2

1

( , , , | , , , , )

1 exp ( ) ( ) .

L L

LH

i i i iNLi

p r r r A b b b

r Ab r Abπ =

⋅⋅⋅ ⋅ ⋅ ⋅

⎧ ⎫= × − − −⎨ ⎬

⎩ ⎭∑

(13)

Ignoring terms which will not affect the result, the corresponding log-likelihood function

becomes Λ

46

(14) 1

( ) (L

Hi i i i

i

r Ab r Ab=

⎧Λ = − −⎨⎩ ⎭∑ ) .⎫⎬

The maximization is achieved when the estimate A satisfies [7]

(15) ˆ .bb brR A R=

Where the sample correlation matrices used in (4) are defined as [7]

1

1

.

LH

bb i iiL

Hbr i i

i

R b b

R b r

=

=

⎧=⎪⎪

⎨⎪ =⎪⎩

∑

∑

Thus, the unconstrained estimates are obtained from the knowledge of the received

signals and the known training sequence. In order to get the estimate A , we need to

compute the correlation matrices and and implement the matrix inversion of the

function (15) to get the estimate.

Rbb Rbr

4.2.3 Multi-user Detection We apply the parallel interference cancellation as the way to implement multi-user

detection. As shown in the Section 3.2, the PIC cancels the interference of all the other

users from the received composite signals to retrieve the data bits of the appointed user. It

is always iterative for multi-stage to achieve the desired performance. And it is

calculation efficient, the complexity of PIC proportion is of the order of O . Another

advantage to apply PIC is that it is possible to insert the channel estimation matrix

directly into the PIC stage instead of explicitly extracting the parameters [7]. So we use

the PIC at the detection part.

(K 2 )

4.3 Iterative Implement of the ML Channel Estimation [7] Based on the equation (15), in order to get the estimate A , we need to compute the

correlation matrices and and implement the matrix inversion, , at the end

of pilot to get the estimate. Since the direct inversion of the matrix is computationally

Rbb Rbr Rbb−1Rbr

47

intense and will induct delays to the detection of the data after the pilot, some iterative

schemes have been invented.

4.3.1 Iterative Schemes for Channel Estimation Since the direct inversion of a matrix is quite complex especially when the dimension is

quite large, some iterative matrix-inversion schemes such as least mean square algorithm

and recursive least squares have be applied. These reduce much of the computational

complexity. These two algorithms are implemented as follows.

1) Least Mean Square Algorithm

Given the set of the input samples u(1),u(2),⋅ ⋅ ⋅,u(N ) and the set of the desired

response , computes the output of the filter:

d(1),d(2),⋅ ⋅ ⋅,d(N )

⋅⋅⋅0

( ) ( ), 0,1, 2, .M

kk

y n w u n k n=

= − =∑

The calculation of the parameters w0 (n),w1(n),⋅ ⋅ ⋅,wM −1(n) is carried out by the

following steps:

1) Initialize w . (0) = 0

2) For each time instant, computes w . (n) = w(n −1) + µu(n)(d(n) − wT (n −1)u(n))

2) Recursive Least Squares Algorithm

RLS algorithm obtains the tap weights w0 (n),w1(n),⋅ ⋅ ⋅,wM −1(n) in a different way:

1) Initialize w . (0) = 0

2) For each time instant, computes

( ) ( 1) ( ) ( )( ( ) ( 1) ( ))1( ) ( ( 1) ( 1) ( ) ( ) ( 1)),

( ) ( 1) ( )

T

TT

w n w n P n u n d n w n u n

P n P n P n u n u n P nu n P n u nλ

⎧ = − + − −⎪⎨ = − − −⎪ + −⎩

−

where the λ ∈(0,1) is an exponential weight factor.

Obviously RLS algorithm has higher computational requirement than LMS, but behaves

much better in terms of steady state MSE and transient time.

While [7] gives another iterative way to calculate the correlation matrices and achieve

matrix inversion based on the gradient descent algorithm to reduce the complexity. That

is, the iterative algorithm updates the channel estimate after every single pilot is received

48

instead of waiting until all the pilots have been received. At every time during, the

channel estimate A moves closer to the ML estimate so that at the end of the pilot, the

full channel estimation has already been obtained.

The computation formulas in each bit during are [7]

(16) Rbb(i ) = Rbb

(i−1) + bibiT

(17) Rbr(i ) = Rbr

(i−1) + biriH

(18) ( ) ( 1) ( ) ( 1) ( )ˆ ˆ ˆ( *i i i i ibb brA A R A Rµ− −= − − ).

The constant µ represents the step size with the value less than the reciprocal of the

largest eigenvalue of [7]. Rbb(i )

This iterative channel estimation algorithm can also be used to track slowly time varying

channel by feeding back the decisions from the MUD to update the estimate. The

correlation matrices can be obtained through [7]

( ) ( 1)

( ) ( 1) .

i i T Tbb bb i i i L i L

i i H Hbr br i i i L i L

R R b b b b

R R b r b r

−− −

−− −

⎧ = + −⎪⎨

= + −⎪⎩ (19)

where is the length of the sliding window. L

4.3.2 Simulation Results of the Iterative Schemes Figure 4.3.1 gives the results of this iterative scheme and the RLS algorithm compared

with the direct matrix inversion. This simulation result is obtained when the data bits of 7

equal power users transmitted through a AWGN channel which have three paths with the

relative strengths 1, 0.5, 0.33, using the Walsh code with the spreading factor equals to

16, at the SNR equals to 10dB. The BER is calculated at the output of the MF filter (stage

0) and the PIC first stage at the end of the pilot. The exponential weighting factor λ = 1

is chosen.

From the curves we can see this iterative scheme performs almost the same as the RLS as

well as the direct matrix inversion. All the curves converge when the preamble length

extends to larger than 128, thus we use L = 128 in later simulation. We can also see that

a large value of µ will lead to a fast convergence, thus it is possible to get the full

channel estimation through a smaller pilot sequence length.

49

This iterative scheme can perform almost the same as the RLS and the exact ML

algorithm but reduce the computation complexity greatly. It will not induce delay at the

end of the pilot so that it can be used in the real-time situation.

0 50 100 150 200 250 30010-3

10-2

10-1

100Comparison of different channel estimation algorithms

Length of training sequence

BE

R

MF-RLSMF-InversionMF-ITER u=1/1024MF-ITER u=1/256PIC-RLSPIC-InversionPIC-ITER u=1/1024PIC-ITER u=1/256

Figure 4.3.1 Comparison of BER performance of different estimation schemes versus different

preamble length at the SNR=10dB, Walsh code, SF=16, 7 equal power users.

Figure 4.3.2 shows the result of the BER performance when using this proposed iterative

scheme and the matrix inversion based scheme to track the slow fading channel. The

result is obtained based on the equation (19) with the assumption that the carrier

frequency is 1.8 GHz, the mobile velocity is 10km/h and the length of the preamble

equals to 128 which is the same as the window size. 15 equal power users are simulated.

The matrix inversion scheme works on static channel assumption and is not updated with

the decision feedback, while the proposed iterative scheme updates the estimate at every

bit interval. From the simulation result we can see that this iterative scheme tracking the

time-varying channel based on the equation (19) works quite effective and avoids the

50

computation of matrix inversion. Therefore, the proposed iterative scheme is a quite

effective technique.

4 5 6 7 8 9 10 11 1210-3

10-2

10-1

100

The error rate performance of iterative scheme and matrix inversion scheme ina multipath fading channel

Eb/No(dB)

BE

R

MF-StaticMF-ITERPIC-StaticPIC-ITER

Figure 4.3.2 Comparison of the BER performance of the proposed iterative scheme and the matrix

inversion scheme at the slow fading channel of 10km/h mobile velocity with the carrier frequency 1.8GHz. The pilot length equals to 128.

4.4 Pipelined Multi-user Detection [7] As we assumed at the Section 4.2.1, all paths are coarse synchronized in one symbol

period so that only two symbols may overlap in the observation window, then the channel

matrix 2N KA C ×∈ can be reset into its even and odd columns 0 1, N KA A C ×∈ to fit with the

continuous bit streams and ; where di−1 di di ∈ −1,+1 K = [d1,i ,d2,i ,⋅ ⋅ ⋅,dK ,i ]T are the bits

of all K users received at the time [7]. Therefore, the received signals can be rewritten

as

i

(20) 10 1[ ] i

ii

dr A A n

d−⎡ ⎤

= ⎢ ⎥⎣ ⎦

.i+

51

Then the signals go to the multi-user detection part.

The matched filter, which is used to get the initial data estimate of the PIC detector,

computes the correlation between the input bits and the received bits. The hard decision

of the received bits at the output of the matched filter can be expressed as

(21) 1 1 0ˆ ( [ ]).H H

i id sign A r A r−= ℜ + i

These initial estimates are input into the multi-stage PIC detector to recover the

transmitted bits more accurately. The hard decisions at the output of the final stage are

fed back to the channel estimation part to track the channel if there is no pilot in the

system.

4.4.1 Pipelined PIC Detector Former parallel interference cancellation can not be directly implemented into this

situation since we have not considered the channel estimation at the detection part.

Whereas the work of [34] and [35] provides a block-based way to implement multi-user

detection. However, this block-based process is complex and there are two main

drawbacks in this kind of implementations. The main disadvantage is that the block-

based way needs a windowing strategy. It can not work unless all the bits in the window

have been received. Another drawback is the windowing effect which makes a window

with size can only be used to detect L L − 2 bits since the edge bits can not be detected

correctly, thus reduces the efficiency. [36] introduces a way to make the multi-user

detection pipelined to avoid edge effects and enhance the efficiency. Implementing this

concept into this case, we can make the PIC algorithm pipelined as [7]

(22) L = ℜ A1H A0⎡⎣ ⎤⎦

C = ℜ A0H A0 + A1

H A1 − diag A0H A0 + A1

H A1( )⎡⎣

⎤⎦ (23)

(24) yi(l ) = yi

(0) − Ldi−1(l−1) − Cdi

(l−1) − LH di+1(l−1)

(25) ( ) ( )ˆ ( )lid sign y= .l

i

The matrix K KL R ×∈ is the partial correlation matrix which contains the information of

the past bits of the desired user and the interfering users. H K KL R ×∈ is the partial

correlation matrix contains the information of the future bits of the desired user and the

52

interfering users. K KC R ×∈ is the matrix contains the correlation information of the

current bits of the interfering users [7]. In PIC algorithm, the interference imposed by all

the other users should be cancelled to get the information bits of the desired user. So in

(23), the last part means to cancel the desired user’s information to make sure only

interfering users’ signals be cancelled. i is the time index and l is the number of

iteration. Then the soft estimation in the equation (24) can be viewed to subtract the

interferences imposed by the past bits and the future bits of the users, which have more

and less delays than the desired user. (25) makes the hard decision to the estimate. The

output of this stage will be the input of the next stage. The process can be repeated for a

few iterations to meet the desired performance.

Figure 4.4.1 Block diagram of the pipelined implementation of multi-user channel estimation and

detection.

Figure 4.4.1 shows the reduced multi-user channel estimation and detection of the whole

system. The channel estimation has been made in an iterative scheme and the multi-user

detection has been made to implement in a pipelined way. The complexity can be

reduced and the whole system can work more efficient to meet the real-time requirement.

53

4.4.2 Simulation Results of the Pipelined PIC Detector

0 2 4 6 8 10 12 14 16 18 2010-5

10-4

10-3

10-2

10-1

100Combined multiuser channel estimation and detection

Eb/No(dB)

BE

R

Sliding correlator - MFMFPIC-stage1PIC-stage2PIC-stage3PIC-stage4single user bound

Figure 4.4.2 Simulation-based BER versus the SNR per bit, Eb/N0. performance of this combined

iterative multi-user channel estimation and pipelined PIC detector for DS-CDMA using BPSK modulation over AWGN channel with 3 different paths, where SF=32 is the length of spreading sequence (Walsh code) and K=15 is the number of users, u=1/256, L=128 is the preamble length.

Figure 4.4.2 shows the result of this iterative reduced multi-user channel estimation and

the pipelined PIC detector at the end of the system. This result is obtained when using

BPSK modulation in the DS-CDMA system, while the spreading code is the Walsh code

with the spreading factor equals to 32. Supposed there are 15 users in the system and the

channel is the AGWN channel with three different paths. Because at the preamble length

the proposed iterative scheme can reach the performance of the maximum

likelihood estimation, we use

L = 128

µ = 1 / 256 and L = 128 in our simulation. From the curves

we can see that with the number of the PIC stages increasing, the performance of the

whole system goes better, which agreed with our results at the Section 3.2.3. The multi-

stage PIC can enhance the performance but can never reach so close to the single user

bound as that in the single path AWGN channel since the multi-path will more or less

54

induce some influence to the final result. If there is no significant change of the data bits

detected at the former stage, then there will be no much difference in the succeeding

stage. But this iterative channel estimation scheme and the pipelined PIC detector can

still provide a good performance and what is more important is that this combined multi-

user channel estimation and detection reduces the computation complexity dramatically

thus it can be used in real-time situation.

0 2 4 6 8 10 12 14 16 18 2010-4

10-3

10-2

10-1

100Comparison of different pilot length with u=1/256

Eb/No(dB)

BE

R

L=50L=80L=100L=128

Figure 4.4.3 Comparison of the BER versus the SNR per bit, Eb/N0. performance of this combined

iterative multi-user channel estimation and pipelined PIC detector for DS-CDMA using BPSK modulation over AWGN channel with 3 different paths, while using the different preamble length at u=1/256, where SF=32 is the length of spreading sequence (Walsh code) and K=15 is the number of users.

Figure 4.4.3 shows the BER performance of this system at the output of the stage 3 of the

PIC detector over 3 paths AWGN channel while using Walsh code with SF equals to 32

and supporting 15 users in the system. From the Figure 4.3.1 we can see the iterative

channel estimation scheme can not reach the best performance until the preamble length

is larger than 128. Therefore when the pilot length equals to 50, the system can not get

the sufficient channel parameters so that the performance degrades. When the preamble

55

length equals to 80 or 100, the channel estimation goes better and leads to a better

performance at the end.

4.5 Summary The signals transmitted to the receiver may travel through different paths in the channel

which will induce several amount of attenuations and delays to the signals. All these

parameters will cause the BER degrades at the receiver. Channel estimation aims to

detect these parameters to mitigate the effects thus leading to a more accurate detection.

Previous channel estimation techniques are computation inefficient and not resistant to

the near-far effect. Maximum likelihood technique presents a novel way to do the channel

estimation since it is near-far resistant and works quite effectively. While multi-user

detection is another way to enhance the BER performance since it can combat the

multiple access interference efficiently. However, combined channel estimation and

multi-user detection can even more reduce the computational complexity and provide a

better performance. In this part of the project, we present an innovative technique to

combine the multi-user channel estimation and detection based on the paper [7]. The

channel estimation is based on the ML but is implemented in another iterative way to

reduce the complexity and meet the real-time requirement. And the multi-user detection

is based on parallel interference cancellation but is implemented in pipelined. Our

simulation results show that this reduced multi-user channel estimation and detection

gives a good performance at the receiver, in the presence of multi-path effects and MAI.

Therefore, it is a practical way to reduce the complexity while at the same time maintains

the required performance.

56

Chapter 5 Spatial Diversity Techniques

Because of the hostility of the mobile channels which will induct multi-path transmission

and fading to the signals, the BER at the receiver degrades. Spatial diversity technique

such as using multiple transmitter and/or receiver antennas to generate multiple

communication paths can be used to overcome multi-path fading, polarization mismatch,

and interference, hence improves the BER performance and increases the capacity of the

system. Another type of spatial diversity techniques can be envisaged is to use some idle

mobile stations which seating between the sender and the destination as a relay to amplify

and forward the data bits in the systems, which can be classified as distributed spatial

diversity [14]. Both types of spatial diversity can mitigate the effects of fading and

improve the BER performance.

5.1 Multiple Transmit and/or Receive Antennas

Using multiple transmit and/or receive antennas to make sure all the signals transmitted

to the receiver through different paths can generate spatial diversity and thus combat the

effects of the fading. In this section we will represent some simulation results of the

multiple antennas system to see how the BER performance can benefit from this type of

spatial diversity technique.

5.1.1 Single Transmit Antenna and Multiple Receive Antennas-Based System The system of single transmitter and multiple receivers means that one or more users

simultaneously transmit their information through one antenna. At the receiver side, more

than one antenna is used to receive.

Assume M is the number of receive antennas. Figure 5.1.1 shows the result of K users

over AWGN channel with single transmit & receive antenna system and single transmit

& multiple receive antennas system. The difference between them is quite distinct. In the

multiple situation, sum of the received signals’ gain is M times larger than the one with

57

single receive antenna which brings on the SNR enhanced by M times than before.

Therefore, the performance can be much better than the performance of single user over

AWGN channel, which can be seen in Figure 5.1.1. And the number of users still affects

the performance. That is, as the number of users increases, the performance degrades. But

if we increase the number of receive antennas, the performance can go better.

Figure 5.1.1 Simulation-based BER versus the SNR per bit, Eb/N0 performance of correlated

detector for DS-CDMA with multiple receivers and single transmitter using BPSK

modulation over uncorrelated Rayleigh channel, where SF =7 is the length of spreading

sequence and K is the number of users.

5.1.2 Multiple Transmit Antennas and Single Receive Antenna-Based System In real systems, the receiver can get data from more than one transmitter. In this case,

sum of received signals’ gain is divided by the factor M. Figure 5.1.2 shows the BER

performance of this kind of system. From the curve we can see that as the number of

users increases, the BER degrades. Since the MAI will not vanish because of the spatial

58

diversity of the system but will increase with the growth of the users. The upper bound is

the performance of single user over uncorrelated Rayleigh channel. If there are infinite

transmit antennas, the performance can achieve the upper bound. However, it is

impossible.

Figure 5.1.2 Simulation-based BER versus the SNR per bit, Eb/N0. performance of correlated

detector for DS-CDMA with multiple transmitters and single receiver using BPSK

modulation over uncorrelated Rayleigh channel, where SF=7 is the length of spreading

sequence and K is the number of users.

5.1.3 Multiple Transmit and Receive Antennas-Based System For a system with M number of transmit antennas and N number of receive antennas, the

transfer matrix H can be expressed as [37]

59

11 12 1 1 1

21 22 2 1 2

31 32 3 1 3

1 2 1

.

M M

M M

M M

N N NM NM

h h h hh h h h

H h h h h

h h h h

−

−

−

−

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

K

K

K

M M O M M

K

The performance of the multiple transmit and receive antennas system is shown in Figure

5.1.3. From the curves we can see that the number of receiver antennas plays a more

important role in improving the BER performance than the transmitter antennas. With the

same number of users, the system can benefit more from investing in more number of

receiver antennas than in transmitter antennas. Also increasing the number of users can

degrade the BER performance dramatically.

Figure 5.1.3 Simulation-based BER versus the SNR per bit, Eb/N0. performance of correlated

detector for DS-CDMA with multiple receivers and transmitters using BPSK

modulation over uncorrelated Rayleigh channel, where SF=7 is the length of spreading

sequence and K is the number of users.

60

5.2 Multi-Relay System [15]

Unlike the system discussed above obtains the spatial diversity by investing in multiple

transmit and/or receive antennas, the work of [14], [38] and [39] has introduced a new

way to gain the spatial diversity by using some idle mobile stations to relay the signals

between the transmitter and the receiver. The transmit diversity is obtained when the

selected stations assist the sender to transfer its information to the destination [15]. The

capacity and performance can be improved by this kind of co-operations between the

mobile stations.

5.2.1 Introduction to Multi-Relay System The advantages of using multiple transmit and/or receive antennas have been presented

above. However, the spatial diversity usually requires more than one antenna at the

transmitter and the receiver. Since not every wireless device can get multiple antennas

due to the size or complexity, the spatial diversity gain can not be obtained by these

single antenna systems. In recent years, a new type of methods called cooperative

communication [12] introduces a novel way to enable single-antenna mobiles to achieve

transmit diversity by choosing some nearby idle mobile stations as the relays to transfer

the information signals from the transmitter to the destination. This type of co-operation

makes the single antenna mobile looks like a virtual multiple-antenna transmitter because

at the receiver, it seems like there are signals transmitted from different locations, thus

the receiver can get several independently copies of the transmitted signals. Therefore the

transmit diversity is generated and can be used to combat the multi-path fading. There are

several ways of cooperative transmissions. Figure 5.2.1 and Figure 5.2.2 represent two

main methods of collaboration. For simplicity, we only picture one relay in the system

since the point is that every mobile has a partner providing another data path to generate

diversity.

61

Figure 5.2.1 Amplify and Forward Strategy, © IEEE Commun. Mag., Nosratinia [12], 2003.

J. N. Laneman first proposed this amplify and forward strategy at [40]. This strategy

works as follows: the mobile station which has been chosen as a relay to the sender

receives a noisy version of the signal suffered from the fading channel, and then

amplifies and retransmits this signal to the receiver. While at the destination, the receiver

receives two versions of the data bits from the transmitter and the relay, combines them

together and makes a hard decision to the received bits. Although the noise will be

amplified at the relay station, the diversity gain will make the final decision more

accurate.

Figure 5.2.2 Detect and Forward Strategy, © IEEE Commun. Mag., Nosratinia [12], 2003.

Sendonaris first developed this kind of cooperative communications at [39]. In this

scheme, when the mobile station which acts as the relay between the sender and the

62

destination receives the data bits from the transmitter, it will try to detect the data bits,

and retransmits the estimate of the transmitted bits to the receiver, which is shown at the

Figure 5.2.2. The receiver gets the two independently faded versions of the signal and is

thus able to make better decisions for the transmitted bits. But the problem arises. Since

the data bits suffered from the fading channel, the relay stations may make an error

decision to the transmitted signals. While this error estimates transmitted to the

destination, it will be detrimental for the receiver to make the detection of the bits.

However, Laneman invented a hybrid detect and forward strategy to avoid the problem of

error propagation in [41], that is, when the signals suffered the serious fading, the data

bits transmit directly to the receiver without using any relay; when the channel quality is

much better, then the system uses this detect and forward strategy to improve the

capacity.

The work of [13] has proofed that in the case of independent flat fading channels which

contain path loss, both these two strategies have the similar BER performance. Unlike the

previous researches focusing on the different relay strategies, we will discuss how the

final BER can benefit from the number of the amplifying relays and the different relay

gains based on the amplify and forward strategy.

5.2.2 System Model

In our multi-relay system model, we assume that there are K stations chosen to be the

relay stations to amplify the signals received from the transmitter and retransmit them to

the destination. Suppose each station in this system only uses one transmit and receive

antenna and there are only K +1 paths from the transmitter and the receiver: one single

hop path and K two hop paths [11]. In order to avoid the relay stations receiving the

signals from the neighbour channels or retransmitting the signals to the neighbour

channels, which will cause diversity between the relay stations and the sender or the

receiver, we allocate different channels to different radio links to make sure each channel

is orthogonal to all the other channels. The receiver is the only place to receive the

signals transmitted from the sender and the relay stations. Figure 5.2.3 briefly represents

the whole system.

63

Figure 5.2.3 Multi-relay system model.

In the Figure 5.2.3 , and h represent the flat fading channel coefficients, which

are assumed to be mutually independent and zero-mean, with the variances Ω ,

h0 h1,k 2,k

0 Ω1,k and

, respectively. , and are the additive white Gaussian noise with

the variances , and . is the data bits transmitted at the time . is

the signals received by the relay station and is the signals received by the

destination came from the relay station .

Ω2,k z0[n] z1,k[n] z2,k[n]

N0 N1,k N2,k x[n] n uk[n]

k yk[n]

k α k represents the relay gain which is

controlled by the automatic gain controller (AGC) to make the output power of the relay

stations meet the CDMA standard [42]. So that at the time when the sender sends out

the information symbols to the relay stations and directly to the receiver, the signals

received at the destination will be [15]

n

x[n]

y0[n] = h0 E0 x[n]+ z0[n] (26)

uk[n] = h1,k E0 x[n − dk ]+ z1,k[n] (27)

2, 2,

2, 1, 0 2, 1, 2,

[ ] [ ] [ ]

[ ] [ ] [ ],k k k k k

k k k k k k k k

y n h u n z n

h h E x n d h z n z n

α

α α

= +

= − + + (28)

Relay K

Relay k

Relay 1

Sender Destinatio

h1,k

h1,1

h2,K

h2,k

h2,1

h0 z0[n]

z1 K[n]

z1 k [n]

z1, 1 [n]

z2 K[n]

z2 k [n]

z2, 1 [n]

α K u K[n]u K[n] y K[n]

u k [n]

u 1 [n]

α k u k [n]

α 1 u1 [n]

yk[n]

y1[n]

· · ·

· · ·

y0[n]

64

where and is the transmitted symbol energy of the transmitter derived from

the

k ∈[1,K ] E0

M − PSK constellation with unit energy [15]. is the delay at the relay dk k which

may induce inter-symbol interference between the transmitter and the receiver if without

the choice of orthogonal channel allocations.

In order to restrict the emitted energy per symbol at the output of the k th relay to be ,

we can deduce from the equation (27) to get that

Ek

22

0 1, 2

0 1,

, [1, ]kk k k k

k

E ,E h E k KE h

α α= ⇒ = ∈ (29)

when ignoring the noise at the relay in this equation. If we add the noise into calculation,

we can get that

2

0 1, 1,

, [1,kk

k k

E k KE h N

α =+

].∈ (30)

From the equations (29) and (30) we can see that the relay gain depends on the magnitude

of the channel coefficients . Therefore, training symbols need be added into the

information sequence to make sure each relay can get the estimate of its own

receive channel [15].

h1,k

x[n]

The multi-relay system, as introduced above, can really provide spatial diversity since the

receiver can collect several independent copies of the transmitted signals at the

destination from different locations, thus generates transmit diversity to combat the

effects of fading.

x[n]

5.2.3 Mathematical Analysis of the Multi-relay System At the transmission destination, the receiver combines the signals came from the 1K +

subchannels and makes the hard decision to the received signals to recover the original

signals. In order to obtain the maximum performance, the receiver combines the signals

based on a maximum ratio mechanism [43]. Since every relay channel has its own delay,

the receiver does not decode the signals until all the relayed signals have been obtained.

Because of the difference of the noise power at the 1K + diversity branches, every

subchannel must be weighted by its particular complex fading gain over total noise power

before the combiner. After signals combined, the estimated symbol can be written as [15]

65

( ) ( )

* **1, 2,0 0

010 1,

* **1, 2,0 0

0 0 0 2, 1, 0 2, 1, 2,10 1,

ˆ[ ] [ ] [ ]

[ ] [ ] [ ] [ ] [ ] .

Kk k k

k kk k k

Kk k k

k k k k k k k k kk k k

h h Eh Ex n y n y n d

N h N

h h Eh Eh E x n z n h h E x n h z n d z n d

N h Nα α

=

=

= + +

= + + + + +

∑

∑ +

(31)

By substituting (29) into (31), we can get

22 *2,0 0 0 0

010 0

2 * *2, 1, 2,

1, 2,1 1,1, 0

ˆ[ ] [ ] [ ]

[ ] [ ]

Kk k

k k

Kk k k k k

k k k kk k kk k

h Eh E h Ex n x n z n

N N N

h E h h Ez n d z n d

h Nh N E

=

=

⎛ ⎞⎜ ⎟= + +⎜ ⎟⎝ ⎠

⎛ ⎞⎜ ⎟+ + +⎜ ⎟⎝ ⎠

∑

∑ ,+

(32)

where 2

2 2,2, 1, 2, 1, 2,2

1, 0

k kk k k k k k

k

h EN h N N N N

h Eα= + = k+ is the total noise power of the signal

from relay k . Training symbols are used to estimate the fading channel coefficients and

the corresponding noise power [15].

Then the SNR on the direct transmission branch will be 20 0 0 / 0E h Nγ = and the SNR of

the subchannel between the sender and the relay will be 2

1, 0 1, 1,/k k kE h Nγ = ,2

2, 2, 2,/k k k kE h Nγ = will represent the SNR between the relay station

and the receiver. Then the SNR of the branch can be calculated as k

1, 2,

1, 2,

, [1,k kk

k k

k K ]γ γ

γγ γ

= ∈+

[44]. Since 0γ , 1,kγ and 2,kγ are independent and exponentially

distributed [15], the mean of them can be written as 0 0 0 0/E Nγ = Ω , 1, 0 1, 1,/k k kE Nγ = Ω

and 2, 2, 2,/k k k kE Nγ = Ω .

The work of [15] proposed an equation of the exact average symbol error rate (ASER) of

this multi-relay system which is [15]

Ps =

1π

1+γ 0gPSK

sin2(φ)⎛

⎝⎜⎞

⎠⎟0

(( M −1) / M )π

∫−1

4γ p,k lk (φ) − γ s,k( )lk

2(φ) − 4γ p ,k

lnlk (φ) + lk

2(φ) − 4γ p,k

2 γ p,k

⎛

⎝⎜⎜

⎞

⎠⎟⎟+ γ σ ,klk (φ) − 4γ p,k

lk2 (φ) − 4γ p,kk =1

K

∏ dφ,

(33)

66

where M is the modulation mode (i.e., in the case of BPSK transmission, 2M = ),

, 2: sin ( / )PSKg Mπ= , 1, 2,k:k kσγ γ γ= + , , 1, 2:p k k k,2

, ,( ) : / sin ( )k k p k PSKσl gφ γ γ φ= +γ γ γ= , .

Because of the complexity to calculate the exact average symbol error rate, [15]

developed a way to calculate the rigid bounds of the ASER instead of calculating the real

symbol error rate, which are [15]

Plow :=1π

1+γ 0gPSK

sin2(φ)⎛

⎝⎜⎞

⎠⎟0

(( M −1)/ M )π

∫−1

Μγ up ,kk=1

K

∏−gPSK

sin2(φ)⎛

⎝⎜⎞

⎠⎟dφ

Pup :=1π

1+γ 0gPSK

sin2(φ)⎛

⎝⎜⎞

⎠⎟0

(( M −1)/ M )π

∫−1

Μγ low ,kk=1

K

∏−gPSK

sin2(φ)⎛

⎝⎜⎞

⎠⎟dφ,

⎧

⎨

⎪⎪

⎩

⎪⎪

(34)

where ,

, 1

,

( ) (1 )up k

p k

k

s sγσ

γγ

−Μ = − and , ,

( ) ( )2low k up k

ssγ γΜ = Μ .

Using the inequality 12 2

2

sin ( ) sin ( )11 sin ( )

aa aφ φ

φ

−⎛ ⎞

< + <⎜ ⎟+ ⎝ ⎠, (34) can be simplified to (35)

( )

1

,0

1 ,

1

,( 1)0

1 ,

: 1 1 ( ,

: 2 ( , ),

Kp k PSK

L PSKk k

Kp kK K

U PSKk k

gP g W K

P g W K M

σ

σ

γγ

γ

γγ

γ

−

=

−

− +

=

⎧ ⎛ ⎞⎛ ⎞⎪ = + +⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎪⎪ ⎝ ⎠⎝⎨⎪ ⎛ ⎞

=⎪ ⎜ ⎟⎜ ⎟⎪ ⎝ ⎠⎩

∏

∏

)M⎠ (35)

to avoid the integral calculation, where ( 1) / 2 2

0

1( , ) : (sin )M M KW K M d

πφ φ

π− += ∫ . (36)

The simulation results of Section 5.2.4 will verify that the bounds in (35) provide a tense

limit to the ASER of the whole system.

Consider the case when the system ensures the same transmit power, that is , and

under the situation of the same noise power, i.e.,

0 kE E=

0 1, 2kN N N ,k= = , with the definition that

the diversity order of the multi-relay system to be the power of , we can find

that and are in the order of

10 0( / )E N −

LP UP ( 1)0 0( / ) KE N − + , which implicates that the whole system

achieves full diversity order 1K + [15].

67

5.2.4 Simulation Results In order to show how single antenna mobiles can enjoy some of the benefits of multiple-

antenna systems by inducing the multi-relay system, we just consider the BPSK

modulated signals pass through the equally balanced uncorrelated Rayleigh fading

channel with the same average energy which makes sure that

and assume that 0 1, 2, 1, [1, ]k k k KΩ = Ω = Ω = ∈ 0 1, 2kN N N ,k= = for all the subchannels.

To make things simply, we also assume equal transmit power over all the branches,

, where is the total energy per symbol in the

system. Now we can see how the number of relays can affect the final ASER at the

receiver from the Figure 5.2.4.

Ek = Et / (K +1),∀k ∈[1, K ] Et = Ekk =0

K∑

From Figure 5.2.4 we can see that as the number of relay stations increases, the

performance goes better at the receiver. It is quite like the multiple antennas system,

while increasing the number of antennas at the transmitter, the BER performance

ameliorates. By collecting mutual independent versions of the transmitted signals through

different paths arrived at the receiver, the diversity is created. It is quite same as using

multiple transmit antennas to send the signals to the receiver. Figure 5.2.4 clearly

illustrates the advantage of this multi-relay system.

68

0 5 10 15 20 2510-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Et/N0(dB)

Ps

Performance of the multirelay network

Ps with K=0Ps with K=1Ps with K=2Ps with K=3

Figure 5.2.4. Simulation-based Average Symbol Error Rate (ASER) performance of different

number of relay stations in the multi-relay system, while K is the number of relays.

Figure 5.2.5 shows the simulation results of the system with a single-hop and a two-hop

transmission branches between the transmitter and the receiver and also draws the curves

of the equations (34) and (35) to see how the theoretic of the low and the up bounds can

limit the real ASER curve.

In this situation, K = 1, M = 2 , we can get that =1. gPSK

Writing these parameters into equations (34), (35) and (36) we get:

W (K, M ) =W (1,2) =1

2 πΓ(5 / 2)Γ(3)

=1

2 π

3 π42

=3

16;

PL =3

161+

Ek

N0

⎛⎝⎜

⎞⎠⎟

1+Ek

2N0

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

−1

; PU =34

Ek

N0

⎛

⎝⎜⎞

⎠⎟

−2

;

Pup =1π

1+Ek

N0 sin2 (φ)⎛⎝⎜

⎞⎠⎟

−1

1+Ek

4N0 sin2 (φ)⎛⎝⎜

⎞⎠⎟0

π /2

∫−1

dφ .

69

From the Figure 5.2.5 we can see that and present a tight bound to the real ASER

at the receiver. Specifically, the ASER curve leaves very close to the curve at low

SNR so that the presents a tight up bound to the ASER; the ASER curve moves close

to the curve at high SNR so that presents a tight low bound to the ASER. Since the

and depart close from each other, the equations (34) and (35) can be used to give

an approximate estimate of the real ASER performance for most SNR while reduces the

calculation complexity dramatically.

PL Pup

Pup

Pup

PL PL

PL Pup

0 5 10 15 20 2510-5

10-4

10-3

10-2

10-1

100

101

Et/N0(dB)

Ps

Bounds of the multirelay network(K=1)

PsPLPUPup

Figure 5.2.5 Simulation-based Average Symbol Error Rate (ASER) performance of the multi-relay

system, while there is one single-hop and one two-hop transmissions between the sender and the destination, to show how exactly the bounds of the equations (9), (10) can work.

70

0 5 10 15 20 2510-7

10-6

10-5

10-4

10-3

10-2

10-1

100Performance of the system with different relay gains

Et/N0(dB)

Ps

Ps with K=1ASER for the system with K=1 and relay noisePs with K=2ASER for the system with K=2 and relay noisePs with K=3ASER for the system with K=3 and relay noise

Figure 5.2.6 Simulation-based Average Symbol Error Rate (ASER) performance with different relay

gains in the multi-relay system, while K is the number of relays. Figure 5.2.6 shows the results of the multi-relay system with the different relay gains

which are indicated by the equations (29) and (30), while the number of relay stations

increasing from K = 1 to K = 3. The main difference of these two equations is that (30)

adds noise up. This relay gain in (30) accounts for the situation when the data bits suffer

from the deep fading in the channel ( h1,k is low). In our simulation results, these two

types of gains only lead to tiny difference of the ASER at the receiver at low SNR while

the number of relays extends form 1 to 3. With the SNR increasing, the difference

becomes a little greater. From the system aspect, we can use (29) instead of (30) because

it is more simply to analysis and gains more processing power.

5.2.5 Extensions and Future Work

In this multi-relay system, the diversity order 1K + is obtained by transmitting the

signals using one single-hop branch and K two-hop branches, each of which is total

different from the others. Therefore, the bandwidth efficiency is 1K + times lower than

71

the system with only one-hop transmissions [15]. In order to transmitting the original and

the relayed signals orthogonally so that they can be separated, time division is the most

straightforward method [12]. Sendonaris in [39] also invented a way to achieve

orthogonality through both time separation and orthogonal spreading codes. But there

still exists some problems in this kind of system.

The main problem is that in multi-user networks, how can the mobiles choose their

partners [45] [46]. In cellular systems, they provide a centralized mechanism for the users

to communicate with the central base station. When the base station accumulates some

knowledge of the mobile channels between the mobile stations, it is possible to assign

some partners to the appointed mobiles to optimize a given performance criteria, for

example, the average block error rate [12] for all users. However, there are no such

control mechanisms in the systems such as sensors network and ad hoc networks. In this

case it is important to let the mobiles decide which station can be chosen to be the partner

to cooperate at any time. Thus every mobile must have some knowledge of its adjacent

stations, which increases the complexity. If the mobile chooses multiple partners to

cooperative to transmit its signals, then a scheme must be developed, which can make the

mobile treats all the users fairly, does not need any additional resources, and can be

implemented feasibly in conjunction with the system multiple access protocol [12]. The

work of [47] has presented some significant work related to how to assign distributed

partner and multiple partners for the mobiles to cooperative.

Another problem about this multi-relay system is the power controls. The simulation

work in Section 5.2.4 assumes equal power in each transmission branch. But according to

the instantaneous channel conditions to change the power of each user may be useful to

improve the performance [12]. Furthermore, power control is an efficient way to mitigate

the near-far effect in the DS-CDMA system.

In future work, we can combine channel coding into this multi-relay system to gain much

better bandwidth utilization so that the performance at the receiver can benefit more from

this kind of cooperation.

72

5.3 Summary In this chapter we mainly discuss two ways to generate spatial diversity gains to

effectively combat the effects of fading. While the advantages of multiple transmit and/or

receive antennas system have been already acknowledged, we partialize to introduce the

effects of the multi-relay system. It is an efficient way to enable some single-antenna

mobiles to benefit from the MIMO systems. The basic idea is that the single-antenna

mobiles choose some idle stations as the relay to retransmit their signals to the

destination. While at the destination, the receiver obtains several independent versions of

the signals from the different locations, thus generates spatial diversity. Our mathematic

analysis and simulation results have shown that this kind of cooperations can reach full

diversity order. Besides, increasing the number of relay stations, the performance at the

receiver can be enhanced, quite like the situation as in the multiple transmit antennas and

single receive antenna system, when increasing the number of transmit antennas, the

performance can goes better. Also we present some formulas of the up and low bounds of

the symbol error rate to reduce the complexity to calculate the exact symbol error rate.

Although the multi-relay system can make the single antenna transmitter benefit from the

MIMO systems, there exists some problems. Since it is a kind of network when the

mobile chooses some stations as its relays, there must have some algorithms to assign and

manage the allocation of the stations. Also power control is an important problem to

mitigate the near-far effect in the CDMA system. All of these lead to our future work to

make the system work more effectively.

73

Conclusion In this thesis we first discuss the factors such as multiple access interference (MAI) and

the time varying characteristic of the mobile channels which will limit the capacity and

performance of the DS-CDMA system. Then we investigate the successive interference

cancellation (SIC) and the parallel interference cancellation (PIC) to implement multi-

user detection. Our simulation results show that when the signals of all the users’

transmitted over AWGN and Rayleigh fading channels, both SIC and PIC can achieve

quite good BER performance and when the number of stage increases, the performance

can nearly reach the single user bound. Comparison between SIC, PIC and some other

multi-user detection algorithms, such as correlating, decorrelator, MMSE and MLD has

been investigated in this report and we can see that SIC and PIC work better than some

linear multi-user detections. In addition, the calculation complexity has been compared

among SIC, PIC and the MMSE algorithm. The complexity of the PIC is more than SIC

because, to get the data decision of one user, all the other users’ signals should be

reconstructed and cancelled, thus increasing the number of calculations. Both SIC and

PIC need less computation than MMSE.

In the simulations of the SIC and PIC algorithms we assume perfect channel estimation.

However, the signals transmitted to the receiver will always be subject to multi-path

fading which will degrade the performance of the multi-user detection dramatically.

Channel estimation should be used to mitigate the effects of these unknown parameters.

In this project, we explore a reduced multi-user channel estimation and detection

algorithm. In this algorithm, the channel estimation is implemented by an iterative

scheme based on the maximum likelihood (ML) technique and the multi-user detection is

actualized by a pipelined PIC algorithm. The simulation results show that this iterative

channel estimation scheme can achieve almost the same performance as the ML when the

length of the pilots is larger than 128 bits. This combined channel estimation and

detection has shown to have good performance at the receiver.

74

We also investigate the spatial diversity techniques to combat the multi-path fading.

Multiple transmit and/or receive antennas system has been explored to gain the spatial

diversity. Another technique called cooperative communication which can make the

single antenna mobiles benefit from the MIMO system has been explored. This technique

can also achieve full diversity order.

As future work, we plan to implement some improved SIC and PIC algorithms such as

GSIC and RPIC into work and the relay allocation mechanism of the multi-relay system

to make the system work more efficiently.

75

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