cdma power control

Predictive Power Control

in CDMA Systems

Adit Kurniawan M.Eng. (RMIT), Ir. (ITB)

Dissertation submitted for the degree of

Doctor of Philosophy

The University of South Australia

Institute for Telecommunications Research, Division of Information Technology, Engineering,

and the Environment.

February 2003

ii

To my wife, Tika,

and to our sons, Azmi and Sandy.

iii

Contents

List of Figures………………………………….………………………….……………vi

List of Tables……………………………..………………………….………………..viii

Glossary…………………………………………………………….………..………….ix

Notation……………………………………………………………...………………….xii

Summary……………………………………………………………………………….xv

Publications………………...………………………………………………………….xvi

Declaration…………………..………………………………………………………..xvii

Acknowledgments…………..………………………………….…………………..xviii

1 Introduction………………………………………………………………………...1 1.1 Motivation……………………………………………………………………….1

1.2 Research Problem……………………………………………………………….3

1.3 Statement of Work………………………………………………………………7

1.4 Summary of Contribution……………………………………………………….9

1.5 Thesis Outline………………………………………………………………….10

2 Power Control in CDMA Systems….………………………………….…….12 2.1 Introduction to CDMA…………………………………………………………12

2.1.1 CDMA Downlink Channel……………………………………………..13

2.1.2 CDMA Uplink Channel………………………………………………...15

2.2 The Mobile Wireless Channel…….……………………………………………16

2.2.1 Large-Scale Propagation Loss...………………………………………..19

2.2.2 Small-Scale Propagation Loss…...……………………………………..20

2.2.3 Rayleigh Fading Channel……………………………………………….27

iv

2.3 Power Control Algorithm.……………………………………………………...28

2.3.1 Open-Loop Power Control…..……………………………….…………29

2.3.2 Closed-Loop Power Control……………………………………………30

2.3.3 Outer_loop Power Control………………………………….………..…33

2.4 Limitations of Imperfect Power Control………………………………….…….33

2.4.1 Power-Update Step Size...……………………………………………...33

2.4.2 SIR Estimation Error…………………………………………..…….…36

2.4.3 Feedback-Loop Delay..…………………………………………………36

2.4.4 Power-Update Rate……………………………………………………..37

2.4.5 BER of Feedback Channel……………………………………………..38

2.4.6 Effect of Deep Fades…………………………………………………...39

2.5 Summary……………………………………………………………………….39

3 SIR Estimation/Measurement ……………………………………………….41 3.1 Introduction…………………………………………………………………….41

3.2 CDMA Signal Model…………………………………………………………..44

3.3 Maximum Likelihood SIR Estimator…………………………………………..48

3.4 SNV Estimator …………………………………………………………………50

3.5 Proposed SIR Estimator………………………………………………………..52

3.6 Performance Comparison of SIR Estimators…………………………………..54

3.7 Summary……………………………………………………………………….57

4 Power Control Simulation……………………………..………………………59 4.1 Introduction…………………………………………………………………….59

4.2 Rayleigh Fading Simulator …………………………………………………….61

4.3 Power Control Simulation……………………………………………………...63

4.3.1 Procedure of Simulation………………………………………………..65

4.3.2 Optimisation of Step Size………………………………………………68

4.4 Performance of Power Control…………………………………………………71

4.4.1 Effect of Step Size………………………………………………………73

4.4.2 Effect of Fading Rate…………………………………………………...76

4.4.3 Effect of SIR Estimation Error………………………………………….78

4.4.4 Effect of Command Bit Error…………………………………………...80

v

4.4.5 Effect of Feedback Delay……………………………………………….82

4.5 Summary………………………………………………………………………..84

5 Predictive Power Control…………………………………...………………….85 5.1 Introduction……………………………………………………………………..85

5.2 Correlation of Rayleigh Fading Channel……………………………………….90

5.3 Channel Predictor………………………………………………………………93

5.4 Power Control with Channel Predictor…………………………………………96

5.5 Summary………………………………………………………………………101

6 Power Control and Diversity Antenna……………………...…………..…102 6.1 Introduction……………………………………………………………………102

6.2 Diversity and Fading Mitigation………………………………………………104

6.3 Diversity Antenna Arrays…………………………………………………..…105

6.4 Power Control and Diversity Antenna…………………………………….….107

6.5 Effect of MRC Diversity on Step Size………………………………………..109

6.6 Performance of Power Control with Diversity Antenna………………………111

6.7 Summary………………………………………………………………………113

7 Conclusion and Further Work……………………….……………………..114 7.1 Conclusion……………………………………….……………………………114

7.2 Further Work…………………………………….……………………………115

Bibliography………………………………….…….………………………………...117

vi

List of Figures

2.1 A baseband single user CDMA system……………………………………………13

2.2 CDMA downlink channel model………………………………………………….14

2.3 CDMA uplink channel model……………………………………………………..15

2.4 Illustration of wireless propagation mechanisms………………………………….17

2.5 Relationship between time spreading of signal and channel coherence bandwidth……………………………………………………..22

2.6 Relationship between Doppler spread and channel coherence time………...……………………………………….…………25

2.7 Mechanism of open-loop power control…………………………………………..29

2.8 Closed-loop power control model…………………………………………………31

3.1 CDMA signal model with QPSK modulation…………………………….….……45

3.2 SIR estimator using MLE method…………………………………………………49

3.3 SIR estimator using SNV method at symbol level………………………………...50

3.4 SIR estimator using SNV method at chip level……………………………………51

3.5 SIR estimator using an auxiliary spreading sequence …………………………….52

3.6 Means of SIR estimate..……………………………………….…………………..56

3.7 Normalised bias of SIR estimate..…………………………………………………56

3.8 Normalised MSE of SIR estimate..………………………………………………..57

4.1 Simulated Rayleigh fading (fD = 100 Hz, Ts = 15.625 µs)...…….. ……………….63

4.2 Mechanism of SIR-based power control…………………………………………..64

4.3 SIR in Rayleigh fading (fD = 17 Hz, CDMA user K = 10)………………………...67

4.4 Power-controlled SIR in fading channel (fD = 17 Hz, ∆p = 2 dB, Tp = 0.667 ms)...68

4.5 Power control error (PCE) as a function of step size for different fading rates……………………………………………………………....70

vii

4.6 BER performance of power control with PCM realisation (fDTp = 0.01)……..….75

4.7 BER performance of power control for different fading rates………………..…..77

4.8 Effect of SIR estimation error on power control performance (fDTp = 0.01)…..…79

4.9 Effect of command bit error on power control performance (fDTp = 0.01)….……81

4.10 Effect of feedback delay on power control performance (fDTp = 0.01)…………...83

5.1 Illustration of feedback delay on uplink power control scheme…..………………87

5.2 Effect of deep fades on power control with feedback delay………………………88

5.3 Correlation of Rayleigh fading (fD = 17 Hz)…...………………………………….92

5.4 D-step linear predictor……………………………………………………………..94

5.5 Power control scheme with channel predictor at basestation……..……………….96

5.6 Performance of power control with channel predictor and delay compensation (fDTp = 0.01)……………………………...……………..99

5.7 Performance of predictive power control at different fading rates………………100

6.1 Effect of deep fades on power control with finite step size……………………...103

6.2 Simplified model of diversity antenna arrays…………………..………………..106

6.3 Architecture of basestation employing power control, channel predictor, and diversity antenna arrays………………………………………….…………..108

6.4 Signal strength and SIR using a two-branch diversity antenna arrays……..…….109

6.5 Power control error as a function of step size using a two-branch diversity antenna arrays at basestation……………………………………………………..110

6.6 Performance of predictive power control with diversity antenna arrays (MRC, L = 2)………………………………………………….………………….112

viii

List of Tables

2.1 Manifestation of multipath fading as time spreading of signal……………………23

2.2 Manifestation of fading as time varying of channel……………………………….26

2.3 Fading channel characterisation………………………………………………...…27

4.1 Simulation parameters……………………………………………………….....…66

4.2 Effect of step size on bit error rate at Eb/I0 = 7 dB………………………………..71

4.3 PCC bits with PCM realisation (q = 4)…………………………………………....74

5.1 Relationship between Doppler spread (fD) and channel coherence time (T0) for carrier frequency, fc = 1.8 GHz………………………………….………….…93

6.1 Effect of step size on bit error rate at Eb/I0 = 7 dB with diversity antenna arrays (MRC, L = 2)…………………………………………………….110

ix

Glossary

Term Definition Page

1G First Generation………………………………………………2

2G Second Generation…………………………………………....2

3G Third Generation……………………………………………...2

AWGN Additive White Gaussian Noise……………………………..47

BER Bit Error Rate…………………………………………………7

BPSK Binary Phase Shift Keying…………………………………..43

CAC Call Admission Control……………………………………...32

CLPC Closed-Loop Power Control………………………………….7

CRB Cramer-Rao Bound………………………………………….44

DA Data Aided…………………………………………………..42

DM Delta Modulation……………………………………………35

DS-CDMA Direct Sequence Code Division Multiple Access……………2

FDD Frequency Division Duplex………………………………….4

FDMA Frequency Division Multiple Access………………………...2

ICI Inter Chip Interference………………………………………16

i.i.d. independent identically distributed………………………….27

IP Interference Projection………………………………………43

x

IS-95 Interim Standard 95…………………………………………..3

ISI Inter Symbol Interference…………………………………...22

LOS Line Of Sight………………………………………………..16

MAI Multiple Access Interference………………………………...3

MLE Maximum Likelihood Estimation……………………………10

MMSE Minimum Mean Squared Error………………………………8

MRC Maximal Ratio Combiner…………………………………….8

MSE Mean Squared Error…………………………………………10

Nbias Normalised Bias……………………………………………..54

NMSE Normalised Mean Squared Error…………………………….54

OFDM Orthogonal Frequency Division Modulation………………...23

PCC Power Control Command…………………………………….6

PCE Power Control Error…………………………………………68

PCM Pulse Code Modulation………………………………………34

pdf Probability Distribution Function…………………………….25

PN Pseudo Noise…………………………………………………45

PSK Phase Shift Keying……………………………………………43

QPSK Quadrature Phase Shift Keying………………………………10

RF Radio Frequency……………………………………………..20

RLS Recursive Least Square………………………………………89

RxDA Receive Data Aided…………………………………………..42

SB Subspace Based………………………………………………43

SINR Signal to Interference plus Noise Ratio………………………42

SIR Signal to Interference Ratio……………………………………5

SNR Signal to Noise Ratio…………………………………………16

xi

SNV Signal to Noise Variance……………………………………...10

SP Signal Projection……………………………………………...43

SSME Split Symbol Moments Estimation……………………………43

SVR Signal to Variance Ratio………………………………………43

TDC Time Delay Compensation……………………………………89

TDD Time Division Duplex………………………………………….2

TDMA Time Division Multiple Access………………………………..2

TxDA Transmit Data Aided………………………………………….42

WSSUS Wide Sense Stationary Uncorrelated Scattering………………21

xii

Notation

Variables

A scale factor of symbol amplitude B number of symbol per time slot C fraction of path amplitude D feedback delay in multiple of power control interval Tp

Eb energy per bit I0 interference power spectral density K number of users L number of multipath or number of antenna elements L0 ½(L/2 –1) L(t) total path loss as a function of time t Ldo mean path loss at a reference distance d0 Lp(d) mean path loss as a function of distance d M number of chip per symbol ( CDMA spreading factor or processing gain) Nt number of samples or trials in time series N0 noise power-spectral density Pe probability of bit error Poff offset power parameter Pp power adjustment parameter in open-loop power control Ppcc BER of feedback channel Pr received power Pt transmit power P’d probability of a mobile station to reduce transmit power P’u probability of a mobile station to increase transmit power Rb bit rate Rc chip rate R correlation matrix for Rayleigh fading channel rv,u the vth row and uth collumn element of matrix R S(τ) multipath intensity profile S(υ) Doppler power-spectral density Ts symbol period T0 channel coherence time Tp power control interval V order of prediction filter Vr reduced order of prediction filter

xiii

Variables (continued)

W bandwidth of signal W0 channel coherence bandwidth a coefficient vector of channel predictor av the vth element of vector a bk complex symbol sequence of the kth user c speed of light ck(m) complex chip sequence of the kth user ca(m) complex chip of auxiliary spreading sequence d distance d0 a reference distance e(t) unquantised feedback information in power control loop fc carrier frequency fD maximum Doppler spread m parameter of Nakagami distribution m(t) shadowing factor n path loss exponent n(t) thermal noise p probability ∆p power-update step size q mode of PCM realisation in variable-step power control algorithm r crosscorrelation vector between input samples and the desired response rv the vth element of vector r r(t) received signal at carrier frequency s(t) complex baseband signal t time v vehicle speed x(t) transmitted signal at carrier frequency ya(n) interference signal at symbol level n yk(m) decision variable at chip level m of the kth user yk(n) decision variable at symbol level n of the kth user w weight vector of MRC diversity wl the lth element of vector w α variable of distribution function β(t) fading factor as a function of time t γ signal to interference ratio γest estimate of γ γt target signal-to-interference ratio λ carrier wavelength φ phase shift ρ(∆f) spaced-frequency correlation ρ(∆t) spaced-time correlation ρ(τ) correlation with lag τ σ standard deviation

xiv

Variables (continued)

σm standard deviation of shadowing factor τ path time-delay τm maximum time-delay τ0 delay spread ψ angle between mobile velocity vector and path direction θ modulation phase of baseband signal µ fraction of signal in the direct LOS component of Ricean distribution υ Doppler-frequency shift ω angular frequency

Scripting

i index of time slot k user index l path or antenna-element index m chip index n symbol index (I) inphase component (Q) quadrature phase component

Functions

E[.] expectation operator I0 modified zero-th order Bessel function J0 zero-th order Bessel function Γ gamma function sign(x) sign function of x H(f) wave shaping filter π/2 900 phase shifter Σ summation Π product x* complex conjugation of x | x | magnitude of complex quantity x

j 1−

x average value of x erfc(x) complementary error function of x Q(x) Q-function of x fX(x) probability density function of variable x FX characteristic function of variable x R –1 inverse of matrix R

)(max ll

x maximum value of xl

xv

Summary

This study is aimed at solving several important problems relating to power control in

CDMA systems. Power control in CDMA systems plays a very important role in

mitigating the effect of multiple access interference under fading conditions. This study

examines the following topics: estimation of signal to interference ratio (SIR); channel

prediction techniques; and applications of diversity antenna arrays; in a power-controlled

CDMA system.

We study a SIR-based power control algorithm in this thesis. Our focus is on the mobile

to basestation (reverse) link. In this study, we propose a new SIR estimator for CDMA

systems, using an auxiliary spreading sequence method. The proposed SIR estimator is

employed at the basestation to estimate the SIR, which serves as a control parameter in

the power control algorithm.

The effects of system parameters (step size, power-update rate, feedback delay, SIR

measurement error, and command error) on the bit error rate (BER) performance of power

control are investigated. Feedback delay is found to be the most critical parameter that

causes a serious problem in the loop. To solve this problem, we propose to use a channel

prediction at the basestation. The proposed channel predictor utilises fading statistics to

predict the future channel conditions and thus the SIR. By using a channel predictor we

then develop a predictive power-control algorithm, which can eliminate the effect of

feedback delay.

To further improve the performance of power control, we then propose to use a diversity

reception technique using antenna arrays at the basestation. We show that this

combination allows solving the problems linked to the use of power control in a real

system affected by multiple access interference under fading conditions.

xvi

Publications

A. Kurniawan, “SIR estimation in CDMA systems using auxiliary spreading sequence,”

Magazine of Electrical Engineering, Institut Teknologi Bandung (Indonesian: Majalah

Ilmiah Teknik Elektro), vol. 5, no. 2, pp. 9-18, August 1999.

A. Kurniawan, S. Perreau, J. Choi, and K. Lever, ”SIR-based closed loop power control in

third generation CDMA systems,” in Proceedings of the 5th CDMA International

Conference (CIC) 2000, Seoul, South Korea, Vol. II, November 2000, pp. 93-97.

A. Kurniawan, “Closed loop power control in CDMA systems based on new SIR

estimation,” Magazine of Electrical Engineering, Institut Teknologi Bandung (Indonesian:

Majalah Ilmiah Teknik Elektro), vol. 6, no. 3, pp. 1-8, August 2000.

A. Kurniawan, S. Perreau, J. Choi, and K. Lever, “Closed loop power control in CDMA

systems with antenna arrays,” in Proceedings of the 3rd International Conference on

Information, Communications, and Signal Processing (ICICS) 2001, Singapore, October

2001, CD ROM 2A1-1.

A.Kurniawan, S. Perreau, and J. Choi, “Predictive closed loop power control in CDMA

systems with antenna arrays,” submitted for publication to IEEE Transactions on

Vehicular Technology, September 2001.

A. Kurniawan, “Power control to combat Rayleigh fading in wireless mobile

communications systems,” in Proceedings of Asia Pacific Telecommunity Workshop on

Mobile Communications Technology for Medical Care and Triage (MCMT) 2002, Jakarta,

October 2002.

A. Kurniawan, “Effect of feedback delay on fixed step and variable step power control

algorithms in CDMA systems,” in Proceedings of International Conference on

Communication Systems (ICCS) 2002, Singapore, November 2002, CD-ROM 3P-02-04.

xvii

Declaration

I declare that this thesis does not incorporate without acknowledgment any material

previously submitted for a degree or diploma in any university; and that to the best of my

knowledge it does not contain any materials previously published or written by any person

except where due reference is made in the text.

Adit Kurniawan

xviii

Acknowledgments

I thank my supervisors, Dr. Sylvie Perreau, Dr. Jinho Choi, and Professor Ken Lever for

their excellent guidance and encouragement during my time at Institute for

Telecommunications Research (ITR), the University of South Australia. I appreciate Dr.

Perreau for her constant patience throughout my candidature. I also acknowledge Dr. Choi

who inspired and motivated our research directions, particularly in the early stage of my

study. I am indebt to them.

I also thank Professor Mike Miller for introducing me to ITR, where I later found good

environments and facilities for doing research. I thank Bill Cooper and Isla Gordon for

providing me with technical assistance and supports. To all of the friends and colleagues I

have had over the past three and half years in ITR, thanks for all of the good things.

The financial support for my PhD study came from AusAID. I thank AusAID for financing

my study through their scholarship program. It took longer than originally expected, but

we made it.

I am indebted to my parents for teaching me the importance of hard work. Thanks for their

commitments to education and to the success of their children. Finally, I dedicate this piece

of work to my wife, Tika and to our sons, Azmi and Sandy. I want to thank Tika for her

love, her unconditional patience, her desire that I succeed in many things, and for the many

sacrifices she has had to make over the past view years. I also wish to thank Azmi and

Sandy for their smiles and enthusiasms. Witnessing them growing up and learn to know

many things has reminded me to realize that I also know nothing.

1

Chapter 1

Introduction

This introductory chapter provides the synopsis of the thesis. In this chapter the author lays

out the background of the subject material that has motivated our research directions. Then

he states our research problems and provides a summary of his contribution. The final

section of this chapter presents the outline of the thesis.

1.1 Motivation

The demand for higher capacity and better service quality in wireless mobile

communication systems has been increasing exponentially in the last decade. This is

because of user mobility and flexibility, particularly on the communication link between

mobile terminals and basestation (wireless channel) that cannot be provided in wired line

communications systems. Unfortunately, this communication link serves as a bottleneck,

which limits the system capacity and performance due to multipath propagation problems

in the wireless channel.

Chapter 1. Introduction

2

The fundamental problem of the wireless channel is how to share the common

transmission medium by many mobile users (multiple access) in order to accommodate as

many users as possible, with good quality of service. This is not an easy task because,

unlike in wired line communications, transmission of a signal through the wireless channel

is very challenging, whereas the frequency spectrum allocation is very limited. However,

we need to solve these problems using various new technologies in order to fulfil the ever-

increasing demand.

It is important to first look at the evolution of mobile communications. Mobile

communication has evolved from the first-generation (1G) to the second-generation (2G),

and is now evolving towards the third-generation (3G) systems. The services provided by

the 1G systems are limited to voice communications, while the 2G systems can also serve

low bit-rate data communications. Although the growth rate of 1G systems was very low,

the 2G systems have been very successful in many countries [1]. However, there are

limitations in 2G systems in terms of system capacity, service quality and flexibility to

accommodate various wideband services with different data rates. Therefore, third-

generation (3G) systems are being developed to overcome the limitations of the 2G

systems.

The evolution of mobile communication systems has been driven by ever increasing

demand and technological development. First-generation systems deployed in the early

1980s employ a frequency division multiple access (FDMA) system, in which the available

frequency spectrum is partitioned into several orthogonal channels, one for each user to

communicate at any time using different frequency bands [2]. Second-generation systems

deployed in the early 1990s use a time division multiple access (TDMA) scheme in

combination with FDMA [3]. In TDMA systems, all users occupy the entire radio

spectrum at different time in round robin fashion. In the late 1990s, another 2G system has

been deployed using a direct sequence code division multiple access (DS-CDMA). In

CDMA, all user occupy the entire radio spectrum simultaneously using different codes

(spreading sequences) to distinguish between different users. Today, multiple access

schemes based on multicarrier modulation, called orthogonal frequency division multiple

access (OFDM), as well as those based on a time division duplex (TDD) scheme are being

studied to further improve capacity and performance [4]-[5].


3

We note that DS-CDMA systems have been used for military applications since the 1960s

because of its anti-jamming capability, a very important aspect required in military

communications. Although spread spectrum had been shown to exhibit an anti-multipath

capability in 1958 [6], research on CDMA application for commercial wireless

communications took approximately four decades before its first deployment of the 2G

interim standard (IS-95) in the late 1990s. This is mainly due to the unavailability of good

spreading codes and the requirement of tight power control. In 3G systems, wideband

CDMA has been chosen because theoretically it can provide higher capacity compared

with FDMA and TDMA schemes [7]-[10]. However, in order to achieve this “promised”

high capacity, good techniques are needed to overcome several wireless impairments. This

is why significant research works are currently being devoted to improve the performance

of DS-CDMA systems, such as interference cancellation or multiuser detection, smart

antennas, and power control, to name a few. Among those areas of research, power control

is the most crucial aspect because it plays an important role in a DS-CDMA system [11].

Without good power control schemes, the capacity of a DS-CDMA system may be

comparable with or even less than the capacity of FDMA or TDMA systems [12]. The aim

of this study is to contribute to this important research area by studying existing power

control systems, identifying several important problems that have not been solved, and

providing solutions to the problems.

1.2 Research Problem

Early work on power control in CDMA is aimed to eliminate the near-far effect and to

reduce multiple access interference (MAI) from other users. In DS-CDMA, each user is

assigned a user’s specific spreading sequence to distinguish between different users that

share the common radio channel. However, every user will receive the MAI from every

other user due to non-zero crosscorrelations between different users’ spreading sequences.

Moreover in the uplink, signals originating from different users will arrive at the

basestation with unequal power levels because of different locations (different distances to

the basestation) within the cell. If the users’ transmit powers are not controlled, a distant

user whose received signal at the basestation is low will suffer due to the MAI from the

nearby user whose received signal level is high. This is known as the near-far problem

[13]. In addition to the near-far problem, the average received power at the basestation may


4

also vary slowly due to, what is called the shadowing problem. The shadowing occurs

when a mobile station is moving through different terrains. As mentioned above, only the

uplink is affected by near-far and shadowing problems. Indeed, on the basestation-to-

mobile station or downlink channel (forward link), all users’ signals originate from the

same source (i.e. basestation), then propagate through the same channel and therefore fade

simultaneously. There is no near-far problem on the forward link. Power control on the

forward link, however, is necessary to compensate for users at the cell boundaries who

may suffer interference from other cells.

Power control to overcome the near-far and shadowing problems was addressed in [14]-

[15]. In these papers, power control algorithm is aimed at controlling the mobiles’ transmit

power to keep their average received power at the basestation equal. To perform the power

control algorithm, the mobiles calculate the required transmit power using the estimate of

the downlink signal they receive from the basestation. This is based on the fact that the

path loss is a deterministic quantity only depending on the distance between transmitter

and receiver, and therefore identical on the reverse and forward links. In other words, this

power control is an open-loop algorithm in which feedback information is not required.

Since the received signal due to path loss and shadowing varies slowly, the power-updating

rate can also be slow. The power control schemes to solve the near far and shadowing

problems have been successfully implemented in the second generation CDMA system of

IS-95.

While an open-loop power control can solve the near-far and shadowing problems,

multipath fading still degrade the transmission performance significantly, which may lead

to an unacceptable error rate at the receiver. Power control to reduce the effects of

multipath fading is more difficult and challenging for the following reasons. First,

multipath fading mechanisms are uncorrelated between uplink and downlink channels due

to different carrier frequency bands on both links in a frequency division duplex (FDD)

system. Therefore to control fading on the uplink, uplink channel condition must be

estimated at the basestation and then fed back to the mobile station via the downlink

channel (closed-loop algorithm), so that the mobile station can adjust the necessary

transmit power. Second, power control updating rates must be much higher than the fading


5

rates. Otherwise, power control may simply not work. Therefore channel measurement

must be done in a short duration of time.

Closed-loop power control is more crucial on the reverse link than on the forward link

because on the forward link, synchronous transmission is possible and therefore orthogonal

spreading sequence can be used. Moreover, all signals from the same basestation will

travel through the same fading channel and will fade simultaneously, resulting in an equal

received power level at the mobile station [16]. With orthogonal spreading sequence and

equal received power level, multiple access interference is no longer a serious problem.

However, downlink power control is still required to compensate for users at the cell

boundaries who may receive strong interference from other cells.

Closed-loop power control to combat multipath fading in CDMA systems has been

discussed in [17] and [18]. Simulation study of power control based on signal strength

measurement at the basestation is shown in [19], while those based on signal to

interference ratio (SIR) and combined SIR with signal strength measurements appear in

[20] and [21]-[22], respectively. These papers conclude that power control is effective

when the power-updating rate is significantly higher than ten times the maximum fading

rate, and that the extra feedback-loop delay must be minimized. In addition, power control

based on SIR exhibits a better performance than that based on signal strength.

In this thesis, the author has identified several important problems associated with SIR-

based closed-loop power control. Firstly, to facilitate a good SIR-based power control in

CDMA systems, a fast and reliable SIR measurement or estimation method is required.

Most SIR estimators for CDMA systems rely on the traditional method, which is based on

statistics (mean and variance) of the received signal. The SIR estimation technique in

CDMA systems is more difficult than that in FDMA and TDMA systems because of the

MAI problem in CDMA systems. In this study, we propose a new method by taking

advantage of the CDMA feature using an auxiliary spreading sequence to estimate the

MAI component.

The second problem is the effect of fading rates on the performance of power control. The

question is how often and by what step size the mobile transmit power needs to be updated

in order to overcome the fading fluctuations. To update the mobile transmit power, the SIR


6

at the basestation is estimated and compared with the target SIR. The difference between

these two quantities is then quantised into a binary information and sent via the downlink

channel to the mobile station. The mobile station then adjust its transmit power according

to the feedback information that is received from the basestation. Most existing power

control algorithms consider a fixed step power-update, which requires only one power

control command (PCC) bit for signalling. The most obvious reason for this is to minimise

the signalling bandwidth and thus preserves the downlink channel capacity. Since the

power-update rate is standardised, the question here is how to determine the power-

updating step size. If the step size is too small power control may not be able to track a

rapid fading. On the other hand, if the step size is too large power control may produce

large residual variations around the target level due to continuous up/down power

adjustments. Another problem is that errors may occur on reception of the PCC bits due to

the impairment of downlink transmission. The PCC bits are error prone because they are

sent without using any interleaving/error correction device in order to minimise delays and

to preserve downlink bandwidth.

The third problem that is inherent in a closed-loop power control algorithm is the feedback

delay. In real systems the PCC bit that is used to control the mobile’s transmission power

can be outdated in a fading situation, particularly when the Doppler frequency increases.

This is particularly due to SIR measurement delay at the basestation, synchronisation

between uplink and downlink channels, and propagation delay on the downlink. In this

situation, we cannot rely on the current observations of the SIR estimator to control the

fading channel because it may be too late. Instead, we need to predict the value of SIR at

the time the power control command should actually take place.

The last problem that needs to be solved in this study is how to combat deep fades, which

occur frequently but in a very brief time. This problem is difficult to control because when

the channel goes into a deep fade, power control fails to track the fade. In addition,

although power control should help mitigate the impact of deep fades, its effectiveness is

clearly limited in a CDMA system. Indeed, if a user experiences a deep fade and requires

its transmission power to be raised significantly, it will affect the SIR experienced by other

users. This could lead to instability problems because every user will increase their

transmit power to achieve their target SIR. These other users will also increase their power,


7

and so on. Therefore, power control should be used in conjunction with another device that

can reduce the effect of deep fades.

1.3 Statement of Work

An extensive literature survey is conducted to identify several problems in a SIR-based

closed-loop power control (CLPC) scheme that need to be solved. The proposed solutions

for the problems that have been identified in the previous section are summarised below.

In a SIR-based power control, a SIR estimator plays an important role. We propose a new

SIR estimator for CDMA systems using an auxiliary spreading sequence in order to

provide a fast and reliable estimate of the SIR for power control. In this proposed method,

we attempt to reduce the complexity and improve the performance of the estimator

compared to existing techniques. We then compare our proposed SIR estimator with other

techniques. The proposed SIR estimator is shown to be the most suitable for fast

measurements because it requires less computation and yet exhibits a reasonable

performance. We use our proposed method in the simulation study of power control.

Computer simulations are performed to evaluate the effect of system parameters (i.e.

power-update rates, step size, feedback delay, and feedback channel error) on power

control performance. The performances of fixed-step and variable-step power control

algorithms in slow-mobility vehicular environments are compared in terms of bit error rate

(BER) as a function of bit energy to interference power spectral density (Eb/I0). We rely on

computer simulations because an analytical solution is very difficult to derive without over

simplification of the system parameters. From simulations, we found that feedback delay is

the most critical problem which degrades the performance of power control significantly

while feedback channel error is the least critical. Therefore, a good technique to overcome

the problem of feedback delay is to be found.

To overcome the effect of feedback delay, a channel prediction method (channel predictor)

is proposed in this study. The channel predictor is used to predict the channel condition

using the correlation property of fading channel. By predicting the channel, the SIR can

also be predicted. Power control decision is then made based on the predicted SIR value,

instead of based on the current measurement/estimation. Therefore, the mobile power


8

adjustment based on the predicted SIR will reflect the actual channel condition. We

develop a prediction filter to predict the fading factor D samples ahead based on the

minimum mean square error (MMSE) criterion. Here, D is the total feedback delay in the

loop including the SIR measurement time. We need to point out here that power control

destroys the fading correlation. Yet the channel predictor utilises the fading correlation to

predict the channel. Therefore, the predictor must restore the fading correlation. To do this,

the power control gains in the previous measurements is compensated before they are used

as input samples to the predictor. We show the predictor has an excellent performance in

solving the feedback delay problem.

The last problem we have solved in this study is the negative impact of deep fades on

power control. To mitigate the deep fades we investigate the use of a well-known diversity

antenna technique, which will result in two major improvements as follows. First, the

performance of power control improves due to its better ability to track the diversity

channel, which has shallower fading dips than the single path (without diversity) channel.

Second, the increase of power at mobile station during deep fades is less significant

because the deep fades have been reduced by diversity technique. Therefore, unstable

conditions due to inter cell interference can be prevented. In this study we concentrate on

the former issue, which is how the performance of power control improves by the use of

diversity antenna arrays.

The benefit of antenna diversity in reducing the fading depth has been well known. In this

study we show how to combine diversity antenna with channel predictor in a closed-loop

power control algorithm. Since diversity antenna will not preserve the fading correlation,

channel predictor has a problem because it relies on fading correlation. We solve this

problem by performing the channel prediction before diversity combining in order to

preserve the channel correlation of each diversity branch. Then we perform the diversity

combining after channel prediction using a synchronous sum of all diversity channels. The

second problem is the effect of diversity combining algorithm used. In maximal ratio

combining (MRC) algorithm, each diversity branch is weighted by a factor that is

proportional to the square root of SIR. This also alters the fading correlation and therefore

must be compensated for in favour of the predictor to restore the fading correlation. Since

SIR is readily available for power control purposes, we will evaluate an MRC diversity


9

method for optimum results. We investigate diversity antenna with two branches in this

study to show the novel technique of our design. Extensions to higher diversity orders are

straightforward. We show that the combination of predictive power control and diversity

antenna can provide reasonable performance in slow mobility vehicular environment.

1.4 Summary of Contribution

Throughout this study the following contributions to the research area of wireless

communication are made:

1. Proposing a new method of SIR estimation/measurement using an auxiliary spreading

sequence in CDMA systems. The new SIR estimator is used in a SIR-based closed-

loop power control for the reverse link of a CDMA system.

2. Performance-parameter characterization of a SIR-based closed-loop power control on

the reverse link of a CDMA system. This is performed by using computer simulations,

which includes: optimizing the power-updating step-size and obtaining the BER as a

function of Eb/I0 to show the effects of SIR estimation error, power updating

rates/fading rates, feedback delays, and feedback channel error.

3. Proposing a channel predictor based on linear prediction filter to overcome the problem

due to feedback delay. The proposed channel predictor utilises the correlation property

of fading channel.

4. Proposing to use antenna diversity arrays at the basestation to help eliminate deep

fades. This technique can improve the performance of power control and reduce the

peak transmit power of the mobiles.

5. Designing a basestation architecture that employs antenna diversity and channel

predictor in a SIR-based closed-loop power control system.

During the course of this study, we have published several ideas of our research

contributions presented in this thesis. The ideas of SIR estimation technique and closed-

loop power control have been published in [88] and [99], respectively. These were

followed by the publication in [70], which shows how the proposed SIR estimator


10

performs in a SIR-based closed-loop power control system. The works on channel

predictor to overcome the feedback delay problem and on antenna diversity to reduce the

effect of deep fades have been initially presented in [105]. A more detailed presentation of

SIR-based closed-loop power control incorporating channel predictor and antenna diversity

techniques has also been submitted for publication in [110].

1.5 Thesis Outline

In this introductory chapter we provide the synopsis of the thesis. This chapter presents the

research motivation, research problem definition, summary of research contribution, and

thesis outline. Chapter 2 describes the problems of power control in CDMA systems. The

first half of this chapter discusses the mobile wireless channel, signal degradations due to

multipath propagation, and various techniques that can be used to overcome the effects of

multipath fading. The importance of power control in the reverse link of a CDMA system

is highlighted. In the second half of this chapter, an extensive literature review of power

control is presented followed by a problem identification of the existing power control

system that need serious attentions. Solutions for the problems are briefly discussed in this

chapter.

In Chapter 3 a new SIR estimator using auxiliary spreading sequence method for CDMA

systems is described. A CDMA signal model associated with an analytical expression of

SIR using quadrature phase shift keying (QPSK) modulation scheme is presented. For

comparison, SIR estimation techniques based on maximum likelihood estimation (MLE)

and signal to noise variance (SNV) methods are described. The performance of all

mentioned SIR estimators is evaluated in terms of bias and mean square error (MSE).

Chapter 4 describes the simulation procedure and shows the simulation results of SIR-

based closed-loop power control. A Rayleigh fading simulator using the well-known Jakes

method is presented. Closed-loop power control based on SIR is simulated to obtain the

BER performance in slow mobility vehicular environments. The step size is optimised

based on the minimum power control error (standard deviation of SIR). The effect of

fading rates, feedback delay, and feedback error on the performance degradation is shown.

The reasons why performance degrades are explained with more emphasis on the effect of


11

feedback delay. Power control simulations are based on fixed-step and variable-step

algorithms.

In Chapter 5 a method that can effectively overcome the problem of feedback delay is

described. The time-frequency correlation of Rayleigh fading is derived, which is needed

to construct the correlation matrix of fading channel. A prediction filter (channel predictor)

based on the orthogonality principle under MMSE criterion is presented, followed by a

brief discussion on how to compute the prediction coefficients. The effect of power control

on fading correlation is discussed and a trick to restore the fading correlation is given. The

simulation results of power control using the channel predictor (predictive algorithm) are

shown.

Chapter 6 evaluates the effect of antenna diversity on power control performance. It shows

how diversity antenna can reduce deep fades. The effect of diversity antenna on the

optimum step size is evaluated by simulations. A basestation architecture that employs

channel predictor and diversity antenna, which can improve the performance of power

control is described. The performance of power control using these combined techniques is

shown. The final chapter, Chapter 7, concludes our research work and makes suggestions

for further research directions.

12

Chapter 2

Power Control in CDMA Systems

This chapter addresses the problem of power control, which is crucial for the reverse link

of a CDMA wireless system. It first introduces the background of CDMA. It then presents

a multiuser CDMA channel model and shows the importance of power control in CDMA

systems. It then provides a brief overview of the mobile wireless channel and signal

distortions introduced by the propagation channels. This preliminary section is useful to

clearly show in which context power control is needed and to recall some mathematical

formulas that will be used in later chapters. The remaining sections of this chapter

concentrate on power control issues. In particular, we address several important problems

that affect the performance of power control in real systems.

2.1 Introduction to CDMA

In CDMA systems the users spread the data symbol by their unique spreading sequence.

The spreading sequence consists of a sequence of chips that is known to the transmitter and

receiver. The data can be recovered at the receiver by correlating the user’s spreading

sequence with the received signal. The spreading sequences can be mutually orthogonal

Chapter 2. Power Control in CDMA Systems

13

(with zero crosscorrelation), or random sequences with low crosscorrelation property. A

simple example of a single user CDMA system is shown in Figure 2.1.

1 1 1 -1 -1 1 -1 -1

–1 -1 -1 -1 1 1 -1 1 1

transmittedsymbol

user’s spreading sequence

1 1 1 -1 -1 1 -1 -1

–1

user’s spreading sequence

recoveredsymbol

-1 -1 -1 1 1 -1 1 1

com

mun

icat

ions

cha

nnel

Figure 2.1 A baseband single user CDMA system.

In this example, only one user is transmitting data through a perfect channel without noise

for simplicity. In a multiuser CDMA system, more than one user transmit onto the channel.

However, the correlating receiver can still recover the transmitted symbols provided that

the spreading sequence crosscorrelation between different users is sufficiently low.

Problems arise when the channel is not perfect such as in a wireless mobile

communications system where the channel is time varying due to multipath propagation

mechanisms and Doppler effects. In a wireless system, the communication channel from a

basestation to a mobile user is called the downlink or forward link, while the

communication channel from a mobile user to a basestation is called the uplink or reverse

link. The uplink and downlink channels exhibit different behaviours to a multiuser CDMA

system, as we will explain below.

2.1.1 CDMA Downlink Channel

In the downlink, the spread signals for all users are transmitted synchronously by the

basestation because they originate from the same location (basestation). These signals will

go into the same multipath channel, experience the same propagation path loss, and fade

simultaneously. Therefore orthogonal spreading sequences can be used in the downlink


14

because the orthogonality of the spreading sequence can be maintained, and coherent

detection can be performed.

A simplified CDMA channel model with K users for the downlink is shown in Figure 2.2.

The message bk(n) generated by the kth user is spread by the kth user spreading sequence

ck(m). By considering a QPSK modulation, bk(n) = bk(I)(n) + j bk

(Q)(n) is the nth symbol of

the kth user and ck(m) = ck(I)(m) + j ck

(Q)(m) is the kth user spreading sequence. The

superscript (I) and (Q) designate the inphase and quadrature component, respectively.

bk(n)ck(m)

Mobile station

Basestation

c2(m)

c1(m)

cK(m)

b1(n)

b2(n)

bK(n)

n(t)All user signals

propagate throughthe same downlink

channelkth mobile user

Figure 2.2 CDMA downlink channel model.

At a mobile station, the kth mobile user recovers the transmitted symbol by correlating the

received signal with the kth spreading sequence. Since orthogonal spreading sequences are

employed in the downlink, there is theoretically no MAI and thermal noise becomes the

dominant interference component. When thermal noise is the major interference

component, a distant user will suffer due to large propagation path loss. Also it has to be

pointed out that these distant users will suffer from other cells’ interference because users

in different cells are not mutually orthogonal. In this case, downlink power control is

needed which can be done at the basestation by letting the distant user to operate at a

higher power level than those located nearby the basestation.


15

2.1.2 CDMA Uplink Channel

In the uplink, synchronous transmission from different users is very difficult to achieve

because the users transmit from different locations. Therefore, orthogonal spreading

sequences are not used in the uplink because their orthogonality cannot be maintained.†

Signals from different mobile users are also subject to different propagation mechanisms,

resulting in different propagation path losses and independent fading that lead to unequal

received power levels at the basesation. Due to non-orthogonal spreading sequence and

unequal received power levels in the reverse link, multiple access interference becomes a

serious problem. Figure 2.3 illustrates the uplink CDMA channels in a wireless

communication system.

c1(m)

b1(n)

b2(n)

c2(m)

n(t)

bK(n)

cK(m)

Mobile stationBasestation

c2(m)

c1(m)

cK(m)

.

.

b1(n)

b2(n)

bK(n)Independent fading channels

Figure 2.3 CDMA uplink channel model.

At the basestation, the kth user recovers the transmitted symbol by correlating the received

signal with the kth user spreading sequence. Due to non-zero crosscorrelations between

spreading sequences of different users, the kth user will observe multiple access

interference from the other K-1 users. If the received power levels at the basestation are not

equal, the correlating receiver may not be able to detect the weak user’s signal due to high

† Orthogonal spreading sequence such as Walsh-Hadamard codes have zero crosscorrelation when

they are perfectly synchronised. The orthogonality cannot be preserved in unsynchroneous uplink channels.


16

interference from other users with higher power levels. Clearly, if a user is received with a

weak power, it will suffer from the interference generated by stronger users’ signals.

Therefore power control in the uplink is very important to keep the interference acceptable

to all users and to obtain a considerable channel-capacity improvement.

We will see in this chapter that the received signal powers can be very different from one

user to another for two main reasons. Firstly, the received signal from a user that is close to

the basestation can be much stronger than the signal received from those distant users. This

is called the near-far problem, which may cause a distant user to be dominated and jammed

by the nearby users. Secondly, the received signal from a multipath fading channel may

cause not only rapid fluctuations, leading to a loss of signal to noise ratio (SNR), but also

time-spreading of the transmitted symbol that results in inter chip interference (ICI). If

power control is not performed, only users associated with the highest received power will

be able to communicate with the basestation without being jammed by other users.

Therefore, this will obviously decrease the capacity of the CDMA system. In fact it is easy

to show that the system capacity of a multiuser CDMA system is optimum when the

signals from all users are received with an equal level [16]-[18], which is only achievable

with a perfect power control scheme.

2.2 The Mobile Wireless Channel

It is very important to understand the impairments of wireless channels. Indeed, due to

severe distortions introduced by such channels, sophisticated signal design and smart

transmission and reception technologies are required to maintain a reliable communication

[23]-[27]. In order to do so, an accurate characterisation and modelling of the wireless

channel is essential.

In a mobile communication system, a signal transmitted through a wireless channel will

undergo a complicated propagation process that involves diffraction, multiple reflections,

and scattering mechanisms. Figure 2.4 illustrates the multipath propagation mechanism

from a mobile user who is transmitting a signal to a basestation. In most cases, a line-of-

sight path (LOS) between the mobile and the basestation may not exist due to a very dense

propagation environment between the mobile and the basestation.


17

Scattering by a roughsurface

Diffraction by bigstructures

Reflection by a smoothsurface

Basestation

Mobile

Figure 2.4 Illustration of wireless propagation mechanisms.

As illustrated in Figure 2.4, there are three propagation effects that lead to fluctuation of

the received signal. First, reflection occurs when a radio wave propagates and incidents

onto a smooth surface with large dimensions compared to the signal wavelength (e.g.,

walls of buildings, road surface, etc.). A single path may experience multiple reflections.

Second, diffraction occurs when a large body obstructs the radio path between the

transmitter and the receiver, causing secondary waves to be formed behind the obstructing

body and continue to propagate towards the receiver. This mechanism is often termed as

shadowing because it occurs when the propagation path between the transmitter and the

receiver is partly shadowed (obstructed), for instance, by hilly terrains or by big structures.

Third, scattering occurs when a radiowave incidents onto a large rough surface, causing the

reflected rays to spread out in various directions. Scattering can also take place due to the

wave propagating through very dense foliage.

The signals arriving at the basestation are therefore a combination of signal paths with

different amplitudes and time delays (phases). The superposition of these paths may be

constructive or destructive, depending on the phase differences between all the arriving

paths. If the user and structures that make up the propagation environment are stationary,

the received signal level at a certain fixed point will be constant. However, this constant


18

level may differ for different points, depending on the relative position between user and

basestation (spatial variation). When a user is in motion, the multipath mechanism is

further complicated by continuous changes in the propagation paths, resulting in the

received signal to fluctuate as a function of time (time variation). The received signal from

a stationary user may also vary if one or more scattering or reflecting objects are in motion.

In addition to the rapid signal fluctuation, the received signal also decays dramatically with

increasing the transmitter-receiver separation distance because of severe path loss. This

path loss also may vary from area to area due to the shadowing effect. Therefore, a signal

propagating through a mobile channel will experience a large attenuation, shadowing

variation, and multipath fading, which will result in an overall path loss. Expressed in

decibel (dB), this total path loss is calculated using the propagation equation

)()()()( ttmdLtL p β++= . (2.1)

Here Lp(d) is the mean path loss as a function of the transmitter-receiver separation

distance d, m(t) represents the shadowing variation, and β(t) represents the fading

fluctuation.

It will be more convenient for power control purposes to classify the overall path loss

expressed in (2.1) into two categories:

• Large-scale propagation loss which is normally represented in terms of the mean path

and its variation around the mean due to shadowing. The mean path loss and its

variation are expressed in the first two terms of (2.1), respectively.

• Small-scale propagation loss that refers to rapid and dramatic changes of signal

amplitude and phase due to the multipath phenomena. It is characterised by deep and

rapid fades, which are very localised. Indeed, the fading characteristics of two signals

received at locations distant from half a wavelength are statistically uncorrelated.

If the propagation loss is fairly constant over a large area, it is labelled as large-scale

propagation loss. In the contrary, if the propagation loss changes dramatically within a

small area, it is labelled as small-scale propagation loss. The adjectives small and large are

defined as compared to the wavelength of the transmitted signal.


19

This classification is important because power control scheme to overcome the large-scale

propagation loss is different from that for the small-scale propagation loss. As we will

explain later, the former can employ a slow open-loop power control and the later uses a

fast closed-loop algorithm. In the following, we review in more details these two types of

propagation losses, which will serve as a necessary basis for introducing how power

control operates.

2.2.1 Large-Scale Propagation Loss

In an ideal situation where only the direct path between the transmitter and receiver exists,

the received signal can be analytically determined using the free-space path loss formula.

In this model, the mean path loss Lp(d) is proportional to an nth power of distance d

relative to a reference distance d0, which is expressed in decibel (dB) as

+=

00 log.10)(

d

dnLdL dp . (2.2)

Here Ld0 is the mean path loss at a reference distance d0, n is the path loss exponent. The

value of path loss exponent n depends on carrier frequency, antenna height, and

propagation environments. In urban areas, path loss exponent is shown to be n = 4 or

greater [28]-[29].

Most empirical studies show that large-scale path loss has a lognormal distribution due to

shadowing [30]-[33]. In this case, when the average received signal level is measured in

dB, it follows a normal (Gaussian) distribution. Therefore m(t) in (2.1) is a zero-mean

Gaussian variable in dB with standard deviation σm. Measurements have shown that a σm

between 6 and 10 dB is quite common in most urban areas [34]-[35]. The statistics of

large-scale scale propagation loss are often required to determine various design

parameters in a cellular mobile communications system, such as reliability of service,

hand-off, and cell coverage.

Another important aspect of large-scale propagation statistics is that the mean path loss is

reciprocal between the uplink and the downlink channels. Therefore, we can predict the

large-scale path loss on the uplink using measurements of the downlink signal. This is a


20

very important property, which is used to justify an open-loop power control device to

compensate for the large-scale propagation loss. We will study this in more details in

Section 2.3.1.

2.2.2 Small-Scale Propagation Loss

Small-scale propagation model is important to explain the effect of multipath propagation

not only on rapid amplitude fluctuation, but also on time dispersion of the received signal

(time-shifted copies of the same signal). As has been mentioned earlier, the received signal

is a superposition of all signal paths with various amplitudes, phases (or time delays), and

angle of arrivals as a result of reflection, diffraction, or scattering of a transmitted signal

through the propagation environment. There are two manifestations of multipath

propagation:

• Amplitude fluctuation due to constructive or destructive superposition of the incoming

signal paths (time-variant channel).

• Time dispersion (time spreading) of the received signal because of different arrival-

time instant of different paths.

A mathematical model to describe the received multipath signal can be determined as

follows. Let the transmitted signal be x(t) which can be expressed as

)2()()( tfj cetstx π= , (2.3)

where s(t) is the complex baseband signal with bandwidth W, fc = c/λ is the carrier

frequency, c is the speed of light, and λ is the wavelength of the radio frequency (RF)

signal. The received signal r(t) as the superposition of L multipath components can be

expressed as

])cos[(2

1

)()( lclDc ftffjll

L

l

etsCtr τψπτ −+

=

−= ∑ , (2.4)

where Cl is the fraction of the lth path of the incoming signal amplitude, τl is the lth path

delay, fD = v/λ is the maximum Doppler spread, and ψl is the direction of the lth scatterer


21

with respect to the mobile velocity vector, v. We will evaluate the small-scale propagation

in both the time domain and frequency domain below.

In the time domain, we look at the multipath fading from two different aspects: time

spreading of the signal and time varying of the channel [36]. From the signal time-

spreading aspect, we classify the multipath fading into a frequency selective fading and a

frequency nonselective (flat) fading. While from the channel time-varying aspect, we

distinguish the multipath fading between a fast fading and a slow fading.

In the frequency domain, we consider the multipath fading as the frequency response of a

channel (transfer function) and as the Doppler spread of a channel. While frequency

selectivity of a channel can be easily understood using the frequency response, time

selectivity (fading rapidity) is more obvious from the Doppler spread evaluation.

Time Spreading of the Signal

In the time domain, time spreading of signal due to multipath channel can be characterized

by using a multipath-intensity profile, S(τ) versus time-delay, τ. The multipath delay-

spread, τm, is defined as the difference of time-delay between the first arrival of multipath

component (τ = 0) and the last arrival component (τ = τm). All signal paths arriving at the

receiver can be considered as a wide-sense stationary uncorrelated scattering (WSSUS)

model [37]-[38]. When the channel has τm greater than the symbol time, Ts, the multipath

channel will exhibit a frequency-selective fading. Intersymbol interference occurs when

the received multipath components of a symbol extend beyond the symbol-time duration.

In addition to ICI distortion, a signal transmitted through a frequency-selective fading

channel will suffer from amplitude fluctuation due to constructive and destructive

superposition of multipath components. A channel with τm << Ts is called a frequency-

nonselective or flat-fading channel, in which all multipath components of the received

symbol arrive at nearly the same time-instant and fall within the symbol-time duration,

hence only amplitude fluctuation experienced by the received signal (no ICI distortion).

In the frequency domain, a channel is characterized by a spaced-frequency correlation

function, |ρ(∆f)|, which is the Fourier transform of S(τ) and behaves as the channel’s

frequency transfer function. The frequency correlation function can be thought of as the


22

channel frequency-response. The channel coherence bandwidth, W0 is defined as the

frequency within which the channel passes all the spectral components with approximately

equal gain and linear phase. A channel is said to exhibit frequency selective fading if W0 is

much less than the signal bandwidth W, because the signal’s spectral components is

affected by the channel with unequal channel gains resulting in signal distortion. If W0 >>

W the channel is said to have a frequency nonselective fading because all signal’s spectral

components have an equal channel gain. Note that τm and W0 are reciprocally related, in

that a channel with a large multipath delay-spread will have a low coherence-bandwidth.

The relationship between the time spreading of signal represented by multipath intensity-

profile (time domain) and channel coherence bandwidth (frequency domain) is shown in

Figure 2.5.

|ρ(∆f)|S(τ)

Delay spread, τm Channel coherence bandwidth, W0

W0 ∝ 1/τm

(a) (b)

Figure 2.5 Relationship between time spreading of signal and channel coherence

bandwidth: (a) Multipath intensity profile; (b) Spaced-frequency correlation.

In a frequency-selective fading channel, the signal degradation (distortion) is not only the

loss of SNR due to amplitude fluctuation, but also ICI distortion due to a large delay

spread. It is important to see the impact of a frequency selective channel on a CDMA

signal. In most cases, when the spreading gain is large enough, a frequency selective

channel will only lead to ICI, in which the multipath components extend on a number of

chips smaller than the spreading factor (the number of chip per symbol). During a symbol

interval, there will be mostly ICI and a little amount of inter symbol interference (ISI) at

the beginning and the end of the symbol interval. In this case, the Rake receiver [39] will

make use of frequency diversity of the various multipath components and will provide very

good performance. In other words, if one multipath component is affected by a deep fade,


23

it is unlikely that the other multipath components will experience the same fading

condition. However, the existing ICI even small will lead to additional multiple access

interference and therefore, power control is important even though not as crucial as in a flat

fading situation. For flat fading channels, only one resolvable multipath component exists

for each symbol and power control plays an important role because the rake receiver

cannot make use of frequency diversity. In practice, CDMA systems employ several

techniques to combat various effects of multipath fading.

A summary of multipath fading characterization, types of degradation, and mitigation

techniques viewed in the time and frequency domains when the effect of fading is

considered as a signal time-spreading is shown in Table 2.1.

Table 2.1

Manifestation of multipath fading as time spreading of signal.

Characterisation Frequency selective fading Flat fading Time domain τm >> Ts τm << Ts

Frequency domain W0 << W W0 > >W

Signal degradation ISI, loss of SNR. Loss of SNR.

Mitigation Channel equalization, spread Diversity, error control, spectrum (Rake), Orthogonal power control. Modulation (OFDM).

Time Varying of the Channel

The time varying manifestation of multipath fading can be seen in the time domain as a

result of the motion between the transmitter and the receiver. We can also consider that the

time variation of the channel is equivalent to the spatial variation because the channel time

variation depends on the relative positions between the transmitter and the receiver (spatial

variation). The time varying channel in the time domain can be characterized by the

spaced-time correlation function, ρ(∆t), defined as the autocorrelation function of the


24

channel as shown in Figure 2.6(a). Using the spaced-time correlation function of the

channel, we can define the channel coherence time, T0, as the time duration over which the

channel response is time-invariant due to high autocorrelation within that time duration.

If the channel coherence time T0 is much less than the symbol-time duration Ts, the channel

is referred to as a fast fading channel, which implies that the channel exhibits time-

variation within a symbol-time duration. If T0 >> Ts, the channel is defined as a slow

fading channel, or the channel remains time-invariant for at least within a symbol-time

duration. A symbol transmitted through a slow fading channel will not be distorted because

the channel gain is approximately constant during a symbol period. However, a time-

variation of a slow-fading channel will result in a loss of SNR due to signal fluctuation

over several symbols. In a fast-fading channel, a transmitted symbol suffers from unequal

channel gains within the symbol period, leading to a pulse-shape distortion. The problems

caused by such distorted pulses are not only a loss of SNR, but also loss of symbol

synchronization and difficulties of designing a matched filter [36].

When viewed in the frequency domain, the time-variation of the channel can be

characterised by the Doppler spread of the channel. The Doppler power-spectral density,

S(υ), defined as the spectral broadening or Doppler spread of the channel, is used as a

measure of fading rapidity of a time-varying channel. The Doppler power-spectral density

can be expressed as [40]

≤

−=

otherwise,,0

||,

1

1

)(2 D

DD

f

ffS

υυπυ (2.5)

where fD is the maximum Doppler spread, and υ is Doppler-frequency shift. The Doppler

power-spectral density as a function of υ described in (2.5) has a bowl shape as shown in

Figure 2.6.(b).


25

S(υ)ρ(∆t)

Channel coherence time, T0

T0 ∝ 1/fD

Doppler spread

fc - fD fc fc + fD

(a) (b)

Figure 2.6 Relationship between Doppler spread and channel coherence time: (a) Spaced-

time correlation function; (b) Doppler power spectral density.

In frequency domain, a time-varying channel is said to exhibit a fast-fading mechanism if

fD >> W because the fading rate (represented by fD) is higher than the symbol rate

(represented by the signal bandwidth, W). A fading channel with fD << W is referred to as a

slow-fading channel. Viewed in frequency domain, fast fading causes a pulse-shape

distortion on the transmitted symbol because the channel fading rate is higher than the

signal bandwidth. Of course fast fading also causes the loss of SNR due to amplitude and

phase fluctuation. The mitigation techniques that can be used to combat fast fading are

error control and interleaving, robust modulation, and the use of signal redundancy to

increase the signalling rate. Ideally, power control could be used to compensate for the loss

of SNR. However, we will see in a following section that in such a situation, there is a

power control command delay, which makes it unsuitable for fast fading applications.

On the other hand, a slow fading channel may only suffer from the loss of SNR and can be

mitigated by power control. It is important to note that in a slow fading channel, the use of

error-control coding is not effective due to long burst errors. In this case, the required time

frame to interleave the symbol errors will be prohibitively long. Therefore, power control

applications are complementary with error-control: the former is effective for slow fading

and the later is good for fast fading.


26

Table 2.2 summarises the fading characteristics, types of degradation, and mitigation

techniques viewed in time and frequency domains when the effect of fading is considered

as a time-variation of the channel.

Table 2.2

Manifestation of multipath fading as time varying of channel.

Characterisation Fast fading Slow fading Time domain T0 << Ts T0 >>Ts

Frequency domain fD >> W fD << W

Signal degradation Loss of SNR, pulse-shape Loss of SNR. distortion, synchronization problem.

Mitigation Error control and interleaving, Diversity, error control, robust modulation. and power control.

In practice, a mobile wireless channel may exhibit one or more fading behaviours

depending on the environment where the radiowave propagates. A mobile user may also

experience different fading conditions when it moves from area to area. Therefore, to

obtain reliable performance in a wireless communication system, various techniques to

mitigate different effects of fading channel should be used. Table 2.3 characterises the

fading channel models in the time and frequency domains.

Following this necessary classification of wireless channels and the study concerning the

effectiveness of power control on different channel types, we will concentrates next on the

problem of power control in a flat fading situation. Indeed, we have seen that it is in this

context that not only power control is effective, but also it is the only way to recover a

signal affected by a long deep fade. In the following section, we describe the mathematical

model of Rayleigh fading, which will be used throughout this thesis.


27

Table 2.3

Fading channel characterisation.

Channel models Ts >> T0 Ts << T0 W >> W0 Time-frequency Frequency-selective selective fading. time-nonselective fading.

W << W0 Time-selective Time-frequency frequency-nonselective fading. nonselective fading.

2.2.3 Rayleigh Fading Channel

We have shown in the time domain that for a frequency-nonselective or Rayleigh fading

channel, the time-delay is much less than the symbol duration or the inverse bandwidth of

the signal (τm<<W-1). Then, by using the transmitted signal expressed in (2.3), the received

signal in (2.4) can be rewritten as

tfjtjl

L

l

cl eeCtstr πφτ 2)(

10 .).()(

−= ∑

=

, (2.6)

where φl(t) = 2π(fD cosψlt – fcτl), and τ0 ∈[minτl, max τl]. The phase φl(t) can be modelled

as independent and identically distributed (i.i.d.) random variables [42] that is uniformly

distributed over [0, 2π].

The first two terms in (2.6) is the equivalent low pass received signal. The first term shows

that the transmitted baseband signal is delayed due to propagation time, and the second

term reflects the amplitude fluctuation of the baseband signal by

)(

1

)( )()( tjL

l

tjl eteCt l φφ αβ == ∑

=

. (2.7)


28

If the number of paths is large then β(t) will approach a complex Gaussian random variable

[43], and α(t) has a Rayleigh probability distribution function (pdf) as

0,exp2

)(2

2

2≥

−= α

σα

σααf , (2.8)

where σ2 = E[α2]. Therefore the received signal variation that is governed by α(t) has a

Rayleigh distribution, which has been confirmed by experiments in [44]-[45]. If the direct

LOS path exists, then α(t) will exhibit a Rician distribution [46]

0,2

exp2

)(202

22

2≥

+−= ασαµ

σµα

σαα If (2.9)

where µ2 is the average power in the direct LOS path and I0 is the modified zero-th order

Bessel function [47]. A more general distribution model of the multipath fading amplitude

that takes into account both Rayleigh and Rician distribution is described by the Nakagami

pdf expressed as

−

Γ=

−

2

2

2

12

exp.)(

2)(

σα

σαα m

m

mf

mm

, (2.10)

where σ2 = E[α2], m = σ4/E[(α2 - σ2)2], and Γ is the gamma function. When the received

signal has a direct LOS path, the Nakagami distribution approximate the Rice distribution

(m > 1), and when there is no LOS path, then m ≈ 1 in (2.10) and the Nakagami pdf is

identical to the Rayleigh pdf expressed in (2.8).

2.3 Power Control Algorithm

As mentioned in Chapter 1, power control plays a very important role in a CDMA system.

There are three types of power control algorithms: open-loop, closed-loop, and outer-loop

power control. The open-loop power control is designed to overcome the near-far problem,

while the closed-loop power control aims at reducing the effect of Rayleigh fading. The

outer-loop power control is used in a closed-loop power control to adjust the target SIR or

signal strength.


29

2.3.1 Open-Loop Power Control

To overcome the near-far and shadowing problems on the reverse link of a CDMA system,

an open-loop power control can be used [48]. The open-loop power control is designed to

ensure that the received powers from all users are equal in average at the basestation. In the

open-loop algorithm, the mobile user can compute the required transmit power by using an

estimate from the downlink signal (no feedback information is needed). This is because the

large-scale propagation loss is reciprocal between uplink and downlink channels. Figure

2.7 shows how an open-loop power control algorithm solves the near far problem in the

reverse link of a CDMA system.

User 2

User 1

d1

d2

Basestation

Pr2

Pr1

Pt2Pt1

Figure 2.7 Mechanism of open-loop power control.

In Figure 2.7, user 1 located at distance d1 from the basestation receives a power level Pr1.

This power level is higher than that received by user 2, Pr2, who is located at distance d2

from the base station because d1 < d2. Therefore to deliver an equal power received at the

basestation, user 2 must transmit a higher power level than user 1 or Pt2 > Pt1. The

procedure to determine the transmit power can be expressed as

Pt = - Pr + Poff + Pp, (2.11)

where Pt (dBm) is the required transmit power for a mobile user, Pr (dBm) is the received

power at the mobile, Poff (dB) is the offset power parameter, and Pp (dB) is the power

adjustment parameter. The offset power parameter is used to compensate for different


30

frequency bands, i.e. Poff = –76 dB for the 1900 MHz and Poff = –73 dB for the 900 MHz

frequency band [49]. The power adjustment parameter is used to compensate for

differences with regards to different cell sizes and shapes, basestation transmit power, and

receiver sensitivities.

In designing a power control scheme, we need to consider the power control parameters,

such as the dynamic range, power-update rate, and power-update step size. To illustrate the

dynamics range, consider one user that is located at 100 m away from the basestation and

another user is at 10 km from the same basestation. Using the path loss equation shown in

(2.2) the received power of the first user is 80 dB higher than the second user if they are

located in an environment that has a path loss exponent n = 4. Therefore, the dynamic

range can be very large. The power-update rate depends on the measurement period of the

downlink signal. A higher power-update rate will require a shorter measurement period.

However, it is important to obtain a good method of the downlink signal measurement. If

the measurement period is too short, rapid fluctuation due to multipath may still exist and

may not give an accurate result for the mean power measurement. On the other hand if

measurement period is too long it may average out the effect of shadowing and therefore

open-loop power control may not compensate for the shadowing effect. The method

described in [34]-[35] can be referred to, to perform a good measurement method of the

mean received power in a fading environment. In [50] an optimal technique for estimating

a local mean signal is also presented.

We will discuss in more details the effect of system parameters on the performance of

power control in a following section. In this study, we assume that open-loop power

control can perfectly eliminate the near far problem due to large-scale propagation loss.

The power control scheme to deal with the rapid signal variations, which cannot be

eliminated by the open-loop algorithm, will be discussed in the next section.

2.3.2 Closed-Loop Power Control

Closed-loop power control aims at eliminating the received signal fluctuation due to small-

scale propagation loss. In contrast to the large-scale propagation loss, the small-scale

propagation loss is uncorrelated between uplink and downlink. Therefore, to control the

uplink fading, the uplink channel information must be estimated at the basestation and then


31

fed back to the mobile station, so that the mobile station can adjust its transmit power

according to the fed back information.

To obtain the uplink channel information, the basestation can either estimate the received

signal strength or the SIR. In CDMA, however, power control based on SIR is more

suitable than that based on signal strength because CDMA is interference limited. A

closed-loop power control model for the reverse link is shown in Figure 2.8.

Mobile station

Signal strength orSIR measurement

PCCquantizer

Loopdelay, DTp

PCCdetector

Transmitpower

Basestation

Desired level

e(t)BERmeasurement

Channel gainβ(t)

∆pPCCPCC x ∆p

PCCerror

PCC bits

Outer loop

- γtγest

+

Figure 2.8 Closed-loop power control model.

In this model, the signal strength or SIR is first estimated at the basestation for every time

slot, Tp, which corresponds to one power control interval. In Figure 2.8 this estimated

quantity is represented by γest. Then it is compared with the desired or the target level γt.

The difference between the estimated SIR or signal strength and the target level is then

quantised and sent to the mobile user via the downlink channel as a binary representation

of PCC bits. The command bits are multiplexed with the user data. The mobile users then

extract the PCC bits from the downlink data stream and use them to adjust their transmit


32

power. Due to the downlink channel impairments, the PCC bits received by the mobile

user can be in error. The PCC bit error is modelled as a multiplicative quantity with

opposite bit polarity. A delay is also introduced by the control loop. This delay is called the

feedback loop delay and is expressed in a multiple, D, of power control interval Tp, where

D is an integer. After the PCC bits are recovered by the mobile user, they are used to adjust

the transmit power by the required step size, PCC x ∆p. Due to feedback delay, however,

the mobile transmit power (after adjustment) may not compensate the current channel

condition because at the time the mobile adjusts the power, channel conditions may have

already changed in a fading situation.

Closed-loop power control based on measurements of the received signal strength has been

studied in [19], while those based on measurements of the SIR appeared in [20]. It is

shown in [20] that power control based on SIR appears to perform better than that based on

the signal strength. SIR-based power control, however, has the potential for positive

feedback that may occur when the number of active users exceeds the maximum CDMA

system capacity. In this situation, an increase of transmit power from any user will increase

interference to other users, which in turn, are forced to increase their power, and so on.

To avoid positive feedback, a strength-and-SIR-combined power control scheme is

proposed in [21]-[22]. In this scheme, SIR is used to control the desired signal quality,

while signal strength is used to control the interference level. For example when a user’s

SIR is below the required threshold but its signal strength is already high (above the

threshold), that user cannot increase its transmit power. Alternatively, power control

should be operated together with another technique, such as call admission control (CAC)

in order to prevent positive feedback [51]-[53] by assuming that the maximum system

capacity is not exceeded. Another possible technique to reduce the possibility of positive

feedback, a soft dropping technique can be used [54]-[55]. With this technique, a user who

needs a high transmit power to combat deep fades can decrease its target SIR, which is

quite possible for a CDMA system at the expense of a graceful performance degradation.

Adjusting the SIR target can be done by the so called “outer-loop power control” as shown

in Figure 2.7. This mechanism is explained in more details in the next section.


33

2.3.3 Outer-Loop Power Control

In a real system, closed-loop power control is imperfect which means that even though the

transmit power is controlled, the received SIR at the basestation may still have some

variations. This SIR variation is called power control error due to imperfections of power

control itself, and the level of error may vary from user to user depending on propagation

conditions, mobility speeds, etc. The required SIR to achieve the desired BER performance

depends on the distribution of the SIR itself [56]-[58]. To achieve the same BER

performance, a user with high SIR variations will need to be operated at a higher Eb/I0 on

average compared to another user with low SIR variations. Therefore, in order to achieve

the desired performance, different users may require different SIR levels and to do this the

outer-loop power control is needed to adjust the target SIR [59]-[62].

To determine the correct SIR target, the BER needs to be monitored as follows. The

basestation performs the BER measurement, which is then compared with the desired

BER. If the BER obtained from the measurements is better than the desired BER, the target

SIR is decreased. Otherwise the target SIR is increased. Therefore the control parameter

for the outer-loop algorithm is the bit error rate.

The outer-loop power control scheme can also be used in a system that employs various

requirements of quality of service for different users. For example, a data user may require

a better BER performance than a voice user, so that the former may need a higher SIR

requirement than the later.

2.4 Limitations of Imperfect Power Control

In this section we identify several problems related to SIR-based power control in a real

environment. We review the effects of power control parameters and other factors on the

system performance. These factors include power-update step size, SIR estimation error,

feedback delay, power-update rate, feedback channel error, and the effect of deep fades.

2.4.1 Power-Update Step Size

Power-update step size is a factor by which a mobile station adjusts its transmit power at

each power control interval. The power-update step size is determined by the PCC bits or


34

the quantised feedback information e(t), which has been received by the mobile station.

Basically, there are two different methods of quantising the feedback information. The first

method is called a variable-step power control, in which e(t) is quantised into multiple

PCC bits. The second method is called a fixed-step power control in which e(t) is quantised

into one PCC bit. The advantages and disadvantages of these methods are explained below.

In a variable-step algorithm, the quantisation of e(t) can be implemented by using a pulse

code modulation (PCM) realisation [63]. The larger the number of quantised bits, the more

accurate the quantised feedback information. In this algorithm the mobile transmit power is

adjusted by different step sizes depending on the difference between the received SIR and

the target SIR at each power control interval [64].

The variable-step algorithm can be expected to have a good performance because the

fading factor can be directly compensated during one power control interval, Tp with

multiple PCC bits. However in practice, this method is not efficient because it requires

several PCC bits per power control interval to convey the feedback information through

the downlink channel. Note that the power control signalling rates are much higher than

the fading rates to compensate for fading channel. Therefore with multiple PCC bits per

power control interval the variable-step power control method will require a substantial

signalling bandwidth on the downlink channel.

Implementation of the variable-step power control algorithm using the PCM realisation of

mode q can be expressed as

−≥−−−<≤−−−

<≤−

+−<≤+−−+−<−

=−

−−

−−−

−−−

−−

2/12index),12(

2/12index2/32),22(

..

..

2/1index2/1,0

..

..

2/32index2/12,22

2/12index,12

)(

11

111

111

11

qq

qqq

qqq

qq

qDie , (2.12)


35

where e(i-D)q = γest - γt. In (2.12), index is defined as e(i-D)q/∆p, where ∆p is the step size,

and D is the feedback delay expressed in Tp. The quantised value of e(i-D)q on the right

hand side of (2.12) can be expressed using a binary representation as in a PCM system for

digital transmission. Note that q represents the number of PCC bits in each power control

interval.

In the absence of PCC bit transmission error, the transmit power at the next power control

interval can be expressed as

p(i+1) = p(i) - ∆p . e(i-D)q, (2.13)

where e(i-D)q is shown in (2.12) for variable step algorithm or e(i-D)q ∈{-1, +1} for fixed-

step algorithm, p(i) is the transmit power at the ith power control interval, D is the

feedback delay, and ∆p is the power-update step size.

In the fixed-step algorithm, the PCC contains only a single bit to minimise the signalling

bandwidth. This algorithm can be considered as the PCM scheme with mode q = 1. The

PCC bit can be expressed as

≥<−+

=−= = 0 D)-(i1-

0 )(1])([ bit PCC 1 e

DieDiesign q . (2.14)

In the fixed-step algorithm, if the estimated SIR, γest is less than the target SIR, γt, the PCC

bit -1 is sent to the mobile to increase its transmit power by ∆p dB. If γest is higher than γt,

the PCC bit +1 is sent to the mobile to decrease its transmit power by ∆p dB. This scheme

can be implemented in practice using a delta modulation (DM) type realisation [65]. With

only one PCC bit, the mobile can only increment by a fixed step size ∆p to either increase

or decrease its transmit power.‡ However in practice, this method is more attractive than

the variable-step method because with only 1 PCC bit for each power-control interval, the

power control signalling bandwidth on the downlink channel is minimised. This is the

main reason why most existing schemes of closed-loop power control employ a fixed step

algorithm [16]-[20].

‡ A single command bit can be used in an adaptive variable-step power control scheme when the

correlation property of consecutive command bits is utilised at mobile stations.


36

The fixed step size algorithm is also preferred due to the fact that it can reduce peak

transmit power during deep fades. In a variable-step algorithm, the peak transmit power is

high to compensate for deep fades, and therefore may decrease the capacity due to

excessive interference to other users [51] and [66]. We will evaluate a fixed step power

control by computer simulations in Chapter 4 and show that the fixed-step algorithm has

other advantages over the variable-step algorithm as briefly explained in the next section

2.4.2 SIR Estimation Error

The performance of SIR-based power control depends on the accuracy of the SIR estimator

as the control parameter. In the existing literature, very few papers [19], [67]-[69] address

the issue of SIR estimation and implementation. In this thesis, we propose a new SIR

estimation method, which uses an auxiliary spreading sequence to estimate multiple access

interference in CDMA systems.

The major problem in a SIR-based power control is that the transmit power must be

updated in a rate that is much faster than the fading rate. Therefore, fast SIR measurements

are required, resulting in estimation errors. However, the effect of SIR estimation on the

BER performance of a fixed-step power control is not significant [70]. This is explained by

the fact that in this case, the only information fed back to the mobile station is whether the

SIR estimate is below or above the target SIR. On the other hand, a variable-step size

power control algorithm is very sensitive to SIR estimation errors. It is because the actual

step size is a quantisation of the difference between the SIR estimate and the target SIR. In

this case, a better SIR estimator will produce a more accurate feedback information and

thus variable step size, resulting in faster convergence to track the fading.

2.4.3 Feedback-Loop Delay

In a closed-loop power control, the effect of feedback loop delay is an important factor. To

overcome the problem due to feedback delay, power control algorithms may employ a

channel predictor [71]-[72]. The loop delay DTp in Figure 2.7 accounts for the total

feedback delay, from the time the channel is estimated by the SIR estimator at the

basestation until an appropriate power control command is received by the mobile and its

transmit power is adjusted accordingly.


37

The following factors contribute to the total feedback loop delay. First, SIR measurement

at the basestation takes time. Normally, SIR measurement is performed during one time

slot and hence, contributes to a one-slot delay. Once SIR measurement is completed, it

needs to be compared with the target SIR to generate the PCC bit. Although the processing

time at the basestation can be negligible, the PCC bit may not be transmitted on the next

immediate time slot on the downlink channel, because it depends on the synchronization

between the uplink and downlink channels. Therefore, the second contributor is the

synchronization delay between uplink and downlink channel. The third contributor to the

loop delay is the propagation time of the PCC bit from the basestation to the mobile

(distance dependence). Assuming the processing time at the mobile to extract the PCC bit

from the downlink data-stream may also be negligible, a total feedback delay of 2 slots or

more can be expected.

For a Rayleigh fading channel at moderate fading rates, a 2-slot feedback delay may

degrade the power control performance significantly. This is because the SIR estimates

used when the power control command takes place are outdated and do not reflect the most

recent power updates because the channel coefficients change rapidly. The problem of

feedback delay has been studied in [73], in which a time delay compensation method is

proposed to overcome the problem. In this method the estimated SIR is adjusted according

to the power control commands that have been sent but have not come in effect due to the

feedback delay.

In this study a prediction filter techniques is studied to solve the feedback delay problem.

A long-range prediction method to predict a fading signal has been proposed in [24] and

can be applied in power control applications with some modifications. It is expected that a

prediction method will perform better than a compensation method.

2.4.4 Power-Update Rate

In [16], power control is shown to be effective when the power-update rate is much higher

than ten times the fading rate. For illustration, a vehicle travelling at 60 km/h will

experience a maximum Doppler spread of 100 Hz in the 1.8 GHz frequency band. Since

the maximum Doppler spread reflects the fading rate, the mobile power-update rate should

be much higher than 1 kHz to make power control effective. Power-update rate of 800 Hz


38

has been used in the second-generation CDMA systems (IS-95), while in third generation

CDMA systems power-update rate of 1.5 kHz has been proposed [74]. Since the carrier

frequency of third generation systems is twice as high as the second generation systems,

the maximum Doppler spreads for third generation systems is also twice as high as that for

second generation systems. Therefore, even though the power-update rate in third

generation systems is approximately twice as high as that for second generation systems,

the power update-rate relative to fading rate is not higher.

With 1.5 kHz power-update rate in third generation systems, SIR measurement can be

performed every 0.667 ms, corresponding to one power control interval, Tp. Note that the

accuracy of SIR estimator is dependent on the measurement period. However in [66], we

have shown that the effect of SIR estimator error on the performance degradation of a

fixed step power control is not significant. In a variable-step algorithm, however, the

accuracy of SIR measurement may have a more significant effect on the performance

because any variation of SIR will translate into different step sizes. Therefore, a fixed step

power control scheme is less sensitive to SIR estimation error making the algorithm robust.

We will further investigate the effect of SIR estimation error on the performance of fixed-

step and variable-step algorithms in Chapter 4.

2.4.5 BER of Feedback Channel

Another problem related to closed-loop power control is the error on the PCC bits when

they are received by a mobile station due to the impairment of downlink (feedback)

channel. If PCC bits are received in error, a mobile will experience a wrong power

adjustment. If the downlink channel error has a BER of Ppcc, the probability that the mobile

transmit power will be reduced is

P’d[γest] = (1- Ppcc) Pd[γest] + PpccPu[γes], (2.15)

and the probability that the mobile transmit power will be increased is

P’u [γest] = (1-P’d[γest] ) = (1-Ppcc) – (1-2Ppcc) Pd[γest], (2.16)

where Pd[γest] = P[γest > γt] and Pu[γest] = P[γest < γt], γest is the estimated signal strength or

SIR to which the power control algorithm is based, and γt are the target level.


39

However, the effect of downlink transmission error on the performance of a fixed step

power control is not significant since the loop is of delta modulation type, which adjusts

the power up and down continuously [49]. The insignificant effect of BER of the downlink

channel on a fixed step algorithm is another reason why the fixed step algorithm is

preferred, in addition to its efficient signalling bandwidth requirement. The effect of BER

of the downlink channel can be crucial in a variable-step algorithm. We will investigate the

effect of BER of the downlink transmission on the performance of variable-step power

control in Chapter 4.

2.4.6 Effect of Deep Fades

As mentioned in Chapter one, there are two important problems related to deep fades.

First, the power control ability to track deep fades is limited due to imperfect parameters in

real systems. Second, if power control algorithm is improved (e.g. by using a variable-step

algorithm) to better track deep fades, a user experiencing a deep fade will raise its transmit

power significantly and will affect the SIR experienced by other users. This could lead to

instability problems, because other users will also raise their power.

The problem that we want to solve here is how to eliminate or reduce deep fades, so that

the power control algorithm can better track the fading channel. Combating deep fades by

power control alone is not only difficult, but also resulting in another problem of possible

instability as described above. Therefore, we need to solve this problem using a different

approach. A well-known method to reduce the effect of deep fades is to use an antenna

diversity technique. With antenna diversity, deep fades can be reduced by a factor that is

proportional to the Lth power, where L is the diversity order [75]. Therefore, we will

investigate the use of diversity antenna arrays at the basestation. There is no fundamental

implementation issue associated with antenna diversity technique because diversity

antenna technology is usually available at basestations in any cellular system.

2.5 Summary

The differences between the uplink and the downlink of a DS-CDMA system have been

presented in this chapter. In the downlink, there is no near far distance problem, orthogonal

spreading sequences can be employed, and multiple access interference is not significant.


40

In the uplink, the near far distance problem is inherent, orthogonal spreading sequences

cannot be used, and multiple access interference becomes a serious problem. The need of

power control in CDMA systems is also described, and the importance of uplink power

control is emphasised.

We have also explained that open-loop power control can overcome the near far distance

problem but cannot solve the problem of rapid fading fluctuations. The impairment due to

fading is more difficult to control because of uncorrelated fading behaviours between

uplink and downlink, which requires a closed-loop power control algorithm. This closed-

loop algorithm is further complicated by the fact that the algorithm must be performed at a

rate that is much faster than the fading rate in order for the power control to be effective.

Finally we have seen that, in real systems power control is imperfect because of the

limitations of system parameters. These parameters include channel estimator or SIR

estimator, power-update rate and power-update step size, feedback delay, and feedback

channel error. To achieve a good power control performance in a real system, the effect of

imperfect parameters need to be minimised. We will show the effects of imperfect system

parameters on the performance of SIR-based power control by computer simulations in

Chapter 4.

41

Chapter 3

SIR Estimation/Measurement

This chapter describes a new SIR estimation/measurement method that we propose for

CDMA systems using an auxiliary spreading sequence. This new SIR estimator will be

used as a control parameter in the SIR-based closed-loop power control algorithm. A

CDMA signal model with QPSK modulation scheme is first presented followed by an

analytical expression of SIR for CDMA systems. Then existing SIR estimation methods

based on MLE and SNV are described. A new SIR estimator for CDMA system is

proposed using an auxiliary spreading sequence method. The performance of these SIR

estimators is evaluated in terms of estimate bias and MSE. We then discuss their

competitive advantages/disadvantages.

3.1 Introduction

In present mobile communication systems there are many new technologies emerging to

improve transmission and reception techniques of digital symbols over a fading channel.

These new technologies include smart antenna, transmitter/receiver diversity, interference

cancellation, and power control. Most signal processing techniques used in these new

Chapter 3. SIR Estimation/Measurement

42

technologies are based on SIR that serves as a control parameter. Therefore, good and

reliable SIR estimators are very important. It is important to distinguish between SNR,

SIR, and SINR (signal to interference plus noise ratio). SNR is used for a noise-limited

system in which thermal noise is the dominant component of unwanted signal. SIR is used

for an interference-limited system, such as CDMA system in which the major component

of unwanted signal is multiple access interference from other users. Since thermal noise

always presents in all systems, SINR is more accurate to represent the unwanted signal

components in a CDMA system. However in this thesis the author uses SIR to mean SINR

in CDMA systems.

A good SIR estimator is one that is unbiased (or has a very small bias) and exhibits a small

variance. In practice, however, the complexity of the estimator often becomes an important

issue since good estimators, in general, require more complex operations. The basic

challenge of the SIR estimation problem is to find an efficient way to separate the signal

component from the interference component.

There are two categories of SIR estimators. Those that require the knowledge of data-

bearing information (data aided estimators) and those that solely rely on the observation of

the received signals. The data-aided estimators (DA) can either use the known transmitted

data (TxDA), such as training or pilot symbols if they are available, or use an estimate of

the transmitted data from the receiver decisions (RxDA). Of course, there is no additional

penalty in the transmission overhead if a TxDA estimator is used in systems that already

employ training or pilot symbols for other purposes, such as synchronization, coherent

demodulation, or channel estimation.

Early work on a real time SNR estimation that relies on the training sequence was

presented in [76]-[78]. The SNR is estimated using the MLE technique to monitor the

decoded data at the receiver. This method is well known to be optimal and has an

asymptotic property, but in addition to its reliance on the training sequence, it requires a

complex computation to solve an algebraic equation numerically of a large number of

samples [77]. In addition, this technique is originally developed for applications in a noise-

limited system in which the interfering signal is Gaussian (thermal) noise, hence the name

SNR estimator. We will evaluate applications of MLE method for CDMA systems in a

following section.


43

In [79] and [80], an SIR estimator for a TDMA system was presented using interference

projection (IP) and signal projection (SP) method, respectively. Both IP and SP methods

basically utilise the null space of the training sequence signal space to cancel the signal

part from the total received signal. In addition to the training sequence requirement, both

IP and SP method need to know the channel memory length, which for a fading channel

communication, is another difficult parameter to estimate.

A method based on a signal subspace approach using the sample covariance matrix of the

received signal is proposed in [81] and [82]. This method is referred to as the subspace-

based (SB) method. Unlike the SP and IP methods, the SB method does not require any

training sequence or channel information, but it needs to deal with the eigenvalue problem,

which obviously requires high computational burdens, particularly for a large number of

users (high matrix dimension). In addition, such subspace methods are well known for

their poor robustness towards the noise.

Another method based on the split symbol moments estimation (SSME) described in [83]

is interesting. This method relies on using the sample statistics from two separate halves of

the same symbol. However, this method can only be applied on a binary phase shift keying

(BPSK) modulated signal since it is not easy to be extended to higher orders of modulation

for which complex form expressions are required. In [84], a signal-to-variance ratio (SVR)

method is described based on the moments method to operate on M-ary phase shift keying

(PSK) modulated signals. With this method, however, the resulting estimates exhibit a

certain degree of bias.

In [85], the method of histogram matching based on a short-term probability distribution

was proposed. Compared to the moments method, this technique can performs better. This

is because the moments method uses only the first few moments of the received signal,

which contains only partial information of the signal statistics. However, an estimation

method that is based on higher orders statistics or distribution is time consuming and

computationally intensive, which is not preferable for real time applications.

A comprehensive comparison on the performance of several SNR estimators is given in

[86]. In addition to SSME, MLE, SVR, and moments (second and fourth order) methods,

an SNV estimator is also presented in this paper. In the SNV method, SNR is estimated


44

based on the first absolute moment and the second moment of the sampled output of the

match filter. It is obvious that, in general, a more accurate SIR estimator requires a more

complex operation and needs a longer measurement time. In the context of this study, we

need to estimate the SIR within a very short period of time because we are going to use it

in a fast power control algorithm. In order to perform a fast real-time SIR measurement,

computational complexity should be low. Therefore the abovementioned methods may not

be suitable for power control applications in CDMA systems and thus a better technique is

to be found.

In this thesis, we propose an SIR estimator for power control applications in a CDMA

system using an auxiliary spreading sequence technique. By using an auxiliary spreading

sequence, the multiaccess interference can be estimated after despreading (at symbol level)

and thus reduce the complexity. For comparison, however, we evaluate the MLE and SNV

estimators because the MLE method, as we will show in a later section, has a very good

performance that approaches the Cramer-Rao bound (CRB) and therefore can serve as an

upper bound; while the SNV method is chosen for comparison because it has a wide

application in practice due to its low complexity. The other SIR estimators described above

are computationally more complex than our proposed technique, and therefore are not

suitable for fast real-time measurements.

3.2 CDMA Signal Model

In a DS-CDMA system the spread spectrum waveform is characterised by the number of

chips (spreading sequence) per symbol M, the chip waveforms, and the types of spreading

sequence of length M. We will consider each of these parameters in the CDMA signal

model as follows.

Consider a CDMA transmission system with a QPSK modulation scheme described in

Figure 3.1. In a CDMA system, the nth transmitted symbol of the kth user bk(n) = bk(I)(n) +

jbk(Q)(n) is spread by the kth user’s spreading sequence ck(m) = ck

(I)(m) + jck(Q)(m), m ∈ {1,

2, …, M}. It is important to realise that the user’s spreading sequences ck(I) ={ck

(I)(1),

ck(I)(2), …, ck

(I)(M)} and ck(Q) ={ck

(Q)(1), ck(Q)(2), …, ck

(Q)(M)} are known to the receiver.

The number of chips per symbol M is called the processing gain or spreading factor of a


45

DS-CDMA system. It reflects the ratio of the signal bandwidth after spreading to that of

the unspread data symbol.

Q

bk(Q)(n)

bk(I)(n) H(f)

carrierWaveshapingfilters

ck(I)(m)

H(f)

π/2

+

ck(Q)(m)

AWGN

Waveshapingfilters

ck(Q)(m)

ck(I)(m)

∑m

carrier

π/2

H(f)

H(f)

+Decision

yk(m) yk(n)

(a)

(b)

I

I

Q

Figure 3.1 CDMA signal model with QPSK modulation: (a) modulator; (b) demodulator.

In practice, various types of spreading sequences such as pseudonoise (PN), Walsh and

Hadamard (orthogonal codes), and Gold and Kasami spreading sequences that can achieve

low crosscorrelations can be constructed. As mentioned in Chapter 2, the uplink of present

CDMA architecture employs a random spreading sequence, while the downlink employs

an orthogonal spreading sequence.

A PN spreading sequence can be used to approximate the random spreading sequence and

can be easily generated using a feedback shift register, and thus has widespread

applications. Although a rectangular chip waveform can be easily generated, it has a

considerable frequency spectral component beyond the spectral null at 1/Tc, where Tc is the

chip period. Therefore, a smooth chip waveform such as a sync chip waveform is usually


46

used for the sake of spectral efficiency. Since the uplink is considered in this study, a

random spreading sequence is assumed and will be used for simulations. The correlation

property of a random spreading sequence can be expressed as follows

=

≠==

=

=∑ jk

jkmcmc

M

mjkkj M

Efor0

0andfor1)()(

1

*1)]([

ττρ . (3.1)

Here, τ is the chip asynchronism in a multiple of chip period, cj* is the complex conjugate

of cj, and M is the number of chips (spreading sequence) per symbol or the spreading

factor. In (3.1), m is the chip index in every symbol period. The second moment of the

crosscorrelation function of a random sequence with rectangular chip waveform can be

expressed as [87]

=≠≠=≠==

0,for3/1

0,for/1

0,for1

)]([ 2

τττ

τρjkM

jkM

jk

kjE . (3.2)

For the real systems using PN spreading sequence, the synchronous correlation property of

a PN spreading sequence can be expressed as

≠−

==

=∑=

jkM

jkmcmc

M

mjkkj

Mfor

1for1

)()(

1

*1

ρ . (3.3)

We can see that the crosscorrelation of PN spreading sequence differs only by -1 from that

of the pure random sequence. In the simulations, we normalise the amplitude of the

quadrature spreading sequence, so that the magnitude of its complex form is unity and can

be expressed as

)(2

1)(

2

1)( )()( mcjmcmc Q

kI

kk += . (3.4)

The superscripts (I) and (Q) in Figure 3.1 represent, respectively, the in-phase and the

quadrature components of the QPSK modulation. In a QPSK modulation scheme, the

transmitted symbols sequence bk(n) from the kth user can be expressed as

}...,,2,1{,)()( Bnj

enAnb knkk ∈= θ

. (3.5)


47

Here Ak(n) is the scale factor of symbol amplitude, θkn ∈{± π/4, ± 3π/4} is the modulation

phase, and B is the number of the transmitted symbols. If Ak(n) = 1 (the transmission power

is normalised to unity), the spread sequence of the transmitted symbol expressed in a chip

index m can be written as

}...,,2,1{),(2

1)(

2

1)( )()( MBmmbjmbmb Q

kI

kk ∈+= , (3.6)

where bk(I)(m), bk

(Q)(m) ∈{+1,-1}. The spread sequence is modulated by a carrier and then

filtered before transmission through the channel. For SIR estimation purposes, we assume

perfect carrier modulation/demodulation and filtering, so that we can simplify the model

by only considering the signal at the baseband level. In a fading channel situation, the

received baseband signal from all K users at demodulator can be expressed as

)()()( tncbttr kkkkk

σβ +∑= . (3.7)

Here βk(t) is the fading channel coefficient and n(t) is the additive white Gaussian noise

(AWGN) with unit power spectral density (σk is the standard deviation of the AWGN,

experienced by the kth user.

After carrier demodulation and filtering in a QPSK CDMA scheme, the received baseband

signal is despread by the conjugate of the kth user’s spreading sequence ck* and then

integrated over one symbol period (over M chips) to obtain the decision variable, yk(n). For

a slow fading channel (βk(t) is constant over one symbol period), the SIR of the kth user

computed during one symbol period can be expressed as follows

∑≠

+=

kjkjj

kkk

nnAM

nAn

22

2

)(|)(|1

|)(|)(

σβ

βγ . (3.8)

The factor 1/M (crosscorrelation between spreading sequences) in the denominator of (3.8)

is the result of despreading user j by the kth user’s spreading sequence. The first term of

the denominator represents the multi access interference from the other K-1 users due to


48

non-zero crosscorrelations between users’ spreading sequences, and the second term

represents the thermal noise.

In practice, the channel gains are either unknown or not perfectly estimated. Therefore it is

not easy to separate the desired signal from the total interference plus noise (MAI and

AWGN). In the following sections, we will review in more details several existing

techniques for doing so, and we will finally propose our new method, which estimates the

SIR in a CDMA system using auxiliary spreading sequence.

3.3 Maximum Likelihood Estimator

The SNR estimator based on the MLE theory was described in [76]-[78]. The description

of the MLE in [78] is more detailed, but only considers the estimation for a BPSK-

modulated signal in real AWGN channel. For M-ary PSK signals in AWGN channels, the

MLE technique is derived in [86]. In this method, the data symbol is oversampled to obtain

a larger number of observations. The estimation of the SNR can be performed within

several symbol periods. The original work of SNR estimator using MLE method is used in

a non spread spectrum system. In our study, we will extend the use of MLE method in a

CDMA system by considering the CDMA spreading sequence (chips) as an oversample

process of a symbol. Figure 3.2 shows the implementation of the SIR estimator using MLE

method at the baseband level (after carrier demodulation and filtering).

Consider B symbols are available for averaging in the SIR estimator. Since each symbol is

spread by M chips, we have BM new samples per symbol. When each symbol is despread

by the desired user’s spreading sequence at the receiver, however, the processing gain M

will be attained by the desired user due to the correlation with its own spreading sequence

(despread and integrate over one symbol period). Therefore, the MLE SIR estimator for

CDMA systems differs from that for a non spread system by a factor of M, which is the

processing gain of the CDMA system (no processing gain is involved in a non spread

system). Note that in addition to the kth user spreading sequence ck(m) = ck(I)(m) + j

ck(Q)(m), knowledge of the kth user’s data symbol bk(n) = bk

(I)(n) + j bk(Q)(n) is used in this

SIR estimator


49

γk

bk(I)(n)

I

Q

ck(Q)(m)

ck(I)(m)

bk(Q)(n)

B

∑ ( | . | )2

n=1

_+

ratio

MB

∑ ( | . | )2

m=1

∑ m

+

bk(n,m)

Figure 3.2 SIR estimator using MLE method.

For a single path signal reception (without a rake diversity technique), the SIR estimate of

the kth user based on the MLE method can be expressed as

2

1

*

11

*

1

2

1

*

1

),(),(1

),(),(1

),(),(1

−

=

∑∑∑∑

∑∑

====

= =

M

mk

B

n

M

m

B

n

B

nk

M

mk

mnrmnbMB

mnrmnrMB

mnrmnbMB

γ . (3.9)

Here bk(n,m) is the known sequence for the mth chip sequence of the nth symbol, r(n,m) is

the received signal corresponding to the mth chip of the nth symbol, B is the number of

symbol considered during the estimation period. The | x | operator in Figure 3.2 is used to

obtain the magnitude of the complex quantity x.

In CDMA systems, the user’s spreading sequence ck(m) is always available at the receiver

for despreading operation. However as shown in (3.9), the MLE method uses the sequence

of bk(n,m), which requires not only the knowledge of ck(m) but also bk(n). The symbol

sequence bk(n) can be obtained from the training or pilot symbols (MLE-TxDA) or from

the estimated receiver decisions (MLE-RxDA). There is also a fundamental

implementation issue in this method because part of the processing is performed at the chip

level while the other part is done at the symbol level. However, a good performance can be


50

obtained from this estimator. We will show the performance of MLE SIR estimator and

will compare it with the performance of other estimators in Section 3.6.

3.4 SNV Estimator

This estimator was also originally used to estimate the SNR in an AWGN channel for

applications in a non spread-spectrum signal. In contrast to the MLE method, this estimator

relies on processing only the received signal. Therefore no pilot or training symbol is

required to estimate the SNR. Here we use this method to estimate the SIR in CDMA

signals. Figure 3.3 shows the implementation of the SIR estimator using the SNV method

in CDMA systems.

+

yk(m) yk(n)

I

Q

ck(Q)(m)

ck(I)(m)

E[ | . | ] ∑ m

+

-

γk

ratio

( . )2( . )2

E[ ]

| . |

Figure 3.3 SIR estimator using SNV method at symbol level.

This method proposes estimates of the desired signal and interference signal using

respectively the average and variance of the received signal. The processing is performed

entirely at the symbol level (after the despreading). The SIR for the kth user based on the

SNV method can be expressed as

2

1 1

2

1

|)(|1

|)(|1

1

|)(|1

∑ ∑

∑

= =

=

−

−

=B

n

B

n

B

nk

nyB

nyB

nyB

kk

k

γ , (3.10)


51

where B is the number of symbols used in the averaging or expectation operator E[.]. The

processing gain M has been attained in the quantity yk(n) after despreading by the kth

user’s spreading sequence. It is well known that this estimator exhibits an irreducible bias

at low SIR. This is due to the fact that for low SIR the error caused by the averaging

process becomes higher relative to the mean value, resulting in an overestimated mean

power. This estimator also has a higher variance compared to that of the MLE method.

This is because the averaging operation is performed at the symbol level rather than the

chip level, hence decreasing significantly the number of samples involved in the averaging

process.

We can reduce the variance of the SIR estimator in the SNV method by processing the

signals partly at the chip level. In this case, we can estimate the total received signal using

the chip level processing and estimate the desired signal at the symbol level as shown in

Figure 3.4.

+-

yk(m) yk(n)

γk

I

Q

ck(Q)(m)

ck(I)(m)

E2[ | . | ]

ratio

∑ m

+

E[ | . |2]

1/M

Figure 3.4 SIR estimator using SNV method at chip level.

By using such an implementation using B symbols and spreading factor M, the estimated

SIR for the kth user can be expressed as

2

11

2

2

1

|)(|11

|)(|1

|)(|1

−

=

∑∑

∑

==

=

B

n

MB

m

B

nk

nyBM

mrMB

nyB

k

k

γ . (3.11)


52

In this modified SNV method, we estimate the average signal at the symbol level, but we

compute the total interference power at the chip level as has been shown in [89]. Since

interference is estimated at the chip level in this modified SNV method, a better accuracy

of the estimated SIR can be expected. However, it also has a practical implication that part

of the processing needs to be done at the chip level.

3. 5 Proposed SIR Estimator

We propose an SIR estimator for a DS-CDMA system using an auxiliary spreading

sequence [88]. In this method, we estimate the SIR at the symbol level (after despreading)

as can be seen in Figure 3.5.

-

+

yk(m)

ya(m)

yk(n)

γk

ya(n)

I

QE2[ | . | ]

E[ | . | 2 ]

ck(Q)(m)

ck(I)(m) ∑

m

∑m

Signal estimate

Interference estimate

ca(I)(m)

ca(Q)(m)

1/M

ratio

Figure 3.5 SIR estimator using an auxiliary spreading sequence.

In our method, we estimate the kth user signal by despreading the received signal with the

complex conjugate of the kth user spreading sequence ck*(m) = ck

(I)(m) - jck(Q)(m), where

ck(I)(m), ck

(Q)(m) ∈ }2/1,2/1{ −+ . Then we estimate the MAI by despreading the received

signal with an auxiliary spreading sequence, ca(m) = ca(I)(m) + jca

(Q)(m), where ca(I)(m),

ca(Q)(m) ∈ }2/1,2/1{ −+ .

The auxiliary spreading sequence is a spreading sequence that is reserved for estimating

the interference and is not assigned to any user in the system. However, all users can use


53

the same auxiliary spreading sequence to estimate the MAI, therefore the spreading

sequence is not wasted.

When the chip sequence is perfectly synchronised to the received signal of the kth user, the

decision variable yk(n) can be obtained after despreading the received signal with the kth

user’s spreading sequence and integrating the chips over one symbol period. The expected

value of yk(n) can be expressed as

E[yk(n)] = M.E[βk].bk(n). (3.12)

Here M is the CDMA processing gain, βk is the fading factor experienced by the kth user,

and n is the symbol index. However when the received signal is despread by the auxiliary

spreading sequence and integrated over one symbol period, we have ya(n). The expected

value of this quantity is

E[ya(n)] = 0, (3.13)

because of the correlation property of the spreading sequence as given in (3.1) and

assuming the binary data sequence bk(n) to have an equal probability of being +1 and -1.

However, both yk(n) and ya(n) have a non-zero variance due to crosscorrelations between

spreading sequences as given in (3.2). A comprehensive treatment of first and second order

statistics of the demodulator output in multiple access interference can be found in [90].

We can then derive the estimate for the SIR of the kth user as follows

2

11

2

2

1

|)(|11

|)(|1

|)(|1

−

=

∑∑

∑

==

=

B

n

MB

ma

B

nk

nyBM

nyB

nyB

k

k

γ . (3.14)

It is clear that our proposed SIR estimator does not require knowledge of the transmitted

data sequence. Therefore, it can be implemented in any transmission scheme (general

application). Another benefit is that our estimator operates entirely at the symbol level

(after despreading) resulting in a less computational complexity. This method also fits

within the present CDMA architecture, which employs correlation detector techniques. We


54

will discuss the advantages/disadvantages of our SIR estimator performance compared

with other estimators described above in the following section.

3.6 Performance Comparison of SIR Estimators

In evaluating the performance of SIR estimators, we use the statistical MSE to reflect the

variance of the estimators. If the estimator is not biased, the MSE is equal to the variance.

We define the MSE as follows

MSE[γest] = E[(γest - γ)2]. (3.15)

Here, γest is an estimated SIR and γ is the true SIR We compute the sample bias and MSE

for each estimator that have been described in the previous sections. The MSE and the

sample bias of the estimators are estimated respectively as follows

2])([1

1][MSE γγγ −∑

== iest

t

test

N

iN

, (3.16)

and

])([1

1][Bias γγγ −∑

== iest

t

test

N

iN

. (3.17)

Here Nt is the number of trials for each value of SIR. In our simulation we use the number

of trials Nt large enough for all cases to ensure an error of less than 20 % with 95 %

confidence. Then the CRB is used as a reference to assess the MSE performance of SIR

estimators. The minimum variance obtained from the CRB can be expressed using our

notation as [86]

MBBest

22]var[

γγγ +≥ . (3.18)

Assuming the SIR estimate is unbiased or exhibits a very small bias, the MSE of SIR

estimate equals the variance. We then define the normalised MSE (NMSE) and the

normalised bias (NBias) to show the asymptotic behaviour with increasing SIR as follows


55

MBBest

est

12]var[][NMSE

2+≥=

γγγ

γ , (3.19)

and

γγγ

γ][ )(

1

1][NBias

−∑=

=iest

t

test

N

iN

. (3.20)

To make a fair performance comparison between different SIR estimators described above,

we evaluate their performance in a CDMA system under the same scenario, i.e. the same

number of users, the same number of symbols used in averaging process, and the same

processing gain. We consider a reverse link CDMA system with the number of users K =

10 and we add AWGN to represent the receiver noise with variance σ2 = -7 dB below the

signal level. The number of symbols for averaging is B = 192, and the number of samples

per symbol is M = 256 (spreading factor). We evaluate and compare the performance of the

SIR estimators for the SIR values from -10 dB to 30 dB. We show the mean value, the

normalised sample bias, and the NMSE of the estimated SIR obtained from these

estimators, respectively in Figures 3.6 to 3.8.

Clearly, the MLE method performs best among all SIR estimators considered here. It is

unbiased for the entire range of SIR values from –10 to 30 dB, and its variance approaches

the CRB performance. However as mentioned earlier, the MLE method may not be

feasible for fast real time measurements due to its implementation complexity.

The SNV (chip level) and our proposed methods appear to have a similar bias

performance. They are biased for SIR < 10 dB and the bias increases approaching an

irreducible floor as SIR decreases. The normalised MSE of our proposed estimator is the

same with that of the chip level SNV method for low SIR (< 5 dB), but higher for high

SIR. As mentioned before, this higher MSE is due to the fact that our proposed estimator

has a smaller number of samples than the SNV method. Therefore our proposed estimator

can be more desirable than the chip level SNV method because a comparable performance

can be obtained, yet the complexity is M time less, where M is the CDMA spreading

factor.


56

-10 -5 0 5 10 15 20 25 30-10

-5

0

5

10

15

20

25

30

True SIR (dB)

Est

ima

ted

SIR

(d

B)

SNV method at symbol levelOur proposed method SNV method at chip level MLE method True SIR

Figure 3.6 Means of SIR estimate.

-10 -5 0 5 10 15 20 25 30-2

0

2

4

6

8

10

12

14

SIR (dB)

No

rma

lise

d b

ias

(dB

)

SNV method at symbol levelOur proposed method SNV method at chip level MLE method

Figure 3.7 Normalised bias of SIR estimate.


57

-10 -5 0 5 10 15 20 25 30-50

-40

-30

-20

-10

0

10

20

30

SIR (dB)

No

rma

lise

d M

SE

(d

B)

SNV method at symbol levelOur proposed method SNV method at chip level MLE method Cramer-Rao Bound (CRB)

Figure 3.8 Normalised MSE of SIR estimate.

When compared with the SNV method that processes the signal at the symbol level (i.e.,

under the same complexity), our proposed method outperforms the SNV method in terms

of both bias and normalised MSE performance. In fact, the symbol level SNV method is

biased for the entire SIR of interest, and also exhibits the worst MSE performance among

all the estimators considered here.

3.7 Summary

In this chapter, we have presented and compared several existing SIR estimators for

applications in CDMA systems. The accuracy of SIR estimator depends on the estimator

algorithm and the length of the measurement period. A new proposed SIR estimator using

an auxiliary spreading sequence is described and its performance is compared with the

MLE and SNV estimators in terms of estimate bias and MSE.

In real time applications, the implementation feasibility of algorithm is very important. As

a conclusion we can state that, from a practical point of view our proposed method is more

attractive for CDMA applications than the MLE and the SNV methods. While is


58

outperformed by the one provided with the MLE technique, it is by far less complex with a

much reduced processing time. Most important, its implementation is more appropriate to a

CDMA system and it does not require any training sequence as the MLE does.

When compared with the SNV estimator, we have shown that its performance is similar

when the SNV method is implemented at the chip level but is much better than the SNV

implemented at the symbol level. We have therefore shown that our proposed method

offers the best trade off between performance, complexity and implementation feasibility.

We will use our proposed SIR estimator for applications on a fast closed-loop power-

control scheme that will be presented in Chapter 4.

59

Chapter 4

Power Control Simulation

The aim of this chapter is to raise several issues associated with closed-loop power control

and discuss them. In particular, we show the effects of step size, SIR estimation error,

fading rate, PCC transmission error, and feedback delay, on the performance of closed-

loop power control. The performance is evaluated in terms of BER as a function of average

SIR or Eb/I0. This evaluation is based on computer simulations.

This chapter is organised as follows. First, a Rayleigh fading simulator (Jakes’ method) is

described. Then a SIR-based power control simulation model for uplink CDMA channel is

presented followed by a description of simulation procedure and parameters used in this

study. The effects of imperfect parameters on the performance of fixed-step and variable-

step algorithms are shown.

4. 1 Introduction

Performance of any digital communications is usually expressed in terms of BER, i.e. the

average probability that a transmitted bit is received in error at the receiver. In an AWGN

channel, the BER performance can be derived analytically from the probability distribution

Chapter 4. Power Control Simulation

60

of noise or interference because the desired signal power is constant. In a Rayleigh fading

environment, the BER performance can also be derived analytically because the pdf of the

received signal power is known, despite the fluctuations of the received signal. The BER in

a fading channel environment when power control is employed is not easy to derive

because it depends on the performance of power control itself.

Analytical studies, computer simulations, and field trials have been previously conducted

to evaluate the performance of CDMA systems in fading channel environments. Most

analytical evaluations of CDMA systems are based on the assumption that the received

signals from all users are equal and constant [7]-[11] using a perfect power-control

assumption. In practice, an equal and constant received power level cannot be achieved

because of imperfect power control. As a result, analytical evaluations become difficult

without oversimplification [72]. In fact, most analytical studies rely on approximations or

bounds, or on a quasi-analytical evaluation that combines some analyses with simulation

works.

Assuming a lognormal distribution of the power controlled SIR [9]-[16], the BER as a

function of the SIR is presented in [53]. This approach utilises the power-controlled SIR

statistics (mean and standard deviation), that have been obtained from field experiments of

a power controlled CDMA system in a slow fading environment [15]-[18]. In [91]-[92], an

optimization of power control parameters is presented using a statistical linearisation

approach of the nonlinear power control loop. In [91], a general analysis to study the effect

of mobile speed, power control step size, and fading rate on power control error is

presented for a fixed step size power control algorithm. Power control error in this paper is

defined as the standard deviation of the power controlled SIR. The optimum quantisation

step size for variable step-size algorithm is presented in [92]. However, the effect of the

power-control parameters (step size, fading rates, feedback delay, etc.) on BER are not

shown in these papers.

Previous simulation studies on closed-loop power control in multipath fading environments

appear in [19]-[22]. In [19] and [20] the statistics of the SIR are evaluated to estimate the

system capacity of fixed step power controlled CDMA systems based on signal strength

and SIR measurements, respectively. The results show that power control based on SIR

measurement performs better than that based on signal strength measurement. This is


61

because SIR can serve as a better signal-quality indicator than signal strength, particularly

in an interference-limited system such as CDMA. However, these studies do not deal with

BER performance evaluation.

In this chapter, we perform computer simulations of a SIR-based power control to evaluate

the direct effect of the power control parameters on the BER. We will start this chapter

with a description of Rayleigh fading simulator using a well-known method developed by

Jakes [93].

4.2 Rayleigh Fading Simulator

One of the most commonly used methods to simulate a Rayleigh fading channel is

described in [93] and is referred to as the Jakes’ method. The Jakes’ method invoke the

central limit theorem to show that the baseband signal received from a multipath fading

channel is approximately a complex Gaussian process when the number of paths, L is

large. The Jakes’ method assumes that the line-of-sight component is absent. To briefly

describe the model, we rewrite the second term of (2.6) as follows

∑=

=L

l

tjl

leCt1

)()( φβ (4.1)

where φl(t) = 2π(fD cosψlt – fcτl). Assuming the angle of arrival, ψ has a uniform

distribution in [0, 2π], we can express

....,,2,1,2

LlL

ll == πψ (4.2)

By normalizing Cl so that the total average power is unity (Cl2 = 1/L) and letting L/2 be an

odd integer, (4.1) can be expressed as

{

}.

][1

)(

)(2)(2

)cos(2()cos(212/

1

LcDLcD

lclDlclD

ftfjftfj

ftfjftfjL

l

ee

eeL

t

−

−

−−−

−−−−

=

+

++= ∑τπτπ

τψπτψπβ (4.3)


62

The first term in the sum of (4.3) represents waves with Doppler spread from +fD cos(2π/L)

to – fD cos(2π/L) as l runs from 1 to L/2 –1, while in the second term waves have Doppler

spreads that go from – fD cos(2π/L) to + fD cos(2π/L). The third and fourth terms represent

waves with the maximum Doppler spread of +fD and –fD, respectively. The expression in

(4.3) shows that the frequencies are overlap.

We can also rewrite (4.3) in terms of waves whose frequencies do not overlap by using the

index of sum from l = 1 to L0, where L0 = ½(L/2 –1) as follows

{}.

][21

)(

)(2)(2

)cos(2()cos(2

1

0

LcDLcD

lclDlclD

ftfjftfj

ftfjftfjL

l

ee

eeL

t

−

−

−−−

−−−

=

+

++= ∑τπτπ

τψπτψπβ (4.4)

In [94] the accuracy of Jakes’ method is evaluated. In this paper, the number of paths, L is

suggested to be equal or greater than 10 in order to obtain a sufficient accuracy. We

implement the Rayleigh fading simulator using L = 34 as given in [93], so that L0 = 8. We

generate 8 frequency oscillators with Doppler spreads fD cos(2l/L0), l = 1, 2, …, 8, and one

with frequency fD to represent waves whose frequencies are shifted from the carrier

frequency fc. A detailed description of the realization of fading simulator is given in [93].

The simulated Rayleigh fading channel with a maximum Doppler-spread fD = 50 Hz during

a 200 ms period is shown in Figure 4.1.

The fading channel described in Figure 4.1 can be experienced by a mobile which is

travelling at 30 km/h when the carrier frequency is fc = 1.8 GHz. When the mobile is

transmitting data at a symbol rate of 64 kilosymbols/s (the symbol period, Ts = 15.625 µs),

the number of symbols that span over a 200 ms time-axis shown in Figure 4.1 is 12800

symbols. In this situation, the channel can be considered as to exhibit a slow fading since

the channel fading rate is much lower than the symbol rate.

We can see in Figure 4.1 that due to Rayleigh fading in a wireless channel, the received

signal fluctuations frequently drops far below its average level. Fading depths of up to 40

dB below the average level are often encountered in practice [93].


63

0 2000 4000 6000 8000 10000 12000-30

-25

-20

-15

-10

-5

0

5

10

Time x Ts (s)

Re

ce

ive

d s

ign

al s

tre

ng

th (

dB

)

Figure 4.1 Simulated Rayleigh fading (fD = 50 Hz, Ts = 15.625 µs).

4.3 Power Control Simulation

In this section, we describe the simulation procedure and system parameters to model the

uplink channel of a CDMA system that employs SIR-based power control. We assume that

the open loop power control can perfectly overcome the near-far and shadowing problems,

so that the average received power is constant and the closed-loop power control algorithm

is used only to overcome the fluctuation due to Rayleigh fading. In this case, the dynamic

range for power updates in the closed-loop algorithm can be reduced because the algorithm

is only required to track the Rayleigh fading fluctuation (not to track the signal variation

due to the near-far problem).

We recall the model of power control described in Figure 2.5 in order to explain the

algorithm in more detail here. For power control based on SIR, the mechanism of power

control algorithm is shown in Figure 4.2. The power control algorithm proceeds as follows.

First, the SIR for each user, γest is estimated at the basestation for the ith time slot. Then the

estimated SIR γest(i) is compared with the target SIR γt to produce the error signal e(i). The


64

error signal e(i) is then quantised using a binary representation, so it can be transmitted via

the downlink channel to the mobile station. The quantised form of error signal is called the

PCC bits, which can be implemented using a PCM realisation of mode q, where q is the

number of PCC bits required in each power control interval.

∆pTp

IntegratorStep size

+

+

+ _

+

-γt

γest

PCC bit error

e(i) PCC bits

MAI andAWGN

Mobile station

DTpLoop delayU

plin

kch

anne

l β(t

)

Dow

nlink channel

Basestation

Figure 4.2 Mechanism of SIR-based power control.

The PCC bits are transmitted to a mobile station via the downlink channel. However, the

PCC bits are subject to high bit error rates because they are not coded or interleaved in

order to minimise signalling bandwidth on the downlink channel and to avoid the

corresponding delays due to the interleaving. The feedback loop delay, however, is

unavoidable. Therefore, transmission of the PCC bits on the downlink channel suffers from

two major impairments: PCC bit errors and feedback delay. The PCC bits error is

represented as a multiplicative disturbance on the PCC bits, while feedback delay is


65

represented by a delay operator of DTp in the loop as shown in Figure 4.2. After the PCC

bits are received by a mobile station, the mobile station computes the required power

adjustment, ∆p x PCC. The step size ∆p is preset at 1 or 2 dB, while the PCC is either ±1 in

a fixed-step algorithm or any integer between –q and +q in a variable-step algorithm. The

integrator over one power control interval, Tp is used to increment the transmit-power level

from the previous level as shown in (2.13).

In the simulations, we do not consider error control coding, interleaving, and rake receiver

techniques because we want to investigate how power control alone can mitigate the effect

of fading. A single-path frequency nonselective fading is simulated in this study.

Therefore, the rake receiver is not effective because there is only one resolvable path. In

addition, we only consider a slow fading situation, where coding and interleaving are less

effective.

4.3.1 Procedure of Simulation

In the simulation, s single-cell CDMA system with the number of users K = 10 is

considered. To reflect a practical situation, we consider that all users are in motion with

different vehicle’s speeds and thus have different maximum Doppler spreads. We model

this situation by varying the users’ vehicle speeds from 10 to 100 km/h at 10 km/h interval

(i.e., the speed of the kth user is vk = 10 k km/h for k = 1, 2 , …, 10.

We use the carrier frequency fc = 1.8 GHz, so that the corresponding maximum Doppler

spreads for the users are approximately ranging from 17 to 170 Hz at 17 Hz interval. The

DS-CDMA processing gain is M = 64 and the modulation scheme is QPSK with a data bit

rate Rb = 120 kbps (symbol rate Rs = 60 ksps in QPSK scheme). The power-update rate of

1.5 kHz is considered, which corresponds to the power control interval Tp = 0.667 ms.

SIR estimation/measurement is performed in every time slot that corresponds to one power

control interval Tp = 0.667 ms. All data symbols in the time slot are utilised by SIR

estimator to estimate the SIR. The chip rate Rc = 3.84 Mcps as given in the 3G

specification for uplink data channel [71] is assumed in the simulation, resulting in each

time slot to contain 2560 chips. Therefore, 40 binary symbols per time slot are available

for SIR estimation. We summarise the simulation parameters in Table 4.1.


66

Table 4.1

Simulation parameters.

Parameters Notation and value

Number of users K = 10

Carrier frequency fc = 1.8 GHz

Vehicle’s speed vk = 10.k km/h, k = 1, 2, …, K

Maximum Doppler spread fD = 1.67 vk Hz, (vk = 10, 20, …, 100 km/h)

Processing gain M = 64

Chip rate Rc = 3.84 Mcps

Power control interval Tp = 0.667 ms (power-update rate = 1.5 kHz)

Data rate Rb = 120 kbps (symbol rate = 60 ksps)

Power update step size ∆p = 1 dB or 2 dB.

To produce a QPSK baseband signal for the kth user, we first generate a quadrature

random binary sequence bk(n) = bk(I)(n) + j bk

(Q)(n). Then the binary sequence bk(n) is

spread by the kth user’s quadrature spreading sequence ck(m) = ck(I)(m) + j ck

(Q)(m). Each

symbol bk(n) has 64 chips. The user’s spreading sequence is a random spreading sequence

described in Chapter 3. Note that n and m indicate the symbol and chip index, respectively.

To simulate the uplink fading channels, an independent and uncorrelated Rayleigh fading

for each user βk(n), k = 1, 2, …, 10, is generated using the Jakes’ method as described in

Section 4.2. Here, we consider a slow Rayleigh fading channel in which the channel

coherent time, T0, is much larger than the symbol duration Ts. In a slow fading channel, the

fading factor is considered constant within the symbol duration, and therefore we produce

a discrete fading factor βk(n) that is indexed by n (symbol index). The maximum Doppler

spread for each user is varied from 17 to 170 Hz at 17 Hz interval to reflect different user’s

mobility as shown in Table 4.1. In this simulation we assume perfect open loop power

control, so that only the fluctuation due to Rayleigh fading is considered. The Rayleigh

fading is normalised to have a unit power for all users.


67

To simulate the receiver thermal noise in our simulation, we add the AWGN with the noise

variance σn2 = 7 dB below the signal power level (SNR = 7 dB). Therefore at the

basestation, the composite CDMA signals consist of all users’ signals and AWGN. The

simulated fading envelope with Doppler spread fD = 17 Hz and its corresponding SIR re

shown in Figure 4.3. The SIR in Figure 4.3 is estimated using our proposed SIR estimator

described in Chapter 3. The true SIR is also plotted for our comparison.

0 50 100 150 200 250 300-30

-20

-10

0

10

20

30

Time x 0.667 ms

SIR

or

sig

na

l st

ren

gth

(d

B)

Estimated SIR True SIR Signal strength

Figure 4.3 SIR in Rayleigh fading (fD = 17 Hz, CDMA with K = 10).

From Figure 4.3, we can see that our proposed SIR estimator overestimates the SIR when

the channel goes into deep fades. This is due to the bias of the proposed estimator at low

SIR, as has been discussed in Chapter 3. It can also be observed from Figure 4.3 that the

SIR in CDMA varies according to the channel fluctuations, which justifies the Gaussian

assumption of the MAI under central limit theorem.

With a SIR-based power control, the SIR variations seen in Figure 4.3 can be reduced. If

power control is good, the SIR will be constant or nearly constant around the target level.

Figure 4.4 shows a simulated SIR in a fading channel with Doppler spread fD = 17 Hz


68

using a SIR-based power control with 2 dB power-update step size and 1.5 kHz power-

update rate. In Figure 4.4, the target SIR is set at 10 dB.

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0- 5 0

- 4 0

- 3 0

- 2 0

- 1 0

0

1 0

2 0

3 0

T im e x 0 .6 6 7 m s

SIR

or

sig

na

l str

en

gth

(d

B)

P o w e r-c o n tro lle d S IR ( ta rg e t = 1 0 d B )C o n tro lle d tra ns m it p o w e r U n c on tro lled re c e iv ed s ig na l

Figure 4.4 Power-controlled SIR in fading channel

(fD = 17 Hz, ∆p = 2 dB, Tp = 0.667 ms).

We can see from Figure 4.4 that closed-loop power control can turn a slow fading channel

into an AWGN channel almost perfectly, except when channel goes into deep fades. For

higher fading rates, however, power control may not perform so well.

In the following section we aim at determining an optimum step-size, ∆p which we will see

that the optimum step size depends on the fading rates.

4.3.2 Optimisation of Step Size

Updating step-size and updating rate are interrelated variables. Two strategies to track

fading fluctuation are either adjusting the transmit-power less frequently by a larger step-

size, or adjusting it more frequently by a smaller step-size. Since the power-updating rate is

standardized (1.5 kHz in 3G system), then we can optimize the step size for different

fading rates.

Before we evaluate the BER performance of power control system, we first determine the

optimum step size ∆p by simulation. We perform power control simulations using a fixed


69

step size and we measure the power control error (PCE), which is defined as the standard

deviation of the power-controlled SIR. Then we repeat the simulations using different step

sizes. The power control error is plotted as a function of step size to find the optimum step

size, which is one that produces the minimum PCE. We then define the variance of the

power-controlled SIR as follows

2][ )(

1

1][var test

t

test i

N

iN

γγγ −∑=

= . (4.5)

Here Nt is the number of samples, γest(i) is the power-controlled SIR in decibel estimated at

the ith slot, and γt is the SIR target in decibel. Therefore we can define the PCE for each

value of step size ∆p as

]var[][PCE estp γσ γ ==∆ (4.6)

Since the power control performance is also affected by fading rates, we optimise the step

size for three different velocities of vehicle: 10, 30, and 60 km/h, representing low-speed

mobility environments for which power control is still effective. To see the effect of fading

rates, we introduce the parameter fDTp, which is defined as the ratio of the fading rate to the

power-updating rate. Since the power-updating rate is standardised at 1.5 kHz, the

parameter fDTp will only depend on the fading rate fD, which is directly proportional to the

vehicle’s speed. For 1.8 GHz carrier frequency, the vehicles’ speed of 10, 30, and 60 km/h

correspond, respectively, to the maximum Doppler spread of 16.7, 50, and 100 Hz. With a

power control interval of Tp = 0.667 ms (power-updating rate is 1.5 kHz) and for a mobile

travelling at 10 km/h, the parameter fDTp equals 0.01, which means that the mobile transmit

power is updated 100 times faster than the fading rate. For mobile speeds of 30 and 60

km/h, the parameter fDTp are 0.033 and 0.067, which correspond to the transmit power

updating rates of 30 and 15 times faster than the fading rates, respectively.

Using the parameters described in Table 4.1, we evaluate the power control error as a

function of the step size ∆p as follows. For a preset value of ∆p, we perform power control

simulation and we use (4.5) and (4.6) to obtain the power control error. The number of

samples Nt is chosen large enough to achieve a confident interval of at least 99 % (in our

simulation, we use Nt = 300 time slots). Then we repeat our simulation for different values


70

of the step size. The dynamic range of fading fluctuation and the choice of lower and upper

limit of step-sizes need to be carefully chosen, so that the power control error as a function

of step size is continuous to obtain the optimum step-size. We increment the step size from

0.2 to 4 dB at 0.2 dB interval. The target SIR is set at 7 dB. The PCE as a function of ∆p

for different values of fDTp is shown in Figure 4.5.

0 0 . 5 1 1 .5 2 2 .5 3 3 . 5 41 .5

2

2 .5

3

3 .5

4

4 .5

5

S t e p s ize ( d B )

Po

we

r c

on

tro

l e

rro

r (d

B)

fD

Tp

= 0 . 0 1

f D T p = 0 . 0 3 3

fD

Tp

= 0 . 0 6 7

Figure 4.5 Power control error as a function of step size for different fading rates.

We can see from Figure 4.5 that the optimum step-sizes are different for different fading

rates. For fDTp = 0.01 and 0.033 the optimum step size is approximately 2 dB, while for

fDTp = 0.067 the optimum step size is approximately 2.5 dB. For constant vehicle’s speed,

we note that the power control error increases when the step size is decreased below the

optimum value. This means that if the step size is too small, the power control algorithm is

too late to track the channel fading. We also can see that when the step size is increased

above the optimum value, the power control error also increases. This can be explained

that with higher step sizes, the algorithm will track the channel fading more quickly, but

due to the up/down commands, a residual variation of SIR around the target level will be

high if the step size is too high. In practice, the choice of step size is rather loose (between

1.5 and 2.5 dB) for low speed mobility environments considered here.

To see the effect of step size on the BER performance, the BER is also monitored during

the power control simulations. Table 4.2 shows the BER for different values of the

parameter fDTp when the step size is varied and the target Eb/I0 is set at 7 dB.


71

Table 4.2

Effect of step size on bit error rate at Eb/I0 = 7 dB.

Step size (dB) 0.2 0.6 1.0 1.6 2.0 2.6 3.2 3.6 4.0

BER x 10 –2

fDTp = 0.01 6.7 5.2 4.2 3.5 2.9 3.4 3.6 3.7 3.9

fDTp =0.033 3.6 4.1 3.6 3.4 3.3 3.5 3.9 4.4 4.3

fDTp = 0.067 7.0 6.7 6.4 5.6 4.8 4.6 4.9 5.1 5.9

We can see from Table 4.2 that the minimum BER is achieved when the step size is set at

approximately 2 dB. We also can see by comparing the PCE in Figure 4.5 with the BER in

Table 4.2 that the BER is proportional to the PCE.

Since the optimum step size depends on the fading rates, the step size should be changed

when a mobile user experiences different velocities. If the Doppler spread or mobile

velocity can be estimated at a mobile station, an optimum step size can be maintained. By

using Doppler spread estimators [95]-[97] at a mobile station, the mobile user with fixed-

step power control can adjust the step size, so that an optimum step size can be maintained

when the mobile’s velocity changes. In a variable-step algorithm, however, the step size

varies according to the channel conditions and therefore, Doppler spread estimation is not

necessary.

In the next section a SIR-based closed-loop power control will be simulated in order to

show the effects of system parameters on the BER performance. Based on the step size

optimisation described in the previous section, the step size of 2 dB will be used.

4.4 Performance of Power Control

We evaluate the performance of power control in terms of BER as a function of average

Eb/I0. The BER performance of CDMA systems depends on Eb/I0, and the pdf of Eb/I0. In


72

an AWGN channel, Eb/I0 is constant and the BER as a function of Eb/I0 for QPSK

modulation scheme can be expressed as

( )

=

=

≈=

0

0

2

1

2

I

Eerfc

I

EQ

QBERP

b

b

e γ

(4.7)

where γ is the signal-to-interference ratio. The relationship between Eb/I0 and signal-to-

interference ratio, γ, depends on modulation schemes employed. In a QPSK modulation

scheme, one modulation symbol represents a two-bit binary data, so that Eb/I0 = γ/2. The

probability of error for QPSK expressed in (4.7) assumes that the probability of bit error is

one half the probability of symbol error. In this case, only one bit is assumed to be in error

within a two-bit QPSK symbol. This can be implemented in practice with a Gray code

[98], which maps the two-bit symbols corresponding to adjacent signal phases differs in

only a single bit.

In a Rayleigh fading channel, the SIR varies with channel as can be seen in Figure 4.3. The

BER as a function of Eb/I0 in a Rayleigh fading channel for QPSK modulation is expressed

as [46]

+−=

+−==

0

0

/1

/1

2

1

2/1

2/1

2

1

IE

IE

BERP

b

b

e γγ

(4.8)

Here the over bar on Pe, γ and Eb/I0 indicates the average value of those variables. If the

power control is perfect, it will turn the varying SIR or Eb/I0 in a fading channel into a

constant SIR or Eb/I0 as in an AWGN channel. Therefore the BER performance of an

AWGN channel is the best achievable performance (lower bound) for power control, and

the BER performance of a Rayleigh fading is the upper bound (without power control at

all). In fact, power control can even degrade the BER performance of fading channel if the


73

algorithm and the parameters of power control are not properly designed to suit the channel

condition.

We will evaluate the effect of system parameters and other affecting factors on the

performance of power control. These parameters are step size, fading rate, feed back delay,

and command error on the feedback channel (downlink transmission).

4.4.1 Effect of Step Size

In this section, the BER performance of a fixed-step and a variable-step algorithm are

compared. The variable-step algorithm is implemented using a PCM realisation described

in Chapter 2 with modes q = 2, 3, and 4. In the variable-step algorithm with mode q = 4,

the quantised error signal can be derived from (2.12) as follows

≥−<≤−<≤−<≤−<≤−−<≤−−<≤−−<≤−

−<

=− =

5.3index,4

5.3index5.2,3

5.2index5.1,2

5.1index5.0,1

5.0index5.0,0

5.0index5.1,1

5.1index5.2,2

5.2index5.3,3

5.3index,4

)( 4qDie , (4.9)

where the index is defined as e(i-D)/∆p. It clear from (4.9) that the required number of bits

for PCC is 4 for each power control interval The mapping of PCC bits is shown in Table

4.3.

The first bit of the PCC bits sequence represents the sign of the command, i.e. 0 represents

the positive sign and 1 represents the negative sign. The remaining bits represent the value

of step size in a multiple of ∆p for the mobile to increase or decrease its transmit power.

The first four rows in Table 4.3 reflect the instructions to decrease the mobile transmit

power, the fifth line indicates the instruction for the mobile to keep the same transmit

power as in the previous interval, and the last four lines are instructions to increase the


74

transmit power. The mobile will change its transmit power with variable step sizes of

∆p.e(i-D)q=4 as expressed in (2.13).

For PCM realisation with modes q = 2 and q = 3, the mapping technique is the same with

that shown in (4.9) and Table 4.3, with the index quantity of error signal e(i-D) /∆p are

mapped to integer numbers of between –2 and 2 for q =2 and between –3 and 3 for q = 3.

Therefore, the number of PCC bits required for PCM realisation of modes q = 2 and q = 3

are 2 and 3 bits, respectively.

Table 4.3

PCC bits with PCM realisation (q = 4).

e(i-D)q = 4 PCC bits

4 0100

3 0011

2 0010

1 0001

0 0000 or 1000

-1 1001

-2 1010

-3 1011

-4 1100

In the fixed step power control algorithm (q = 1), only the sign of the error signal e(i-D) is

needed by the mobile to either increase or decrease its power by a fixed step size. In the

fixed step size algorithm the algorithm is now simplified as follows. If the estimated SIR,

γest(i) is less than the target SIR, γt, the PCC bit -1 is sent to the mobile to increase its

transmit power by ∆p dB. While if γest is higher than γt, the PCC bit +1 is sent to the mobile

to decrease its transmit power by ∆p dB. Note that with one PCC bit, the power control

algorithm will still increase or decrease the mobile transmit power by ∆p even when the

target SIR has been achieved.


75

To see the effect of different modes of variable-step algorithm, the BER performance is

evaluated for the same channel condition with the parameter fDTp = 0.01. The BER

performance is shown in Figure 4.6. The top curve is the BER for fading channel without

power control, while the bottom curve is the BER for AWGN channel.

0 2 4 6 8 10 12 14 16 18 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channel Fixed step (q=1) Variable step (q=2)Variable step (q=3)Variable step (q=4)AWGN channel

Figure 4.6 BER performance of power control with PCM realisation (fDTp = 0.01).

We can see in Figure 4.6 that the BER performance of power control with variable-step

algorithm is better than that with the fixed-step algorithm. This is because with variable-

step algorithm, power control can track the fading slope more quickly by using a higher

step size and can reduce the oscillation when the target SIR has been achieved by using a

smaller step size. Note that the performance improvement by using a higher mode (higher

number of PCC bits) is obtained at the expense of a higher signaling bandwidth on the

downlink channel. This is not desirable because the downlink channel capacity in third

generation systems is crucial for internet downlink traffic, and thus needs to be preserved.

Moreover, as we can see from Figure 4.6, the performance improvement at a voice quality

BER of 10-3 is not significant when the quantisation mode is increased from q = 1 (fixed


76

step size with 1 PCC bit) to q = 4 (variable step size with 4 PCC bits). Yet the required

signaling bandwidth for power control updates is four times higher. This result can answer

the question why most practical power control schemes rely on a fixed-step algorithm,

because the gains offered by the variable-step algorithm over the fixed-step algorithm may

not be justified.

4.4.2 Effect of Fading Rate

In this section we study the effect of fading rates, or more specifically, the effect of the

parameter fDTp on the power control performance. Since Tp is standardized (Tp = 0.667 ms

in 3G systems) we will simulate different fading channels with Doppler spreads of 17, 50,

and 100 Hz, which correspond to vehicle’s speeds of 10, 30, and 60 km/h in 1.8 GHz

frequency band.

To evaluate the effect of fading rates on the power control performance, we perform

simulations using a fixed step algorithm and variable step algorithm with mode q = 4. The

simulation results are presented in Figure 4.7 (a) and (b), respectively.

From Figure 4.7(a) we can see that the fixed step power control is less effective at higher

fading rates with fDTp greater than 0.033. However it works effectively at slow fading

channel, as it is shown by the BER performance at fDTp = 0.01. Similar behaviour is

obtained with variable-step algorithm, i.e the performance improves with decreasing values

of the parameter fDTp. For the same value of fDTp, the variable step algorithm has a better

performance than the fixed step size algorithm as has previously explained in Section

4.4.1.

The limited performance of fixed-step algorithm to combat higher fading rates is due to the

fact that the algorithm is too late to follow the channel variations. In a higher fading rate,

the fading factor changes dramatically, while the fixed-step power control can follow the

channel variation step by step.


77

0 2 4 6 8 10 12 14 16 18 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channelfDT

p = 0.067

fDT

p = 0.033

fDT

p = 0.01

AWGN channel

(a)

0 2 4 6 8 10 12 14 16 18 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channelfDT

p = 0.067

fDT

p = 0.033

fDT

p = 0.01

AWGN channel

(b)

Figure 4.7 BER performance of power control for different fading rates:

(a) fixed-step algorithm; (b) variable-step algorithm (q=4).


78

A higher power-update rate can be used in order to improve the performance of fixed-step

power control in a higher fading-rate situation. However, if the power-update rate is

increased, the required signalling bandwidth also increases. We will describe our approach

to improve the performance of fixed-step power control using a diversity antenna arrays

technique in Chapter 6.

4.4.3 Effect of SIR Estimation Error

We have shown the performance of different SIR estimators in Chapter 3 in terms of bias

and mean squared error. Now we evaluate the effect of SIR estimation error on the power

control performance when it is used as the control parameter of a SIR-based power control

algorithm. To evaluate the effect of SIR estimation error, we perform power control

simulations using the parameter fDTp = 0.01 for both the fixed-step and variable-step

algorithms based on our proposed SIR estimator described in Chapter 3.

To compare different SIR estimators the simulation is performed using the same

parameters but it is controlled by different SIR estimators. We compare the performance of

power control based on our proposed SIR estimator and based on the SNV method (symbol

level). For a reference, we also compare the power control performance based on the true

SIR. The MLE estimator is not used because we do not consider a data aided technique in

our power control simulation. The performance of power control based on different SIR

estimators is shown in Figure 4.8.

In Figure 4.8, we can see that the performance of power control is best when the power

control algorithm is based on the true SIR in both the fixed step and variable step

algorithms. Compared with the SNV estimator, our proposed estimator gives a better

performance. This confirms that the performance of a SIR-based power control is

dependent on the performance of the SIR estimator used in the power control algorithm.

An important result that can be drawn is that the effect of SIR estimation error is less

significant on the fixed-step algorithm compared to that on the variable-step algorithm, as

we can see by comparing the curves in Figure 4.8(a) with (b). The performance of

variable-step power control degrades more significantly when the SIR estimation error

increases.


79

0 2 4 6 8 10 12 14 16 18 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channel Based on SNV est. Based on our SIR est.Based on true SIR AWGN channel

(a)

0 2 4 6 8 10 12 14 16 18 2010

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10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channel Based on SNV est. Based on our SIR est.Based on true SIR AWGN channel

(b)

Figure 4.8 Effect of SIR estimator on power control performance (fDTp = 0.01):

(a) fixed-step algorithm; (b) variable-step algorithm (q = 4).


80

The more sensitive behaviour of the variable-step algorithm can be explained by the fact

that in the variable step algorithm, the quantised step size is proportional to the difference

between the estimated SIR and the target SIR. Therefore, an error on the estimated SIR

will propagate to the step size. As a result, the step size may not be optimal and thus the

power control performance degrades as discussed in Section 4.2.

In a fixed step algorithm, the step size is not directly proportional to the difference between

the estimated SIR and the target SIR, because the algorithm only needs to know whether

the SIR is above or below the target level. Therefore, the impact of SIR estimation error on

the step size is reduced, resulting in a robust algorithm.

4.4.4 Effect of Command Bit Error

We have mentioned that the PCC bits transmitted from the basestation to the mobiles via

the downlink channel (feedback channel) are subject to high bit error rates because they are

sent without error correction. In this section we evaluate the performance degradation of

fixed- step and variable-step algorithms when the transmission of the command bits is

subject to error with BER = 0.001, 0.01, and 0.1. A Gaussian distribution of the feedback

channel BER is assumed. The simulation results are shown in Figure 4.9.

From Figure 4.9, we can see that the variable-step algorithm is more sensitive to the

feedback error than the fixed-step algorithm, as its performance degrades more

significantly when the BER on feedback channel increases. This is because if the command

bits are in error, the variable-step algorithm will result in larger power command errors

than the fixed-step algorithm.

In the fixed-step algorithm if the command bit is wrong, the resulting power control

command error is limited by the fixed step size, which is usually preset at 1 or 2 dB.

Therefore, the fixed step size algorithm is more robust than the variable step size when the

feedback channel is subject to high bit error rates.


81

0 2 4 6 8 10 12 14 16 18 2010

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10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channel Command BER = 0.1 Command BER = 0.01 Command BER = 0.001Command BER = 0 AWGN channel

(a)

0 2 4 6 8 10 12 14 16 18 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channel Command BER = 0.1 Command BER = 0.01 Command BER = 0.001Command BER = 0 AWGN channel

(b)

Figure 4.9 Effect of command bit errors on power control performance (fDTp = 0.01): (a) fixed-step algorithm; (b) variable-step algorithm (q=4).


82

4.4.5 Effect of Feedback Delay

The feedback delay issue is inherent to any closed-loop algorithm. In the simulations of

power control described in the previous sections, we adjust the mobile transmit power

immediately after the SIR measurement is completed. In real systems, however, there is a

delay between these two operations, due to processing time, propagation time of the

command bits, and synchronization between uplink and downlink transmissions.

In this section we evaluate the power control performance degradation introduced by

feedback delay D of 1, 2, and 3 slots. A feedback delay of 1 slot (D = Tp) is simulated by

using a one-slot memory for the estimated SIR in the power control loop. In other words,

the estimated SIR for the ith slot is immediately used to control the (i+1)th slot of the

mobile transmit power as soon as the SIR estimation in the ith slot is completed. The

memory is then override by the estimated SIR of the next slot. To simulate the system with

a feedback delay D >Tp the estimated SIR is stored in the memory and the mobile transmit

power for the ith slot is controlled by the estimated SIR stored in the (i-2)th for D = 2Tp

and by the (i-3)th slot for D = 3Tp. The BER performance of the power control for different

feedback delays are shown in Figure 4.10(a) and (b) for the fixed and variable-step

algorithms, respectively.

From the results shown in Figure 4.10, the effect of the feedback delay on the performance

of power control is more significant in the variable-step algorithm than in the-fixed step

algorithm. We can see from Figure 4.10(b) that with feedback delays of D = 2Tp and D =

3Tp the performance of variable step algorithm is much worse than that of the fixed step

algorithm. This is due to the larger step size error in the variable-step algorithm when the

command bits are subject to the feedback delay.

Compared with other parameter imperfections in the power control system, i.e. SIR

estimation errors and command bit errors, the feedback delay introduces the most serious

problem in the loop. This can be seen by comparing the performance degradation of power

control due to parameter imperfections as shown in the previous sections.


83

0 2 4 6 8 10 12 14 16 18 2010

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10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channelD = 3 T

p

D = 2 Tp

D = Tp

AWGN channel

(a)

0 2 4 6 8 10 12 14 16 18 2010

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10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channelD = 3 T

p

D = 2 Tp

D = Tp

AWGN channel

(b)

Figure 4.10 Effect of feedback delay on power control performance (fDTp = 0.01):

(a) fixed-step algorithm; (b) variable-step algorithm.


84

We also note that the effect of feedback delay on the performance of fixed step algorithm

is more crucial compared to that of the effect of other factors (SIR estimation errors and

feedback-channel errors). Indeed, while the fixed-step algorithm is shown to be robust in

regard to the SIR estimator error and feedback-channel error, it is quite sensitive to the

feedback delay. Therefore, a technique to overcome the problem caused by feedback delay

is essential in order for the power control to be effective.

4.5 Summary

We have shown by computer simulations that, in order for the power control to be

effective, the power-updating rates must be much higher than the fading rates. We have

also evaluated the impact of several limitations and imperfections associated with the

implementation of power control algorithms in practical systems, such as feedback delay,

feedback channel error, and SIR estimation error.

The fixed-step power control algorithm is more desirable than the variable-step algorithm

in order to minimise the signalling bandwidth. We have also shown that the variable step

algorithm is more sensitive to disturbances (feedback-channel error) and other

imperfections of the real system (SIR estimation error and feedback delay) than the fixed-

step algorithm. Therefore, the fixed-step algorithm is preferable for implementation in the

real systems. The variable step algorithm can be advantageous when imperfections of the

real system can all be overcome, and the bandwidth of feedback channel is not a constraint.

The fixed step algorithm is also robust to small variation of step sizes. This is because

optimum step size varies with fading rates or vehicle’s speeds. While the fixed-step

algorithm is robust to disturbances and imperfections of the real systems, it is sensitive to

the feedback delay. Therefore, a technique that can mitigate the effect of feedback delay,

such as a prediction method, is essential. We will present a prediction method to solve the

feedback delay problem in Chapter5.

85

Chapter 5

Predictive Power Control

In this chapter an improved power control scheme using a predictive algorithm is

described. Predictive algorithm aims at solving the problem of feedback delay in existing

power control systems. The prediction filter (channel predictor) is employed at the

basestation to predict the uplink channel. The known statistical property of the fading

channel is utilised by the channel predictor to compute the predictor coefficients.

This chapter is organised as follows. First, time-frequency correlation of fading channel is

derived. Then a linear predictor of order V is described and the predictor coefficients are

determined using the orthogonality principle under the MMSE criterion. Simulations are

performed to show the performance improvement of power control by the use of channel

predictor at the basestation.

5.1 Introduction

It has been shown in Chapter 4 that the performance of power control in an actual system

is limited due to non-ideal parameters of the real system, i.e. feedback delay, feedback-

channel error, and SIR estimation error. In practice, a fixed-step power control scheme is

Chapter 5. Predictive Power Control

86

preferred because it consumes less signalling bandwidth than the variable-step algorithm. It

is also less sensitive to the SIR estimation error and feedback channel error, compared to

the variable-step algorithm. However, both fixed-step and variable-step algorithms do not

perform well in a real system because of inherent feedback delays of the real systems. It

has been shown in Chapter 4 that the feedback delay is the most critical parameter in the

loop and the bit errors on feedback channel is the least critical. These results agree with

that presented in [64]. Therefore, overcoming the power control impairment due to the

feedback delay is more important than controlling the feedback channel bit error rate.

Feedback delay is defined as the total time from which the channel is estimated at the

receiver until the power control command is received at the transmitter and power

adjustment is made. Note that in the uplink power control scheme, the channel condition is

estimated at the basestation. Then the mobile user adjusts its transmit power according to

the power-control command received from the basestation to compensate for the channel.

Due to the feedback delay, this power adjustment may no longer correspond to the channel

condition that can change rapidly, particularly when the Doppler effect increases.

Therefore, the power adjustment at the mobile user is outdated and does not compensate

for the current channel condition.

The following processes contribute to the feedback delay in a SIR-based power control.

First, the SIR measurement/estimation takes time. It contributes a measurement delay.

After the estimated SIR is compared with the target SIR to produce the power control

command bit, the command bit is inserted into the downlink data stream but may not be

transmitted immediately because the downlink and uplink transmissions are not

synchronized in an FDD system. This may contribute to another delay.

The other delay is the propagation time of the command bit between the basestation and

mobile station. Therefore, the total delay depends on SIR measurement time,

synchronization between uplink and downlink transmission, and the propagation delay of

the command bits transmission. Since the power control interval is standardized, the

feedback delay can be expressed in multiples, D, of power control interval, Tp. A feedback

delay of D = 2Tp or D = 3Tp is usually assumed to model a real system. Figure 5.1

illustrates the condition of a real system from which the feedback delay can be determined.


87

Consider that a mobile begins transmitting data in the time slot 1 at time t0. This time slot

(slot 1) will arrive at the basestation at time t1, which takes (t1 – t0) for this slot to

propagate in the uplink. Then the basestation estimates the SIR using data in the slot 1 of

uplink transmission. The SIR measurement is completed at time t2. In this case, SIR

measurement is performed over one time slot duration. At this time, the basestation

compares the estimated SIR with the target SIR to produce the command bit.

As we can see from Figure 5.1, the command bit should wait until time t3 when the

downlink begins transmission slot 2. After propagating in the downlink, the command bit

is received by the mobile user at time t4, in which slot 2 of the downlink has been received

by the mobile station. This mobile station then adjusts its power at time t5 (the beginning of

slot 4 transmission in the uplink). This situation leads to a total feedback delay D = 3Tp.

t0

t1 t2

t5

Slot 1 Slot 2 Slot 3 Slot 4

Slot 1 Slot 2 Slot 3 Slot 4

t3

t4

Slot 1 Slot 2

Slot 1 Slot 2

Basestation

Mobile user

Uplink transmission

Downlink transmission

Figure 5.1 Illustration of feedback delay on uplink power control.

However, if the SIR measurement is performed within a fraction of time slot duration, the

total delay can be reduced [100]. For instant if SIR measurement is completed before the

beginning of slot 1 of the downlink transmission, the command bit can be inserted into this

slot and can be received by the mobile user before the beginning of slot 3 of uplink


88

transmission. This will only cause a total delay D = 2Tp. This can be done if the SIR

measurement is performed within a fraction of slot duration. If the command bit can be

received by mobile station before the beginning of next immediate slot, the total feedback

delay is only 1 slot (D = Tp).

Due to the feedback delay and fixed step size in a conventional power control system, the

received SIR at the basestation will oscillate around the target SIR. Figure 5.2 describes the

controlled SIR in a system with feedback delay D = 2Tp. The target SIR is set at 10 dB.

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

-30

-20

-10

0

10

20

30

40

Time x Tp (s)

SIR

or

sig

na

l st

ren

gth

(d

B)

Controlled SIR (target = 10 dB)Controlled transmit power Received fading signal

Figure 5.2 Effect of deep fades on power control with feedback delay.

We can see in Figure 5.2 that the power-controlled SIR has variations around the target

SIR, with even larger variations when the channel experiences deep fades. This is because

of the feedback delay and finite step size. When the channel goes into a deep fade, the

basestation sends consecutive increasing commands to the mobile station and the mobile

station increases its transmit power continuously to compensate for the deep fade.

However, when the channel returns from the fade, the mobile station continues to increase

its transmit power because of the delayed commands due to feedback delay. This situation


89

will cause an excess of SIR after deep fades, which is not desirable in a CDMA system

because it creates unnecessary interference to other users.

To overcome the impairment of power control due to feedback delay, the feedback delay

needs to be compensated for. Feedback delay compensation is aimed at allowing a mobile

user to adjust its transmit power according to the current channel condition. The problem

of feedback delay has been identified in [68], and [71]-[73]. A technique to compensate for

feedback delay is proposed in [73] and [101] using a time delay compensation (TDC)

method. In this method, the estimated SIR at the basestation is adjusted according to the

power control commands that have been sent by the basestation but whose effect have not

taken place at the mobile station.

In [68] the problem of feedback delay is overcome by using a linear prediction filter at the

basestation to predict the future channel strength. The prediction filter utilises the previous

and present channel correlation to perform the prediction. The filter coefficients can be

computed in several ways [102]. In [72], a recursive least squares (RLS) algorithm is used

to compute the predictor coefficients. In [103] a linear prediction method is described and

the prediction coefficients are computed using the orthogonal principle under the MMSE

criterion.

In fact, as shown in [104] the predictor coefficients for uplink fading can be determined

from the downlink fading correlation. This is because the autocorrelation function for both

uplink and downlink are approximately the same despite their carrier frequencies differ by

several tens of megahertz. In this method, the predictor coefficients are computed using the

autocorrelation function of the downlink channel. Then, the predictor coefficients obtained

from the downlink channel can be successfully used for uplink prediction. However, this

prediction method needs to be implemented at the mobile station, which may not be

desirable due to complexity restrictions at mobile stations.

In this chapter we will study a linear prediction filter, which can predict the channel or

signal strength and thus the SIR at the basestation. Our approach is similar to the technique

described in [103], but we extend the use of this method to predict the SIR at the

basestation. The effect of power control on fading correlation is also taken into account.

Our preliminary study of using a channel predictor for applications in power control


90

algorithms is presented in [105]. In the next section we describe the correlation property of

Rayleigh fading, which will be used to compute the predictor coefficients. The idea of

prediction filter is that instead of using the present channel strength, the predicted channel

strength is used in the power control algorithm.

5.2 Correlation of Rayleigh Fading Channel

In this section we derive the time-frequency autocorrelation function of a Rayleigh fading

channel. The auto correlation function of fading channel is important because it will be

utilised by the channel predictor that we propose to overcome the feedback delay. We

rewrite the complex fading-factor expressed in (2.7) as

∑=

=L

l

tjl

leCt1

)(),( φωβ (5.1)

where φl = ωD cos ψlt- ωτl is an i.i.d. and uniformly distributed variable over [0, 2π]. We

also assume that the time delay τl is an i.i.d. variable with probability density function

fT(τ), where fT(τ) is nonzero for 0 ≤ τ < ∞ and zero otherwise. The time frequency

correlation of the fading factor β(ω, t) is then

[ ]

=

+=+

∑∑= =

+−L

i

L

l

ttjli

lieCCE

ttEtt

1 1

)),(),((

2*

121

21

),(),(),,,(

υωφωφ

β υωβωβυωωρ (5.2)

which will vanish for i ≠ l. In the case i = l or φi(ω1, t) - φi(ω2, t+υ) = ωD cos ψiυ - ∆ωτi,

where ∆ω = ω1 - ω2, the autocorrelation function becomes

[ ] )cos(2

21 ),(),,,(

iiDj

ii eCE

ttωτυψω

ββ υωρυωωρ∆−∑=

∆=+ (5.3)

where E [Ci2] is the average value of the fraction of incoming power in the ith path that can

be expressed as

E [Ci2] = σ2fψ(ψi)fT(τi)dψi dτi . (5.4)


91

Here, σ2 is the total radiated power from the mobile, and fψ(ψi)fT(τi)dψidτi represents the

average fraction of incoming power within dψi of angle ψi and within dτi of the time τi .

For a large number of L (assume L → ∞), the sum in (5.3) can be replaced by integrals that

is independent of i as follows

)().(

)().(

)(.2

)(2

),(

02

0

02

2

0 0

)cos(2

2

0 0

)cos(2

ωυωσ

ττυωσ

ττψπσ

τψτπσυωρ

ω

πωτψυω

πωτψυω

β

∆=

=

=

=∆

∫

∫ ∫

∫ ∫

∞∆−

∞∆−

∞∆−

jFJ

dfeJ

dfede

ddfe

TD

Tj

D

Tjj

Tj

D

D

(5.5)

where J0 is the zero-th order Bessel function of the first kind, and FT(s) is the characteristic

function of the time delay τ, which is also the Fourier transform of the probability density

function fT(τ) defined as

∫∞

−=0

)()( ττ dfssF Tst

T (5.6)

For a frequency-nonselective Rayleigh fading channel, only the time correlation is

considered and the autocorrelation of the Rayleigh fading is expressed as

ρβ = σ2J0(2πfDυ) (5.7)

where fD is the maximum Doppler spread and υ is the time shift.

In order to show the autocorrelation function of Rayleigh fading, we generate a Rayleigh

fading using fading simulator described in Section 4.2. The amplitude variations and

autocorrelation function of a Rayleigh fading with Doppler spread fD = 17 Hz are shown in

Figure 5.3. The time scale in the horizontal axis of Figure 5.3 is shown in Tp to illustrate

the fading fluctuation and autocorrelation in regard with the power control interval (Tp =

0.667 ms).


92

0 50 100 150 200 250 300 350 400 450 500-30

-25

-20

-15

-10

-5

0

5

10

15

Time x Tp (s)

Re

ce

ive

d s

ign

al s

tre

ng

th (

dB

)

(a)

0 50 100 150 200 250 300 350 400 450 500-0.5

0

0.5

1

Time x Tp (s)

Au

toc

orr

ela

tion

fu

nc

tion

(b)

Figure 5.3 Correlation of Rayleigh fading (fD = 17 Hz): (a) amplitude

fluctuation; (b) autocorrelation function.


93

The time correlation function of a fading signal can be used to characterise the fading

statistics in terms of the channel coherent time T0. As mentioned in Chapter 2, the channel

coherence time is inversely proportional to the Doppler spread fD. In [38], T0 is defined as

the time duration over which the channel’s response to a sinusoid has a correlation greater

than 0.5, and the relationship between T0 and fD is approximated as follow

DfT

π16

90 ≈ . (5.8)

For fading channel with Doppler spread fD = 17 HZ as described in Figure 5.3(a), the

channel coherence time is approximately 10.5 ms using (5.8). Table 5.1 illustrates the

relationship between Doppler spreads and channel coherence time in a system operating at

1.8 GHz frequency band.

Table 5.1

Relationship between Doppler spread (fD) and channel coherence time (T0)

for carrier frequency, fc = 1.8 GHz.

Vehicle’s speed (km/h) Doppler spread (ms) Channel coherence time (ms)

10 17 10.5

30 50 3.6

60 100 1.8

100 167 1.1

Since the fading correlation will be utilised by the channel predictor, it is important to take

into account the channel coherence time shown in Table 5.1. The channel coherence time

can be used to determine the order of the predictor.

5.3 Channel Predictor

The proposed channel predictor considered here is a linear prediction filter that is based on

a finite impulse response filter. We consider a Vth order linear predictor to predict the


94

channel coefficient (fading factor) at the ith slot, β(i), using the past V fading factors up to

the (i – D)th slot, [β(i – D) β(i – D –1) … β(i – D – V+1)], where D is the prediction range

expressed in multiples of samples (steps) that is going to be predicted. Figure 5.4 shows

the predictor that consists of a linear filter with the predictor coefficients or the tap weight

vector of dimension V, a(i) = [a0, a1, …, aV-1]T.

aV-1aV-2a1a0

β (i) β (i-D-V+1)β (i-D -v)β ( i-D -1)β (i-D)

Σ

β pred (i)

z -D z -1 z -1 z -1

…

Figure 5.4 D-step linear predictor.

In a D-step linear prediction of order V, the predicted fading-factor is expressed as a linear

combination of the previous samples {β(i – D), β(i – D – 1), …, β(i – D – V+1)} as follows

)()()(1

0

vDiiai v

V

vpred −−= ∑

−

=ββ (5.9)

where av(i), v = 0, 1, …, V-1 are the linear prediction coefficients for the ith slot. By using

the orthogonal principle, the vector a(i) =[a0(i) a1(i) … aV-1(i)]T under the MMSE criterion

can be computed as follow

a(i) = R-1(i)r(i). (5.10)

Here R(i) is the V x V autocorrelation matrix of the input samples, whose elements are

r(i)v,u = E[β(i – D – v) β*(i – D – u)], v, u = 0, 1, …, V-1. The vector r(i) is the cross-


95

correlation between the tap-input samples and the desired response. Elements of vector r(i)

are r(i)v = E[β(i) β*(i – D – v)], v = 0, 1, …, V-1. E[.] is the expectation operator.

To compute the coefficients vector a(i) of the predictor we need to know the

autocorrelation function of the input samples. In Rayleigh fading channels, the

autocorrelation function is expressed in (5.7). Therefore, if we know the Doppler spread of

fading channel, the correlation matrix R(i) is also known. By considering the power

control interval as the time index, we can rewrite the autocorrelation function as follows

E[β(i) β*(i – v)] = σ2 J0(2πfDTpv). (5.11)

Here Tp is the slot duration and v is the slot index. We can also determine the

autocorrelation function of fading channel by using biased estimates of these parameters by

means of the time average as follows

)()()]()([ *

1

* vnnviiEtN

vn

−=− ∑+=

ββββ , v = 0, 1, …, V – 1 (5.12)

where Nt is the total length of the input time series, with Nt >> M.

It is important to note that in the system that employs power control, the correlation of the

received samples is altered by power control. In other words, power control destroys the

fading correlation of the channel. Therefore, the past samples of the power-controlled

fading factors β(i – D – v), v = 0, 1, …, V – 1 must be compensated for by the same factor

that was given by power control at each power control interval to restore its correlation

property. The restored fading factor can be expressed as

)(10)( 20/)]([

1

vDivDi puDiesignv

u

−−′=−− ∆−−

=∏ ββ , (5.13)

where β’(i – D – v) is the power-controlled fading factor and β(i – D – v) is the

uncontrolled fading factor that can be used as input samples to the predictor. The product

term in the right-hand side of (5.13) indicates the total power-control gain accumulated

during v power-control interval.


96

There are several methods that can be used to compute the predictor coefficients. A direct

matrix inversion method as shown in (5.10) is a straightforward solution. However in

practice, this method is not desirable because it is computationally intensive due to the

inverse matrix operation and numerically sensitive because the correlation matrix R(i) can

be ill conditioned. Therefore, recursive algorithms, such as Levinson-Durbin algorithm

[103] or RLS methods are preferable in practice [72]. In the next section we will describe

power control simulations with channel predictor (predictive power control) and present

the results.

5.4 Power Control with Channel Predictor

To show the performance improvement of power control by the use of channel predictor,

we repeat our simulations of closed-loop power control, but now the predictor is used at

the basestation. The power control model described in Figure 4.2 is shown again here in

Figure 5.5 with an additional functional block (channel predictor) at the basestation.

∆pTp

IntegratorStep size

+

+

+ _

+

-γt

γest

PCC bit error

e(i) PCC bits

Predictor

MAI andAWGN

Basestation

Mobile station

ChannelFadingβ(t)

DT pLoop delay

Figure 5.5 Power control scheme with channel predictor at basestation.


97

In a SIR-based power control algorithm, the power control decision is based on the SIR,

instead of signal strength. Therefore the proposed SIR estimator described in Section 3.5 is

modified as follows

[ ][ ]2

1

2

2

)(1

|)(|1

)()(

iyM

nyB

iyi

k

MB

ma

kk

−=

∑=

γ (5.14)

where

)()()(1

0

vDiyiaiy kv

V

vk −−= ∑

−

=

(5.15)

and

)(10)( ’20/)]([

1

vDiyvDiy kpuDiesign

v

uk −−=−− ∆−−

=∏ . (5.16)

Here, yk’(i – D – v) is the actual estimated received signal and yk(i – D – v) is the signal

inputs for channel predictor in which fading correlation has been restored at the (i – D –

v)th slot, u, v = 1, 2, …, V, of the kth user. The channel predictor then uses (5.15) to predict

the signal D steps ahead. In this case we predict the desired signal strength and then the

SIR is computed using (5.14).

In our simulation, we compute the fading correlation matrix R(i) using (5.11). The order of

predictor V is chosen large enough, so that the prediction memory exceeds the channel

coherence time in order for the prediction to fully exploit the fading correlation. We use V

= 10 samples in our simulations for all cases of fading channels considered here. The

predictor coefficient vector a(i) is computed using the direct matrix inversion technique for

the sake of simplicity in the simulation. In a real system, the direct matrix inversion

technique is not desirable because fading condition (Doppler spreads) may change and the

correlation matrix needs to be recomputed. The matrix inversion can also be ill conditioned

(numerically sensitive) and computationally intensive, particularly when the matrix

dimension is large.


98

To reduce the computation complexity, however, the order of the predictor, V, can be

reduced. In this case, the number of samples V can be reduced to Vr (Vr << V) using a

selection mapping technique [106]. Therefore the size of the correlation matrix R is also

reduced. This complexity reduction technique can be applied in a predictive power control

system, i.e. the channel predictor may utilise fewer channel measurements to predict the

fading channel compared to that required by power control. In this study, we fully utilise

all channel measurements required for power control purposes in the channel predictor.

For comparison, we also perform simulations of power control using an approach that is

similar to the time delay compensation method presented in [101]. In this approach, the

effect of feedback delay is reduced because the delay due to the commands that have been

sent by the basestation but have not taken effect in the mobile station, is compensated for.

This is accomplished by adjusting the estimated SIR, γest, as follow

∑=

−∆+=D

i

iestcomp zpii

1

)PCC.()()( γγ , (5.17)

where z -i is the i-step delay operator, PCC is the command bits for each power control

interval, ∆p is the power-update step size, and γcomp is the SIR after delay compensation.

Power control decision is based on γcom. Note that delay compensation D in this approach

does not take into account the SIR measurement time, which is one time slot. The PCC in

(5.17) is the power control command bit.

In the simulation, the feedback channel is assumed to be error free. The performance of

fixed-step and variable-step power control algorithms for fDTp = 0.01 and feedback delay D

= 2Tp using the channel predictor (predictive power control) and delay compensation

approach is shown in Figure 5.6.

We can see in Figures to 5.6(a) that significant performance improvement can be obtained

by using the channel predictor (predictive algorithm). We can also see that the channel

prediction method performs better than the delay compensation technique. This is because

the delay compensation approach does not compensate for the delay due to SIR

measurement time. In Figure 5.6(b), we can see that the channel predictor plays a more

significant role in solving the feedback delay problem because the variable-step algorithm

is more sensitive to feedback delay than the fixed-step algorithm. The superiority of


99

channel prediction over delay compensation becomes more noticeable in the variable-step

algorithm. Although not shown here, it is important to point out that the prediction filter

provides a good performance for short delay (D = 1 slot) as well as for long delays (up to

D = 3 slots).

0 2 4 6 8 1 0 1 2 1 4 16 1 8 201 0

-7

1 0-6

1 0-5

1 0-4

1 0-3

1 0-2

1 0-1

1 00

Bit

err

or

rate

, B

ER

Eb /Io (dB)

F ad ing cha nn el De lay D=2T

p

De lay co mp en satio nCha nn el p re d icto r AW G N cha nn el

(a)

0 5 10 15 2 010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb /Io (dB)

F a ding channe l De lay D=2T p

De lay compe nsationChan nel pred icto r AW G N cha nnel

(b)

Figure 5.6 Performance of power control with channel predictor and time delay

compensation (fDTp = 0.01): (a) fixed-step algorithm; (b) variable-step algorithm (q = 4).


100

To evaluate the performance of the predictive algorithm in higher rates of fading channel,

we show the simulation results in Figure 5.7. These results show how a fixed-step and

variable-step power control with predictive algorithm perform in fading situations for

vehicular environments (vehicle’s speed from 10 to 60 km/h).

0 2 4 6 8 10 12 14 16 18 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channelfDT

p=0.067

fDT

p=0.033

fDT

p=0.01

AWGN channel

(a)

0 2 4 6 8 10 12 14 16 18 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channelfDT

p=0.067

fDT

p=0.033

fDT

p=0.01

AWGN channel

(b)

Figure 5.7 Performance of predictive power control at different fading rates: (a) fixed-step algorithm, (b) variable-step algorithm (q = 4).


101

We can see in Figure 5.7(a) that the performance of predictive power control with fixed-

step algorithm is reasonable for slow mobility situations, i.e. pedestrians or slow moving

vehicles. For example for fDTp = 0.01 (vehicle’s speed of10 km/h), a voice quality BER of

10 –3 only requires Eb/I0 of approximately 1.5 dB higher than that required by an AWGN

channel.

For faster mobility environments, however, the fixed-step algorithm does not perform well

as we can see for the fading situations with fDTp = 0.033 and 0.067, which correspond to

vehicles’ speeds of 30 and 60 km/h, respectively. For a vehicle speed of 60 km/h, the

performance of fixed-step algorithm is only slightly better than the performance of fading

channel without power control. Therefore, to achieve a BER of 10 –3, the required Eb/I0 is

still too high (more than 9 dB higher than that required by AWGN channel)

With variable-step algorithm, reasonable performance for vehicular speeds of up to 60

km/h can be achieved as we can see in Figure 5.7(b). For a vehicle speed of 60 km/h, a

BER of 10 –3 can be achieved by operating the system’s Eb/I0 at approximately 5 dB higher

than that for AWGN channel.

5.5 Summary

In this chapter we have presented a method that can be used to overcome the problem of

feedback delay in a SIR-based closed-loop power-control system. The proposed channel

predictor shows an excellent performance in solving the problem of feedback delay in the

loop. Therefore, a channel predictor is essential in a closed-loop power control system.

While a channel predictor can overcome the feedback delay problem, further

improvements may be needed, particularly for a fixed-step algorithm which fails to control

deep fades. In order to improve the performance of predictive power control schemes, a

diversity antenna technique can be used to help mitigate the effect of deep fades in both

slow and fast fading environments. We will consider a fixed-step power control system in

conjunction with the use of diversity antenna arrays in Chapter 6.

102

Chapter 6

Power Control and Diversity Antenna Arrays

In this chapter we presents simulation results to show the performance of power control in

conjunction with the use of diversity antenna arrays at the basestation. A brief overview on

diversity reception techniques is presented with more emphasis on space diversity

reception technique using antenna arrays. Our focus is on MRC algorithm because it offers

an optimum diversity combining. The performance improvement offered by the use of

diversity antenna arrays over the single path reception on a power-controlled CDMA

system is shown.

6.1 Introduction

In Chapter 4 the effects of system parameters on the BER performance of closed-loop

power control have been shown. The feedback delay was found to be the most critical

parameter in the loop. In Chapter 5 a channel predictor has been introduced to solve the

feedback delay problem. The predictive power control algorithm described in Chapter 5 is

very effective in eliminating the effect of feedback delay. Another limitation of power

Chapter 6. Power Control and Diversity Antenna Arrays

103

control, however, is due to the fact that the transmission power can only be adjusted using

finite step sizes at limited updating rates. Therefore, the tracking ability of power control is

limited, particularly when a channel goes into deep fades. In this situation, the transmission

power needs to be raised significantly in a very short period of time to compensate for the

fade. Figure 6.1 illustrates this situation.

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

-30

-20

-10

0

10

20

30

40

Time x Tp (s)

SIR

or

sig

na

l s

tre

ng

th (

dB

)

Controlled SIR (target = 10 dB)Controlled transmit power Received fading signal

Figure 6.1 Effect of deep fades on power control with finite step size.

In Figure 6.1, the SIR target at the basestation is set at 10 dB and the power update rate is

100 times faster than the fading rate (fDTp = 0.01) using a fixed step size of 2 dB. A

channel predictor is used to eliminate the effect of feedback delay, so that power

adjustments are always current with fading condition. However, we still observe deep SIR

variations when channel goes into deep fades as we can see in Figure 6.1. This is because

of the finite step size of power control algorithm.

To improve the ability of power control in tracking deep fades, transmission power can be

adjusted more frequently using high-resolution variable-step size. However, this approach

may not be feasible in practice because it requires a prohibitively high signalling

bandwidth. Instead of counteracting deep fades with high transmission power, our

approach here is to use diversity antenna arrays, which can improve the performance of


104

power control [107]-[109]. Our preliminary study on using diversity antenna arrays and

predictive power control has shown a promising result [110]. With diversity antenna

arrays, the probability of a channel going into a deep fade can be significantly reduced,

resulting in two major improvements. Firstly, fading dips are shallower and thus become

easier to be tracked by power control algorithm. Secondly, the system can be operated at

lower peak transmit powers resulting in less multiple access interference to other users, and

therefore becomes more stable.

6.2 Diversity and Fading Mitigation

It is important to understand various diversity techniques for fading mitigation because

different fading situations require different implementations of diversity techniques.

Fundamentally, diversity techniques exploit the same information from several

independent and uncorrelated signal paths than can be resolved and combined by the

diversity receiver [111]. If the received paths are correlated, no diversity gain can be

attained. There are three basic diversity techniques that are commonly used for fading

mitigation: time diversity, frequency diversity, and space diversity.

In time diversity, several signal paths carrying the same information that arrive at different

time slots are combined. The time difference between one path and another must exceed

the channel coherence time in order for those paths to be uncorrelated and diversity gain

can be obtained. In frequency diversity, the diversity gain can be obtained when several

signal paths carrying the same information but have different carrier frequency are

combined. The frequency separation of different carriers must exceed the coherence

bandwidth of the channel. In space or antenna diversity, several signal paths bearing the

same information that come from different antennas are combined. The separation between

one antenna and another must exceed the coherence distance of the channel.

Apart from those three basic diversity techniques, other methods are polarisation and angle

diversity. In polarisation diversity, different uncorrelated paths can be obtained through the

exploitation of different polarisations. Angle diversity is very similar to antenna diversity,

but in angle diversity directional antenna is used to utilise uncorrelated signal paths that

come from different directions.


105

There are various ways to implement diversity techniques in fading channel environments

depending on fading conditions. As mentioned in the first half of Chapter 2, in CDMA

systems a frequency selective fading causes inter chip interference due to different time

delays of various signal paths. If these paths are resolvable and the channel coherence time

does not exceed the processing gain, they can be coherently combined by using the rake

receiver technique [112]. In this case, the rake receiver utilises the frequency diversity of

the fading channel. In a frequency nonselective fading, however, the rake receiver is not

effective because the rake receiver may only receive one signal path.

Another example of diversity implementation is the use of coding/interleaving technique in

a fading environment, which fits a model of a bursty error channel. A block interleaving

can be viewed as an attempt to break up the error bursts in order to obtain independent

errors (time diversity). Time diversity using interleaving/coding technique is most effective

in a fast fading but less effective in a slow fading situation because in a slow fading

situation a prohibitively long block is needed by the interleaver [18]. Space diversity using

antenna arrays is an effective way of implementing diversity technique in any fading

situation because in space diversity, independent and uncorrelated diversity paths can

always be obtained when the separation between antenna elements is sufficiently large. In

the following we investigate the use of diversity antenna arrays in conjunction with power

control.

6. 3 Diversity Antenna Arrays

In a cellular system, diversity antenna arrays are usually implemented at the basestation

due to size restrictions at the mobile station. Diversity reception at the basestation is

employed to obtain a diversity gain on the uplink, while transmit diversity at the

basestation is used to obtain a diversity gain on the downlink. We will consider reception

diversity at the basestation because we will use this technique in conjunction with power

control on the uplink.

Consider an L-path spatial diversity reception with independent fadings as shown in Figure

6.2. Usually the separation distance between antenna elements are at least 10 wavelengths

in order to obtained independent signal paths [46]. If p is the probability that a given path


106

falls below a threshold, the probability that all L paths fall below the threshold is pL, which

is considerably smaller than p.

wL

w2

w1

Diversity combining algorithm

Σ

x1 (t)

x2 (t)

xL (t)

y(t)

.

.

.

measurement

Figure 6.2 Simplified model of diversity antenna arrays.

There are three different algorithms for combining the diversity paths: selective combining,

equal gain combining, and maximal ratio combining algorithms. In a selective diversity

combining method, the algorithm selects the signal with the highest signal strength or

SNR, while in an equal gain method the algorithm just directly combines the signals from

all diversity branches. The maximal-ratio-combining algorithm performs the combining

after weighting each signal path with a factor that is proportional to the square root of its

SNR. The output of diversity combiner y(t) can be expressed as

∑=

=L

lll txwty

1

)()( , (6.1)

where xl(t) is the input signals from each diversity branch. The weight vector w = [w1, w2,

…, wL]T depends on the combining algorithm employed. For MRC and equal gain diversity

algorithms wl can be expressed as

= ∑algorithmgain Equal1

algorithm MRC

ll

l

lw γγ

, (6.2)


107

and for selection diversity algorithm wl can be written as

( ) ==

=otherwise0

max1 max, ll

lllw

γγγ. (6.3)

Here γl is the received SIR at the lth element of the antenna arrays. The MRC algorithm is

optimal [107] in that the output SIR can be expressed as

∑=

=L

llMRC

1

γγ . (6.4)

Since the MRC algorithm is optimal, the performance of MRC diversity outperforms the

other two combining methods. The equal gain combining method performs better than the

selection method because all diversity paths are exploited by the former method instead of

just one path by the later method. However, a better performance leads to a more complex

operation. In selection diversity, SIR or signal strength is estimated at each diversity

branch, but the algorithm only compares between them and selects the highest. In equal

gain diversity, SIR or signal strength measurement is not required because all diversity

paths can be directly combined. However, combining all paths coherently is not a simple

task. In the MRC algorithm, SIR estimation, weight factor computation and coherent

combining are performed. However, since in a SIR-based power control SIR is already

estimated for power control purposes, we can also utilise the estimated SIR on each

diversity branch for MRC diversity algorithm in order to achieve optimum diversity

performance.

6.4 Power Control and Diversity Antenna

We now propose a basestation architecture for a system that employs power control,

channel predictor, and diversity antenna arrays. The basestation performs SIR estimation at

each diversity branch in order to obtain the channel information on each branch. For

simplicity, a diversity antenna technique of order two (L=2) is considered.. Extension to

higher diversity orders is straightforward. The proposed basestation architecture is shown

in Figure 6.3.


108

w2

w1

∑

For powercontrol

SIR γdiv

Path 1

Path 2

Channel SIRpredictor estimator

γ1

Channel SIRpredictor estimator

γ2

MRCdiversityalgorithm

Figure 6.3 Architecture of basestation employing power control,

channel predictor, and diversity antenna arrays.

In Figure 6.3, the MRC combining algorithm utilises the estimated SIR at diversity path 1,

γ1 and at diversity path 2, γ2, to compute the weight factors for each branch by using the

first line of (6.2). Power control decision is based on the SIR at the diversity output, γdiv.

Since the basestation also predicts the channel conditions to eliminate the effect of

feedback delay, channel predictions need to be done at each diversity path because the

channel predictor relies on fading correlations. After the channel is predicted and the SIR

is estimated for each diversity branch, the MRC algorithm computes the weight factors w1

and w2. The SIR at the diversity output can be computed using (6.4), which is then used as

the control parameter in power control algorithm. Note that the optimality of the MRC

combiner holds despite the impact on the cross-correlation properties of the spreading

sequences due to the combining of more than one diversity branches.

Since deep fades at the output of the diversity combiner are shallower than that of a single

path channel, power control may require a smaller step size. In the next section power-

control simulation that employs a two-branch diversity antenna arrays is performed in

order to determine an optimum step size.


109

6.5 Effect of MRC Diversity on Step Size

With diversity antenna arrays, the fading dips of the received signal strength and SIR at the

diversity output are reduced. Figure 6.4 shows the signal strength and SIR variations with

diversity antenna arrays of order two.

0 50 1 0 0 1 5 0 20 0 2 5 0 30 0 35 0 40 0-50

-40

-30

-20

-10

0

10

20

T im e x T p (s )

SIR

or

sign

al s

tren

gth

(d

B)

D iv ers ity S IR D iv ers ity signal, M R C , L= 2

S ig nal pa th 1 S ignal pa th 2

Figure 6.4 Signal strength and SIR using a two-branch diversity antenna arrays.

Clearly from Figure 6.4, the received signal strength after diversity combining becomes

shallower compared to that of the individual path. Therefore, the output SIR improves as it

corresponds to the received signal from the diversity channel. The improved channel

conditions after diversity combining will require power control to operate with a smaller

step size.

We perform power control simulations to determine an optimum step size using the

parameter fDTp = 0.01, 0.033, and 0.067. The simulation procedure is the same with that

described in Chapter 4, but now a diversity antenna arrays of order two is employed at the

basestation. The power control error defined in Chapter 4 is plotted as a function of step

size in Figure 6.5. We can see from Figure 6.5 that the optimum step size is less than 2 dB

when a two-branch diversity antenna arrays is employed at the basestation. A step size of


110

approximately 1 dB is optimum in fading situations with the parameter fDTp = 0.01 and

0.033, while a step size of between 1.5 and 2 dB performs best for fDTp = 0.067.

0 0 .5 1 1 .5 2 2 .5 3 3 .5 40 .5

1

1 .5

2

2 .5

3

S te p s ize ( d B )

Po

we

r co

ntr

ol

err

or

(dB

)

fD

Tp = 0 .0 6 7

fD

Tp = 0 .0 3 3

fD

Tp = 0 .0 1

Figure 6.5 Power control error as a function of step size using a two-branch

diversity antenna arrays at the basestation.

We also obtain a similar result when BER is monitored and used as the performance

measure. The effect of step size on BER performance is shown in Table 6.1.

Table 6.1

Effect of step size on bit error rate at Eb/I0 = 7 dB

with diversity antenna arrays (MRC, L =2).

Step size (dB) 0.2 0.6 1.0 1.6 2.0 2.6 3.2 3.6 4.0

BER x 10 –3

fDTp = 0.01 8.1 5.6 4.5 4.2 5.0 5.5 7.0 7.5 9.7

fDTp =0.033 15.2 7.9 4.4 5.3 6.4 6.2 6.9 8.0 12.1

fDTp = 0.067 17.2 12.9 7.7 7.9 9.7 10.1 9.4 11.1 12.0


111

6.6 Performance of Power Control with Diversity Antenna

In order to show the improvement of power control performance offered by diversity

antenna arrays, power control simulations are performed for three different channel

conditions (i.e. the parameter fDTp = 0.01, 0.033, and 0.067). Feedback delay D = 2Tp is

assumed and a 2-step channel predictor is employed to overcome the effect of feedback

delay. Diversity antenna arrays of order two is employed at the basestation. Power-update

step size ∆p = 1 dB is used and fixed-step and variable-step (mode q = 4) algorithms are

investigated. The BER performance obtained from simulations for fixed-step and variable-

step algorithms are shown in Figures 6.6(a) and (b), respectively.

We can see from Figure 6.6(a) that reasonable BER performance can be achieved using a

fixed-step predictive power control in conjunction with the use of diversity antenna arrays

at the basestation. To achieve a voice-quality BER of 10–3 for a mobile velocity of 10 km/h

(fDTp = 0.01), the required Eb/I0 is only approximately 1 dB higher than that required in an

AWGN channel. For higher mobile velocities of 30 km/h (fDTp = 0.033) and 60 km/h (fDTp

= 0.067), a BER of 10–3 can be achieved by employing the system’s Eb/I0, respectively at

approximately 3.5 and 5.5 dB higher than that for AWGN channel.

A better BER performance for higher mobile velocities can be achieved by employing a

variable-step algorithm as we can see in Figure 6.6(b). For mobile velocities of 30 km/h

and 60 km/h, a BER of 10–3 can be achieved by operating the system’s Eb/I0, respectively

at 1.5 dB and 4 dB higher than that required in an AWGN channel. For a mobile velocity

of 10 km/h, however, the improvement offered by the variable-step algorithm over the

fixed-step algorithm is insignificant as the BER curves for both algorithms at fDTp = 0.01

are almost the same.

However, the variable-step algorithm requires a higher signalling bandwidth than the

fixed-step algorithm. A variable-step algorithm of mode q = 4 (as considered in our study)

requires a signalling bandwidth four times higher than a fixed-step algorithm. Therefore, in

a slow fading environment a fixed-step algorithm is preferred because it can achieve a

comparable performance with that offered by a variable-step algorithm, while the required

signalling bandwidth is much less.


112

0 2 4 6 8 10 12 14 16 18 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channelfDT

p = 0.067

fDT

p = 0.033

fDT

p = 0.01

AWGN channel

(a)

0 2 4 6 8 10 12 14 16 18 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

err

or

rate

, B

ER

Eb/Io (dB)

Fading channelfDT

p = 0.067

fDT

p = 0.033

fDT

p = 0.01

AWGN channel

(b)

Figure 6.6 Performance of power control with diversity antenna arrays (MRC, L=2):

(a) fixed-step algorithm; (b) variable-step algorithm (q = 4).


113

6.7 Summary

In this chapter we have shown the performance of uplink power control in conjunction

with the use of diversity antenna arrays at the basestation. This technique offers two major

improvements to power control: reducing deep fades, and preventing excessive peak

transmission power. When deep fades are reduced, the ability of power control to track the

channel improves. The peak transmission power required to combat deep fades is also

reduced because the channel fading is shallower in a diversity channel, resulting in less

multiple access interference.

The predictive power control with two-branch diversity antenna arrays at the basestation

appears to be capable of compensating Rayleigh fading almost perfectly in a slow fading

channel (e.g. a pedestrian environment), but less so in a faster vehicular environment. In a

slow fading environment, both fixed and variable step algorithms perform well. Simulation

results demonstrate that the BER performance of fading channel in a slow mobile velocity

(e.g. 10 km/h) improves significantly by using a combination of predictive power control

and diversity antenna arrays, approaching the performance of an AWGN channel.

While both fixed and variable step power control algorithms have approximately the same

performance in a slow fading environment, the later performs better than the former in a

faster mobile velocity (up to 60 km/h). However, the improvement of using variable step

algorithm is not significant and therefore may not justify the trade off between the

performance and the requirements of variable step algorithms (higher signaling bandwidth

and its sensitivity to disturbances). Of course for faster vehicle speeds, power control

cannot do much and the performance relies upon more suitable techniques, such as error

coding and interleaving.

114

Chapter 7

Conclusion and Further Work

7. 1 Conclusion

A fast and accurate power control is essential in a DS-CDMA system to minimise multiple

access interference under multipath fading conditions. We provide a brief overview of

wireless channels and develop a simple model of CDMA channels under fading conditions

for both uplink and downlink transmissions. This overview has enabled us to demonstrate

the importance of power control in CDMA systems and to highlight that power control on

the uplink is more crucial than on the downlink. Our study in the second half of Chapter 2

reveals that power control devices in real situations are imperfect. This has prompted us to

look for new approaches and technologies in order to improve the performance of existing

power control systems.

Power control is more efficient when the algorithm is based on SIR rather than on signal

strength. However, the main issue with an SIR-based power control is the difficulty to find

a fast, accurate, and easy-to-implement SIR estimator. In Chapter 3 we propose a new SIR

estimator and we show that it offers a very good trade off between accuracy and simple

7. Conclusion and Further Work

115

implementation. We also show, by computer simulations, that this new SIR estimator can

provide a good performance for power control purposes.

Other important parameters affecting the performance of power control are power-update

step size, power-update rate, feedback delay, and feedback channel error. A power control

algorithm that employs variable-step sizes has been shown to perform better than a fixed-

step algorithm. However, a variable-step algorithm is very sensitive to feedback delay, SIR

estimation error, and feedback channel error. A fixed-step algorithm is robust with respect

to SIR estimation error and feedback channel error, but it is also sensitive to feedback

delay. In fact from simulations, we observed that feedback delay is the most critical

parameter while feedback-channel error is the least critical in the loop.

In Chapter 5, we have presented a solution to solve the problem of feedback delay using a

linear prediction filter method. This approach utilises the correlation property of the fading

channel to predict the channel conditions. By using the prediction method, the performance

of power control that is subject to feedback delay improves significantly as the degradation

introduced by the feedback delay is shown to be recovered perfectly. While the predictive

algorithm can successfully solve the most critical problem due to feedback delay, the

power control performance is still limited, particularly when the Doppler spread increases

in a higher velocity environment. From simulation results shown in Chapter 4, power

control performs well in a slow fading environment (e.g. for pedestrian). For a vehicular

environment with a higher velocity of up to 60 km/h, however, power control is not so

effective. We have shown in Chapter 6 that diversity antenna arrays can offer an

appreciable performance improvement to the power control. With diversity antenna arrays,

a reasonable performance in a vehicular velocity of up to 60 km/h can be achieved. In a

slow velocity environment (e.g. at 10 km/h) a combination of power control and diversity

antenna arrays provides an excellent performance, approaching the performance of an

AWGN channel.

7.2 Further Work

There are a number of issues arising as a result of our study that need to be further

explored. These can be summarised as follows. In Chapter 4, the effect of the downlink-

channel bit error rate on the performance of power control is investigated under a Gaussian

7. Conclusion and Further Work

116

distribution assumption of the command error. In a real system, downlink channels are also

under fading conditions in which burst errors will occur. It can be an interesting and

important study to investigate the effect of burst errors of the command bits transmission

on the performance of power control. In addition, a variable-step power control may be

required in next generation systems to achieve better performance. With variable-step

power control, error coding to protect the command bits transmission becomes more

important and can be another interesting exercise.

In Chapter 5, the coefficients of channel predictor are computed using a direct matrix

inversion method under the assumption that the autocorrelation function of fading channel

is known. In practice, autocorrelation of fading channel needs to be estimated. Therefore,

recursive methods are desirable to reduce the computational complexity, which have not

been investigated in this study. Another approach to reduce the complexity in computing

the prediction coefficients using correlation matrix would be to consider a smaller number

of the tap-input samples (reducing the order of the correlation matrix). Note that for power

control purposes, channel measurements are performed with a rate that is much higher than

the fading rate (between 10 and 100 times higher). In channel prediction, the channel

measurements may be performed with a rate that is only slightly higher than the fading

rate. Therefore, optimising the number of tap inputs for prediction filter using a subset of

the available channel measurements for power control can be an interesting issue to study.

Finally, in next generation CDMA systems, the uplink transmission may employ various

new technologies, such as beamforming, multiuser detection, and interference cancellation

schemes, resulting in a better signal reception and less multiple access interference. In

addition, the uplink of next generation systems employs a pilot transmission for coherent

demodulation. The existence of pilot channels on the uplink of next generation systems can

also be utilised to improve estimations of system parameters that are required for power

control and thus improve the performance. Therefore, power control for next generation

systems should also consider these new technologies.

117

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