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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].
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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,
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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,
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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).
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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)
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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
qqq
qqq
qDie , (2.12)
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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.
Chapter 2. Power Control in CDMA Systems
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.
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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)
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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)
Chapter 3. SIR Estimation/Measurement
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)
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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.
Chapter 3. SIR Estimation/Measurement
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.
Chapter 3. SIR Estimation/Measurement
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
Chapter 3. SIR Estimation/Measurement
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
Chapter 4. Power Control Simulation
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)
Chapter 4. Power Control Simulation
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].
Chapter 4. Power Control Simulation
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
Chapter 4. Power Control Simulation
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
Chapter 4. Power Control Simulation
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.
Chapter 4. Power Control Simulation
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.
Chapter 4. Power Control Simulation
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
Chapter 4. Power Control Simulation
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
Chapter 4. Power Control Simulation
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
Chapter 4. Power Control Simulation
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.
Chapter 4. Power Control Simulation
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
Chapter 4. Power Control Simulation
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
Chapter 4. Power Control Simulation
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
Chapter 4. Power Control Simulation
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.
Chapter 4. Power Control Simulation
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
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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 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
Chapter 4. Power Control Simulation
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.
Chapter 4. Power Control Simulation
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).
Chapter 4. Power Control Simulation
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.
Chapter 4. Power Control Simulation
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
-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
(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).
Chapter 4. Power Control Simulation
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.
Chapter 4. Power Control Simulation
81
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
(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).
Chapter 4. Power Control Simulation
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.
Chapter 4. Power Control Simulation
83
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 channelD = 3 T
p
D = 2 Tp
D = Tp
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 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.
Chapter 4. Power Control Simulation
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.
Chapter 5. Predictive Power Control
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
Chapter 5. Predictive Power Control
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
Chapter 5. Predictive Power Control
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
Chapter 5. Predictive 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)
Chapter 5. Predictive Power Control
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).
Chapter 5. Predictive Power Control
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.
Chapter 5. Predictive Power Control
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
Chapter 5. Predictive Power Control
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-
Chapter 5. Predictive Power Control
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.
Chapter 5. Predictive Power Control
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.
Chapter 5. Predictive Power Control
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.
Chapter 5. Predictive Power Control
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
Chapter 5. Predictive Power Control
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).
Chapter 5. Predictive Power Control
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).
Chapter 5. Predictive Power Control
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
Chapter 6. Power Control and Diversity Antenna Arrays
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.
Chapter 6. Power Control and Diversity Antenna Arrays
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
Chapter 6. Power Control and Diversity Antenna Arrays
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)
Chapter 6. Power Control and Diversity Antenna Arrays
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.
Chapter 6. Power Control and Diversity Antenna Arrays
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.
Chapter 6. Power Control and Diversity Antenna Arrays
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
Chapter 6. Power Control and Diversity Antenna Arrays
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
Chapter 6. Power Control and Diversity Antenna Arrays
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.
Chapter 6. Power Control and Diversity Antenna Arrays
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).
Chapter 6. Power Control and Diversity Antenna Arrays
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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