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Optimal power control in CDMA Mobile networks

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of

Master of Science

In Electrical Engineering

By

Eng. Hatem Mohamed M. Zakaria

Under the Supervision of

Prof. Salah Ghazy Ramadan Benha High Institute of Technology - Benha

Dr. Abdel-Aziz Mahmoud El-Bassiouni

ZTE Corporation - Cairo

Dr. Ayman Moustafa Hassan Benha High Institute of Technology - Benha

Benha High Institute of Technology, Benha University Egypt 2006

Optimal power control in CDMA Mobile networks

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of

Master of Science

In Electrical Engineering

By

Eng. Hatem Mohamed M. Zakaria

Approved by the Examining Committee:

1. Prof. Abdel-Halim Abdel-Nabi Zekri ( ) Faculty of Engineering - Ain Shams University

2. Prof. Mohamed E. Nasr ( ) Head, Dept of Electronics & Communications Eng. Faculty of Engineering - Tanta University

3. Prof. Salah Ghazy Ramadan ( ) Head, Dept of Electrical Eng. Benha High Institute of Technology - Benha

4. Dr. Abdel-Aziz M. El-Bassiouni ( ) ZTE Corporation - Cairo

Benha High Institute of Technology, Benha University Egypt 2006

i

ABSTRACT Code Division Multiple Access (CDMA) is interference limited multiple access system. Because all users transmit on the same frequency, internal interference generated by the system is the most significant factor in determining system capacity and call quality. The transmit power for each user must be reduced to limit interference, however, the power should be enough to maintain the required signal energy per bit to noise power spectral density ratio (Eb/No) for a satisfactory call quality. Maximum capacity is achieved when Eb/No of every user is at the minimum level needed for the acceptable channel performance. As the mobile station (MS) moves around, the radio frequency (RF) environment continuously changes due to fast and slow fading, external interference, shadowing, and other factors. The aim of the dynamic power control is to limit transmitted power on both the links while maintaining link quality under all conditions. Additional advantages are longer mobile battery life and longer life span of Base Transceiver Station (BTS) power amplifiers. Successful optimization of any power control algorithm design requires the simulation of many components. This optimization can be achieved with system-level design, which allows the simulation of the physical and link layers of entire communication systems.

In this thesis new closed loop power control algorithms for CDMA cellular communication systems are proposed. To cope with the random changes of the radio channel and interference, adaptive algorithms are considered that utilize ideas from self-tuning control systems. Another problem in closed-loop power control is that extensive control signaling consumes radio resources, and thus the control feedback bandwidth must be limited. A new approach to enhance the performance of closed-loop power control in limited-feedback-case is presented, and power control algorithms based on the new approach are proposed.

The performances of the proposed algorithms are evaluated through both analysis

and computer simulations using MATLAB, and compared with well-known algorithms from the literature. The results indicate that significant performance improvements are achievable with the proposed algorithms.

ii

ACKNOWLEDGMENT

All gratitude is due to ALLAH, who made this success possible and affordable.

No words can ever express my thanks to all persons who contributed to the fulfillment of

this work.

I am proud to work under the supervision of Prof. Dr. Salah Ghazy Ramdan,

Benha University. I would like to express my sincere thanks for his valuable advice,

extensive assistance, valuable effort, and encouragement during the course of this work.

I am honored to work under the supervision of Dr. Abdel-Aziz Mahmoud El-

Bassiouni, ZTE Corporation at Cairo. I would like to extend my deepest thanks and

appreciation to him, for the supervision, useful assistance, inspiration, constructive

discussion and guidance throughout the course of this work.

A special acknowledgment and deepest thanks to Dr. Ayman Moustafa Hassan,

Benha University, for his valuable help, support, supervision and encouragement to

continue the effort to finalize the work in this form.

I dedicate this thesis to my parents, whose sincere love and support have carried

me through all times in life and inspired me to keep my mind in the essentials.

iii

Contents Abstract i

Acknowledgment ii

List of Main Symbols and Abbreviations v

List of Figures ix

List of Tables xii

CHAPTER 1: Introduction 1

1.1 The Need for Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Classification of Power Control Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

CHPTER 2: Theoretical Review of Power Control 14

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Centralized Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.1 Centralized SIR-Balanced Power Control . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.2 Transmitter Removal Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Distributed Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.1 Constrained Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4.2 Distributed SIR-Balancing and Transmitter Removal . . . . . . . . . . . . . . . . 25 2.4.3 Aiming for faster convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5 Cooperative Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5.1 Basic Cooperative Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5.2 Modified Cooperative Power Control Algorithm . . . . . . . . . . . . . . . . . . . . 29 2.5.3 Asynchronous Cooperative Power Control . . . . . . . . . . . . . . . . . . . . . . . . 30

2.6 Joint Power and Rate Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

CHAPTER 3: Case Studies 33

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 The Dirty User Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.2 System Simulation Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Power Control Imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.1 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

CHAPTER 4: Power Control in CDMA IS-95 42

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

iv

4.2 Reverse Link Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2.1 Access Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2.2 Open Loop Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2.3 Closed Loop Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2.4 Open-Loop and Closed-Loop Implementation . . . . . . . . . . . . . . . . . . . . . . 55

4.3 Forward Link Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.4 Power control in soft handover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

CHAPTER 5: Adaptive step-size power control 62

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.1.1 Problem setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 Adaptation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.3 The Adaptive Step Power Control (ASPC) algorithm . . . . . . . . . . . . . . . . . . . . . 64 5.4 Modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.4.1 AS with asymmetric update step sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.4.2 AS with gradually increasing update step size . . . . . . . . . . . . . . . . . . . . . . 66 5.4.3 AS with variable update step size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.4.4 Modified ASPC algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.5 Analysis on the convergence speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.6 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.6.1 Error tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.6.2 Convergence in two-user case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.6.2.1 A note on the convergence of the ASPC-VG algorithm . . . . . . . 76 5.6.3 Performance of the ASPC algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

CHAPTER 6: Simulink Simulation Model 81

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.2 Open-loop power control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.3 Closed-loop power control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.4 Base station algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.5 System simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.5.1 Fixed Step Size Power Control “FSPC” algorithm . . . . . . . . . . . . . . . . . . 87

6.5.2 Adaptive Step Size Power Control “ASPC” algorithm . . . . . . . . . . . . . . . 89 6.5.3 AS with asymmetric update step sizes “AS-A” . . . . . . . . . . . . . . . . . . . . . 89 6.5.4 AS with gradually increasing update step sizes “AS-G” . . . . . . . . . . . . . . 89 6.5.5 AS with variable update step size “AS-VG” . . . . . . . . . . . . . . . . . . . . . . . 89

CHAPTER 7: Conclusion and Future Work 95

References 97

Appendix A 101

v

LIST OF ABBREVIATIONS AND MAIN SYMBOLS

3G 3rd Generation

AS Adaptive Step

AS-A Asymmetric Adaptive Step

AS-G Gradual Adaptive Step

AS-VG Variable Gain Adaptive Step

ASPC Adaptive Step Power Control

ASPC-A Asymmetric Adaptive Step Power Control

ASPC-G Gradual Adaptive Step Power Control

ASPC-VG Variable Gain Adaptive Step Power Control

AWGN Additive White Gaussian Noise

BER Bit Error Rate

BFA Brute-Force Algorithm

BPS Bit Per Second

BS Base Station

BTS Base Transceiver Station

CDF Cumulative Distribution Function

CDMA Code Division Multiple Access

CIR Carrier-to-Interference Ratio

CS Cell Site

CSOPC Constrained Second-Order Power Control

DB Distributed Balancing

DBR Data Burst Randomizer

DCPC Distributed Constrained Power Control

DFB Decision Feedback

DPC Distributed Power Control

DS Direct Sequence

ERP Effective Radiated Power

FDMA Frequency Division Multiple Access

FER Frame Error Rate

FLPC Forward Link Power Control

vi

FSPC Fixed-Step Power Control

IFB Information Feedback

IS-95 Interim Standard-95

MAI Multiple Access Interference

MMSE Minimum Mean Squared Error

MODPC Multi-Objective Distributed Power Control

MS Mobile Station or Mobile Subscriber

MUD Multi User Detection

PCB Power Control Bit

PCG Power Control Group

PCS Personal Communication System

PDF Probability Density Function

PMRM Power Measurement Report Message

PN Pseudo Noise

QI Quality Indicator

QoS Quality of Service

RF Radio Frequency

ROLPC Reverse Outer-Loop Power Control

RS1 Rate Set 1

RS2 Rate Set 2

RSSI Received Signal Strength Indicator

RT Random Time

SIR Signal-to-Interference Ratio

SMIRA Stepwise Maximum-Interference Removal Algorithm

SNR Signal-to-Noise Ratio

SRA Stepwise Removal Algorithm

TDMA Time Division Multiple Access

TDD Time Division Duplex

TPC Transmit Power Control

TPCB Transmit Power Control Bit

UMTS Universal Mobile Telecommunication System

vii

()T matrix transpose

COR combinational OR

e(t) power control misadjustment (error between measured SIR and SIR target) at time instant t

Eb/It bit-energy-to-interference-spectral-density ratio

(Eb/It) target target bit-energy-to-interference-spectral-density ratio

g0 imperfect power control factor

g(t) link attenuation at time instant t

gij link attenuation between receiver i and transmitter j

H normalized channel attenuation and link quality requirement matrix

I identity matrix

Iint internal interference

Iext external interference

I(t) interference power in decibels at time instant t

INIT_PWR initial Power offset

NOM_PWR nominal power offset

P transmission power vector

pout outage probability

pr received power

pt transmit power

pt, intial initial transmit power

p* optimal transmission power vector

PWR_STEP power step size

q-n processing delay

q-m propagation delay

r distance from the user to the base station

R information bit rate

Ta acknowledgment time

Tb bit time

Tc chip time

u(t) process input at time instant t

σp standard deviation of imperfect power control

viii

β power control algorithm parameter

γ signal-to-interference ratio (SIR)

γi SIR of user i

γt(t) SIR target of user i at time t

γ* maximum achievable SIR

δ power control step size

δdown downwards step size in outer-loop power control algorithm

δe error signal threshold for switching to backup controller / power control update parameter

downeδ power control update parameter downwards upeδ power control update parameter upwards

δup upwards step size in outer-loop power control algorithm

δVG variable gain update parameter

ni noise power at the receiver of user i

ncell number of cells in the service area

nu maximum number of users

η normalized noise power vector

sysη system spectrum efficiency of a cellular system

ρ(H) spectral radius of matrix H

ω(n) relaxation factor

ix

LIST OF FIGURES

Figure Title Page

1.1 A base station with two users, each user is transmitting to base station a fixed amount of power pt.

3

1.2 Received power from the two users at the base station, user 2 has a much higher SNR than user 1 does. 3

1.3 The equalization effect of power control on received powers of individual users at the base station, while they are transmitting with different power levels. 4

1.4 Capacity maximization with received powers from all users are equal at the base station. 4

1.5.a The relative power level of the signal received at a mobile unit. 6

1.5.b Variation of the signal received at a mobile unit with average path loss. 6

1.5.c Variation of the signal received at a mobile unit with shadow fading. 6

1.6 Classification of power control techniques. 8

1.7 The network block incorporates the effects caused by the radio channel, such as power gain, noise, and interfering transmitters, while q-n and q-m represent appropriate delays.

9

1.8 Reverse link open-loop power control. 10

1.9 Reverse link closed-loop power control. 12

2.1 Illustration of a two-cell CDMA system with two mobile stations. 15

2.2 Two-User Case. 16

2.3 The effect of )(Hρ and η values in the number of supported users in two user case: (a) )(Hρ < 1 and η > 0; (b) )(Hρ = 1 and η > 0; (c) )(Hρ >1 and η > 0; (d)

)(Hρ = 1 and η = 0. 18

2.4 Overview of power control algorithms. 19

2.5 Example of SIR Balancing for eight users. 21

2.6 Two-user example: Constrained power case. 26

2.7 SIR of a moving terminal (DCPC power update). 27

2.8 Convergence of the norm of the difference between the power vector and the optimal power vector P* of the DB, DCPC, CSOPC and MODPC algorithms in multi-user snapshot simulation (80 users).

28

3.1 Distribution of users and base station positions. 34

3.2 Users that can be supported for a given Eb/It requirement. 36

3.3 Capacity per cell as the fraction of dirty users increase. 37

3.4 BER versus number of users. 40

4.1 CDMA System Access. 43

x

4.2 Access Attempt, Probe Sequence, and Access Probe in Power Control. 44

4.3 A series of access probes by the mobile to access the system. 44

4.4 Effect of open-loop power control. 46

4.5

With traveling through the standing wave pattern, the mobile will experience fades once every half wavelength. Note that the standing wave pattern shown is a simple example resulting from the addition of two equally strong waves that are 180 degrees out of phase.

48

4.6 Effect of fast fading in signal strength. 48

4.7 Mobile Transmitter power as governed by the open-loop power control only. 48

4.8 In the forward traffic channel, the PCBs at 800 bps are multiplexed directly onto the baseband information stream at 19.2 Kbps. 50

4.9 Power Control Groups 50

4.10 Position of the Power Control Bits. 51

4.11 Closed-loop power control using PCBs. 52

4.12 Target Eb/It. 53

4.13 Set Point Value vs. Time. 54

4.14 Flow Chart for Reverse Link Closed-Loop Power Control. 55

4.15.a Reverse-link power-control functions carried out by the base station. 65

4.15.b Reverse-link power-control functions carried out by the mobile. 65

4.16 Flow Chart for Forward Link Power Control. 58

4.17 Forward Link Power Control for RS1. 58

4.18 Forward Link Power Control for RS2. 59

4.19 Flowchart for uplink transmit power control scheme during soft hand over. 61

5.1 Comparison of the BER performance of fixed step size, adaptive delta modulation, and inverse algorithms. 63

5.2 Flowchart of the ASPC algorithm. 65

5.3 Power evolution with various algorithms in the case p(0) = 0, u(t) = 1, t = 0, 1, 2, …. 68

5.4 Example of the power control misadjustment tracking performance of the ASPC algorithms (mobile speed 5 km/h). 71

5.5 Comparison of the convergence of the algorithms for two users and static channel. 73

5.6 Convergence of the SIR to SIR target in two-user snapshot simulation. 74

5.7 Convergence of the norm of the difference between the power vector and the optimal power vector p* with the DCPC, FSPC, ASPC and ASPC-VG algorithms in two-user snapshot simulation.

75

5.8 Power convergence comparison in two-user snapshot simulation. 76

xi

5.9 Power convergence comparison in multi-user snapshot simulation (80 users). 77

5.10 Example of a “deadlock” situation with the ASPC-VG algorithm. 78

5.11 Empirical CDF of Eb/It, mobile speeds from 0 to 5 km/h. 78



6.1 IS-95 Reverse Traffic Channel Open and Closed Loop Power Control model. 82

6.2 Base Station Controller State Machine. 84

6.3 Mobile Controller State Machine. 85

6.4 Mobile Station model using FSPC. 87

6.5 Received Eb/N0, Threshold, and mobile transmitted power for FSPC algorithm. 88

6.6 Block diagram of ASPC algorithm. 90

6.7 Received Eb/N0, Threshold, and mobile transmitted power for ASPC algorithm. 90

6.8 Block diagram of AS-A algorithm. 91

6.9 Received Eb/N0, Threshold, and mobile transmitted power for AS-A algorithm. 91

6.10 Block diagram of AS-G algorithm. 92

6.11 Received Eb/N0, Threshold, and mobile transmitted power for AS-G algorithm. 92

6.12 Block diagram of AS-VG algorithm. 93

6.13 Received Eb/N0, Threshold, and mobile transmitted power for AS-VG algorithm. 93

6.14 Variance of Eb/N0 for FSPC, ASPC, AS-A, AS-G, and ASVG before and after access intervals. 94

6.15 Variance of Eb/N0 for FSPC, ASPC, AS-A, AS-G, and ASVG when the mobile is in the conversation state. 94

A.1 Direction and magnitude of Ax with respect to λ. 101

xii

LIST OF TABLES

Table Description Page

3.1 Capacity loss for Eb/It = 12 dB and BER = 10-3. 40

4.1 Power Control Groups vs. Frame Rate. 51

4.2 ROLPC Parameters for RS1. 54

4.3 ROLPC Parameters for RS2. 54

4.4 Forward Link Power Control Parameters for RS1. 60

4.5 Forward Link Power Control Parameters for RS2. 60

5.1 General framework for the proposed power control algorithms. 67

5.2 Convergence of power with the proposed power control algorithms. 69

5.3 Simulation parameters. 70

6.1 Mobile Controller state machine parameters values 85

Chapter 1

Introduction

Ch. 1. Introduction

1

Introduction

In recent years the cellular communications market has exploded. The main goal of cellular communications systems is to enable communication services irrespective of time and location. It is already possible to imagine a subscriber who, in the near future, makes video calls to friends and colleagues from a mobile terminal while simultaneously accessing a remote data base from the same terminal, or receiving e-mails or phone calls [1]. This requires maximizing the channel capacity, and that is where CDMA technology fits in. CDMA consistently provides better capacity for voice and data communications than other commercial mobile technologies, allowing more subscribers to connect at any given time, and it is common platform on which 3G technologies are built. FDMA is band limited, TDMA is time limited whereas CDMA is interference limited [2]. The channel capacity of any cellular system is significantly influenced by the cochannel interference. To minimize the cochannel interference, several techniques are proposed: frequency reuse patterns, which ensure that the same frequencies are not used in adjacent cells; efficient power control, which minimizes the transmitted power; cochannel interference cancellation techniques; and orthogonal signalling (time, frequency, or code). All of these are being intensively researched, and some have already been implemented. Power control is the main tool used in IS-95 CDMA as an interference reduction mechanism and to combat the near-far problem. It is theoretically unnecessary to have power control if one can successfully implement a more intelligent receiver than that used in IS-95, which is the subject of the field of multiuser detection (MUD), a feature being proposed for the 3G-CDMA systems. Power control is necessary in order for a CDMA system to achieve a reasonable level of performance in practice. The use of power control in the CDMA system necessitates the use of soft handoff when the original and new channels occupy the same frequency band. For power control to work properly, the mobile must attempt to be linked at all times to the base station from which it receives the strongest signal. If this doesn't happen, a positive feedback loop could inadvertently occur, causing system problems. Soft handoff can guarantee that the mobile is indeed linked at all times to the base station from which it receives the strongest signal, whereas hard handoff cannot guarantee this [3]. The performance of CDMA systems is very sensitive to differences in received signal powers from various users on the reverse link. Due to the nonorthogonality of the spreading PN codes by different users, a strong interfering signal may mask out a weak desired signal, causing unreliable detection of the later. This is called the near-far problem. This chapter presents a survey on power control technologies for modern wireless DS-CDMA communication systems.

1.1 The Need for Power Control In cellular communication systems, the service area is divided into cells, each covered by a single base station. If, in the forward link (base station to mobile), all users served by all base stations share the same frequency, each communication

Ch. 1. Introduction

2

between a base station and a particular user would also reach all other users in the form of cochannel interference. However, the greater the distance between the mobile and the interfering transmitter, the weaker the interference becomes due to the propagation loss. To ensure a good quality of service throughout the cell, the received signal in the fringe area of the cell must be strong. Once the signal has crossed the boundary of a cell, however, it becomes interference and is required to be as weak as possible. Since this is difficult, the channel frequency is usually not reused in adjacent cells in most of the cellular systems. If the frequency is reused, the cochannel interference impairs the signal reception in the adjacent cell, and the quality of service severely degrades unless other measures are taken to mitigate the interference. Therefore, a typical reuse pattern for FDMA/TDMA-based cellular networks reuses the frequency in every seventh cell (frequency reuse factor = 1/7). The only exception is for CDMA-based systems where the users are separated by codes, and the allocated frequency may be shared by all users in all cells [4]. Even if the frequency is reused in every seventh cell, there is still some cochannel interference arriving at the receiver. It is, therefore, very important to maintain a minimal transmitted level at the base station to keep the cochannel interference low, frequency reuse factor high, and therefore the capacity of the system and quality of service high. The same principle applies in the reverse link (mobile to base station) the power control maintains the minimum necessary transmitted power for reliable communication. Several additional benefits can be gained from this strategy. The lower transmitted power conserves the battery energy allowing the mobile terminal to be lighter and stay on the air longer. Furthermore, recent concerns about health hazards caused by the portable’s electromagnetic emissions are also alleviated [4]. In the reverse link, the power control also serves to alleviate the near–far effect. If all mobiles transmitted at the same power level, the signal from a near mobile would be received as the strongest. The difference between the received signal strength from the nearest and the farthest mobile can be in the range of 100 dB, which would cause saturation of the weaker signals’ receivers or an excessive amount of adjacent channel interference, consider a single cell that has two users (see Figure 1.1). User 2 is much closer to the base station than user 1 If there is no power control, both users would transmit a fixed amount of power pt; however, because of the difference in distance, the received power from user 2, or pr,2, would be much larger than the received power from user 1, or pr,1. If we assume that the difference in distance is such that pr,2 is 10 times more than pr,1, then user 1 would be at a great disadvantage [5]. If the required SNR, (S/N)required, is (1/10), then we can immediately see the disparity between the SNRs of the two users. Figure 1.2 illustrates that point for a CDMA system where all users share the same RF band through the use of PN codes, so each user looks like random noise to other users. If we ignore thermal noise, then the SNR of user 2, (S/N)2, would be 10, and the SNR of user 1, (S/N)1, would be (1/10). User 2 has a much higher SNR and thus enjoys great voice quality, but user 1’s SNR is barely making the required (S/N)required. This inequity is known as the near-far problem in a spread-spectrum multiple access system. The system at this point is said to have reached its capacity. The reason is that if we attempt to add a third user transmitting pt anywhere in the cell, then the SNR of that third user would not be able to reach the required (S/N)required. Furthermore, if we force a third user onto the system, that third user not only will not attain the required (S/N)required, but also will cause the SNR of user 1 to drop below the required (S/N)required [5].

Ch. 1. Introduction

3

Figure 1.1: A base station with two users, each user is transmitting to base station a fixed amount of power pt.

Figure 1.2: Received power from the two users at the base station, user 2

has a much higher SNR than user 1 does.

Power control is implemented to overcome the near-far problem and to maximize capacity. Power control is where the transmit power from each user is controlled such that the transmitted power at the mobile must be adjusted inversely proportional to the effective distance from the base station. The term effective distance is used since a closely located user in a propagation shadow or in a deep fade may have a weaker signal than a more distant user having excellent propagation conditions. With power control, the received power of each user at the base station is equal to one other. Figure 1.3 illustrates the concept. In the cell, if the transmit power of each user is controlled such that the received power of each user at the base station

Ch. 1. Introduction

4

is equal to pr , then a lot more users can be accommodated by the system. As a continuation of our previous example, if the required SNR (S/N)required is still (1/10), then a total of 11 users can be supported by the cell. The capacity is maximized with the use of power control (see Figure 1.4) [5]. Figure 1.3: The equalization effect of power control on received powers of individual

users at the base station, while they are transmitting with different power levels.

Figure 1.4: Capacity maximization with received powers from all users are equal at

the base station.

Ch. 1. Introduction

5

In a CDMA system, power control is a vital necessity for system operation. The capacity of a CDMA cellular system is interference limited since the channels are separated neither in frequency nor in time and the internal interference generated within the system is inherently strong. A single user exceeding the limit on transmitted power could inhibit the communication of all other users.

The power control systems have to compensate not only for signal strength variations due to the varying distance between base station and mobile but must also attempt to compensate for signal strength fluctuations typical of a wireless channel. These fluctuations are due to the changing propagation environment between the base station and the user as the user moves across the cell or as some elements in the cell move [6]. As shown in Figure 1.5.a the received signal strength is a combination of three parts:

• A linear decrease (mean path loss) with increasing distance (assuming dB and

a log scale for distance). • A slow variation (shadowing) about the linear decrease. • A rapid variation (fading) superimposed on the other two.

The first part (see Figure 1.5.b) is a straight line component called Average Path Loss. As the receiver recedes into the distance with no other irregularities affecting propagation, the signal will go down at something close to 40 dB per decade. If there were two antennas in free space, the loss would be 20 dB per decade as the distance increases. Because of the ground, there's additional loss. The loss varies by location, but on average it is about 40 dB per decade or 1/R4 [7]. The second part (see Figure 1.5.c) is a slow variation about the Average Path Loss. This is due to the relatively large scale variations in the mobile unit's environment. Maybe the subscriber is driving behind a building and the power level falls off. Then perhaps the subscriber goes up a ramp and on to an elevated highway so the received power is relatively high. And when the subscriber gets off the elevated highway, the power drops below the Average Path Loss again. That's called Shadowing. Shadowing in a land-mobile channel is usually described as a process having log-normal distributed amplitude. It's a slow variation about the straight-line path loss curve. The third part is the high-speed quick wiggling on top of the slow variation (see Figure 1.5.c). This fading occurs because of the rapidly changing conditions in the environment, as electromagnetic waves transmitted from the transmitter may follow multiple paths on the way from the transmitter to the receiver. The different paths have different delays and interfere at the antenna of the receiver. If two paths have the same propagation attenuation and their delay differs in an odd number of half-wavelengths (half-periods), the two waves may cancel each other at the antenna completely. If the delay is an even multiple of the half-wavelengths (half-periods), the two waves may constructively add, resulting in a signal of double amplitude. In all other cases (non equal gains, delays not a multiple of half-wavelength), the resultant signal at the antenna of the receiver is between the two mentioned limiting cases. This fluctuation of the channel gain is called Fading. Since the scattering and reflecting surfaces in the service area are randomly distributed (buildings, trees, furniture, walls, etc.), the amplitude of the resulting signal is also a random variable. Since the mobile terminal may move at the velocity of a moving car or even of a fast train, the rate of channel fluctuations may be quite high and the power control has to react very quickly in order to compensate for it.

Ch. 1. Introduction

6

Power Received by Mobile Unit

(dB)

Distance (km)

80

4

1R

Figure 1.5.a: The relative power level of the signal received at a mobile unit.

Figure 1.5.b: Variation of the signal received at a mobile unit with average path loss.

Figure 1.5.c: Variation of the signal received at a mobile unit with shadow fading.

Distance (km)


(dB)

80

AveragePath Loss

AveragePath Loss4

1R

Distance (km)


(dB)

8 dB variationabout the average(log-normal shadow fading)

Ch. 1. Introduction

7

From this section we conclude that the main goal of the power control algorithm is:

1. Achieve optimum power levels in order to serve the maximum number of subscribers (i.e. maximize the channel capacity).

2. Overcome the near far problem to keep the received power of all mobiles at the base station nearly equal.

3. Track time varying channel loss (path loss, shadowing, and multi path fading). 1.2 Classification of Power Control Techniques

Several methods and strategies to control the power in cellular radio systems were proposed. When considering the power control in real systems, the following aspects are interesting [1]: • Quality measure:

Speech quality is a main criterion. People have argued that Signal-to-Interference Ratio (SIR) is an adequate objective measure, and it has been used extensively in previous works, even though it is far from ideal. For example, in the case of data transmission, bit error rate (BER) requirements can be very stringent and SIR might not be an adequate measure. If the signal and interference powers are constant BER and SIR contain equivalent information regarding quality. But in real systems the SIR is time variant and thus the average SIR will not correspond to the average BER. In this case BER is a better quality measure. • Available measurements:

Usually the measurements are given in reports comprising a quality indicator (QI) reflecting the quality and a received signal strength indicator (RSSI) reflecting the received signal strength at the receiver. These values are coarsely quantized in order to use few bits. • Constraints:

The output power levels are limited to a given set of values due to hardware constraints. This includes quantizing and the fact that the output power has an upper and a lower limit. • Time delays:

Measuring and control signaling take time, which results in time delays in the network.

Power control techniques can be classified in many different ways, as shown

in Figure 1.6.

Power control for reverse link (from mobiles to base stations) Reverse link power control manages the transmit power on a mobile's access channel and reverse traffic channel. Power control for DS-CDMA reverse link is the single most important system requirement because of the near/far effect, variations of

Ch. 1. Introduction

8

Figure 1.6: Classification of power control techniques.

up to 80 dB dynamic range can be found between different users. A method of power control with high dynamic range must be used.

Power control for forward link (from base stations to mobiles)

For the forward link, no power control is required in a single cell system, since all signals are transmitted together and hence vary together. However in multiple cell systems, interference from neighboring cell sites fades independently from the given cell site and thereby degrades performance. Thus it is necessary to apply power control in this case also, to reduce intercell interference.

Centralized power control

A centralized controller has all information about the established connections and channel gains, and controls all the power levels in the network or part of the network. Centralized power control requires extensive control signaling in the network and cannot be applied in practice. It can be used to give bounds on the performance of the distributed algorithms.

Decentralized power control

A decentralized controller controls only the power of one single transmitter, and the algorithm depends only on local information, such as measured the SIR or channel gain of the specific user. These algorithms perform well in rather ideal cases, but in real systems there are a number of undesired effects, such as: • Measuring and control signaling take time, which results in time delays in the system. • The possible output powers of the transmitters are constrained due to physical limits and quantization. Different external constraints such as the use of maximum power on specific channels affect the output power. • The signals needed for control may not be available and have to be estimated. • Quality is a subjective measure, and relevant objective measures have to be employed. The surrounding environment as seen by a decentralized controller, for example, is shown in Figure 1.7.

Ch. 1. Introduction

9

Figure 1.7: The network block incorporates the effects caused by the radio channel,

such as power gain, noise, and interfering transmitters, while q-n and q-m represent appropriate delays.

According to what is measured to determine power control command, power control techniques can be classified into three categories (Strength-based, SIR-based, and BER-based).

Strength-based power control In strength-based schemes the strength of a signal arriving at the base station from a mobile is measured to determine whether it is higher or lower than the desired strength. The command to lower or raise the transmit power is made accordingly.

SIR-based power control In SIR-based schemes the measured quantity is the SIR where interference consists of channel noise and multi-user interference. Strength-based power control is easier to implement but SIR-based power control reflects better system performance such as QoS and capacity. A serious problem associated with SIR-based power control is the potential to get positive feedback to endanger the stability of the system. Positive feedback arises in a situation when one mobile under instructions from the base station has to raise its transmit power in order to deliver a desirable SIR to the base station, but the increase in its power also results in an increase in interference to other mobiles so that these other mobiles are then forced to also increase their power, etc. In the case of N mobiles in the system, this becomes a typical non-cooperative N-person game problem.

BER-based power control In BER-based power control, BER is defined as an average number of erroneous bits compared to the original sequence of bits. If the signal and interference powers are constant, the BER will be a function of the SIR, and in this case the QoS is equivalent. However, in reality the SIR is time-variant and thus the average SIR will not correspond to the average BER. In this case the BER is a better quality measure. Since the channel coding is implemented in every practical system, power control can be based on the average number of erroneous frames as well.

Ch. 1. Introduction

10

Also, power control techniques can be classified as (Open-loop power control, Closed-loop power control, and a combined technique consisting of closed-loop and open-loop power control).

Open-loop power control

In open-loop power control the mobile user estimates the channel state on the forward link, and this estimate is used as a measure of the channel state on the reverse link, as shown in Figure 1.8 In the reverse link it estimates the channel by measuring the received power level of the pilot from the base station in the forward link and sets the transmitted power level inversely proportional to it. Estimating the power of pilot is, in general, more reliable than estimating the power of the voice (or data) channel since the pilot is usually transmitted at higher power levels. Using the estimated value for setting the transmitted power ensures that the average power level received from the mobile at the base station remains constant irrespective of the channel variations. However, this approach assumes that the forward and the reverse link signal strengths are closely correlated. Although forward and reverse link may not share the same frequency and, therefore, the fading is significantly different, the long-term channel fluctuations due to shadowing and propagation loss are basically the same [4].

Figure 1.8: Reverse link open-loop power control.

Ch. 1. Introduction

11

These techniques can compensate for path loss and large-scale variations such as shadowing, but it is not possible to compensate multipath fading because reverse and forward links are not correlated. A. Chockalingam and L. B. Milstein, “Open Loop Power Control Performance in DS-CDMA Networks with Frequency Selective Fading and Non-Stationary Base Stations, 1998 ” show that capacity degrades by 5 percent for a 1 dB open-loop power control error, by 25 percent for a 2 dB power control error, and by 44 percent for a 3 dB power control error.

Closed-loop power control

Closed-loop power control involves both the forward and reverse traffic channels, so successful optimization of the algorithm requires the simultaneous simulation of both these physical layer channels [8]. Closed-loop power control is feasible in a terrestrial cellular environment. However, in mobile communications systems using multiple low earth orbital satellites, the fades occur too rapidly for the closed-loop power control to track, due to the large round trip propagation delay. In this case, the solution is open-loop power control.

The closed-loop power control system (Figure 1.9) may base its decision on an actual communication link performance metric, e.g., received signal power level, received signal-to-noise ratio, received bit-error rate, or received frame-error rate, or a combination of them. In the case of the reverse link power control, this metric may be forwarded to the mobile as a base for an autonomous power control decision, or the metric may be evaluated at the base station and only a power control adjustment command is transmitted to the mobile. If the reverse link power control decision is made at the base station, it may be based on the additional knowledge of the particular mobile’s performance and/or a group of mobiles’ performance (such as mobiles in a sector, cell, or even in a cluster of cells) [4]. A special case for the design of power control is TDD-based systems. In TDD systems, the forward and reverse links are highly correlated, and therefore a very good estimate of the channel gain in the forward link can be obtained from the estimate of the reverse link gain and vice versa. An open-loop power control then performs with the precision of a closed-loop power control but much faster since no feedback information has to be transmitted. According to update strategies, power control algorithms can be classified as follows [1]: • Those where the transmit power step size is fixed (fixed step size algorithm). • Those where the transmit power step size is made adaptive to the channel variation.

Fixed step size power control

Power control command in fixed step size algorithms is a simple 1-bit command. It has been shown that the inverse algorithm is superior to the fixed step size algorithm by [9]. However, the fixed step size algorithm is easier to implement because the inverse algorithm needs additional bandwidth on the return channel to carry the power control step size instead of the 1-bit control command as in fixed step size algorithm. A compromise would be to use an adaptive delta-modulation algorithm.

Ch. 1. Introduction

12

Figure 1.9: Reverse link closed-loop power control.

Adaptive step size power control

A specific example of the adaptive step size approach is the inverse update algorithm, which increases or decreases the mobile users’ transmit power by the actual difference between the received signal power and the desired received signal power. Power control can be also classified as follows: • Power control where the transmit power level is controlled in continuous power domain. • Power control where the transmit power level is controlled in discrete power domain.

Continuous and Discrete power control In practice transmission power in digital systems can be updated only at discrete levels. It has been shown in [10] that by simple discretization of continuous power control algorithm using a function ceiling (rounds toward plus infinity) and

Ch. 1. Introduction

13

function floor (rounds toward minus infinity), the convergence and uniqueness of the continuous power control algorithm are lost. The discrete ceiling power control algorithm converges in a weaker sense, i.e., into an envelope of power vectors rather than to a unique vector. The transmitter powers under this algorithm may oscillate, which results in a poorer link quality and in a higher outage probability. In order to alleviate these oscillations, it has been proposed to start updating the powers according to the floor algorithm from any initial power vector until the first entry into the envelope of power vectors, and then to continue with the ceiling algorithm [1]. Power control can be applied in circuit-switched and packet-switched modes of operation. Among various multimedia services circuit switching is suitable for delay-sensitive and long-holding-time media, such as voice, video and large-size file transfer. Packet switching is suitable for delay-less-sensitive and short-holding-time media. Packet communications are provided to bursty information sources, which are characterized as on-off processes, and transmission is discontinued at the end of the data burst and no information is transmitted during the unpredictable off interval. In some cases, synchronization information may be transmitted during these off intervals. Because it is possible to have large intervals between the transmission of consecutive packets, it is very difficult to employ closed-loop power control. The validity of feedback information for closed-loop power control decreases as the interval between packets increases.

1.3 Thesis Outline

This thesis consists of seven chapters and is organized as follows: Chapter 1 gives an introduction about the vital necessity of power control in CDMA cellular communication systems and represents different ways of classifying power control techniques. Power control problem formulation is discussed in detail in Chapter 2, which gives the necessary background to understand the contributions made in the thesis. A literature survey of previous work in this area is also provided. In Chapter 3 some special cases are studied such as power control imperfections and inefficient users that demand more than the average power requirements (dirty users) and its effect on the overall CDMA system capacity have been investigated. Power control in IS-95 CDMA cellular communication system is discussed in detail in Chapter 4. Chapter 5 introduces the Adaptive Step (AS) method and the corresponding Adaptive Step Power Control (ASPC) algorithm. Various modifications to improve the properties of the algorithm are given, and some simulation examples demonstrating these properties are provided. A Simulink simulation model of the algorithms from Chapter 4 and Chapter 5 is provided in Chapter 6. Finally, summary and conclusions are given in Chapter 7 with comments about open issues.

Chapter 2

Theoretical Review of Power Control

Ch. 2. Theoretical Review of Power Control

14

Theoretical Review of Power Control

2.1 Introduction Since all signals in a DS-CDMA system are sharing the same bandwidth and

overlapping in time, it is essential to exercise some kind of control of the transmission powers to maintain acceptable signal-to-interference ratio (SIR) for all users, hence maximizing the system capacity by minimizing the outage probability (the probability that a call will have to be dropped due to inadequate SIR level) [11].

Some of the early work in power control was reviewed in Zander [12]. In Kim, Wu, and Grandhi, centralized power control was studied, and due to the complexity of the system, centralized power control was suggested only for providing theoretical limits [13, 14, 15]. When all users could be accommodated with acceptable signal-to-interference ratios, Foschini suggested a convergent distributed-power-control algorithm to compute the required transmission power of each mobile station [16]. Jeantti presents a second-order constrained power control (CSOPC) algorithm [17]. This approach uses the current and past power values to determine the necessary transmission power of each mobile. CSOPC was compared with the algorithm presented in Foschini and was shown to converge at a faster rate. Convergence analysis of distributed power-control algorithms is investigated in Huang [18]. Yates presented a framework for uplink power control in cellular radio systems [19]. Our review to solving the power control problem will be within such framework.

In general, the problem is related to both link directions, uplink and downlink. However, as our focus in this chapter lies in the investigation of the uplink, it will always assume an uplink scenario, where the transmitters are the MS and the receiver is the BS. In this chapter theoretical review of power control that can be found in the literature has been discussed.

2.2 Problem Formulation

Consider a receiver i and a transmitter j with a link gain gij between i and j. Further, assume there are K transmitters, where transmitter j uses a power Pj. All transmission powers of the transmitters can be arranged as a transposed vector,

P = (P1, P2, … , PK) T (2.1)

Clearly, P has non-negative components (they are powers). In uplink, Pj means the transmission power of terminal j. In downlink, it denotes the transmission power dedicated to terminal j by the BS to which terminal j is connected. SIR which is now at receiver i can be derived to be [20],


15

∑

≠=

+=Γ K

ijjijij

iiii

nPg

Pg

,1

(2.2)

where ni denotes the noise power at receiver i.

The transmitter i is said to be supported if it has a SIR satisfying, ii γ≥Γ (2.3)

where γi is a target threshold indicating the lowest acceptable link quality for user i. Combining equations (2.2) and (2.3) and solving for Pi yields the minimal transmission power that transmitter i should use to achieve the target SIR,

⎟⎟⎠

⎞⎜⎜⎝

⎛+≥ ∑

≠=

K

ijj ii

ij

ii

ijii g

nP

gg

P,1

γ (2.4)

Now, consider a system with only two mobile stations MS1 and MS2 and two base stations BS1 and BS2 as shown in Figure 2.1. Assume that MS1 is connected to BS1 and MS2 is connected to BS2, The uplink of the system is denoted by the gain matrix G [20]:

⎟⎟⎠

⎞⎜⎜⎝

⎛=

38.006.005.033.0

G

The target SIR = γi and the receiver noise are 6 dB and 0.1 W, respectively. The power values that both terminals should use are given by:

04.16249.03826.0

1.03826.00602.06

21.16465.03288.0

1.03288.00534.06

1122

21

22

212

2211

12

11

121

+=⎟⎠⎞

⎜⎝⎛ +=⎟⎟

⎠

⎞⎜⎜⎝

⎛+≥

+=⎟⎠⎞

⎜⎝⎛ +=⎟⎟

⎠

⎞⎜⎜⎝

⎛+≥

PPdBgn

Pgg

P

PPdBgnP

ggP

i

i

γ

γ

Figure 2.1: Illustration of a two-cell CDMA system with two mobile stations.


16

Figure 2.2: Two-User Case. As shown in Figure 2.2 there are four regions:-

- Region A: If both terminals’ powers are in A, both will be supported. - Region B and C: If both are in B or C, only terminal 1 or 2 can be supported. - Region D: If both are in D, neither terminal can be supported.

The feasible region is the gray area in the figure (Region A), and the optimal (minimum power) solution P* = )( *

2*

1 , PP = (3.1657, 3.0235) is in the intersection of the two lines. The optimal power minimizes the sum of transmission powers of the two terminals [21].

In order to formulate the power control inequalities for all users, It was introduced a K×K non-negative normalized link gain matrix H= (hij) such that

⎪⎩

⎪⎨⎧

=

≠=jifor

jiforgg

hii

iji

ij

,0

,γ

and the normalized noise vector η = )( iη such thatii

iii g

nγη = . The equation (2.4) can now

be expressed with the new variables as

( )∑ =+≥

K

j ijiji PhP1

η (2.5)


17

Equation (2.5) can be expressed in vector matrix notation for all K inequalities as

( ) ηPHIη,HPP≥−+≥ or

(2.6)

where I denotes the identity matrix and the inequality holds component-wise. A minimum power solution corresponds to the case where (2.6) is satisfied with equality. This is desirable, as it saves energy and thus prolongs the mobile station battery life.

It can be observed that in some cases if the target SIR or the link gain increases, not all users can be accommodated by the system. One of the main goals of power control is therefore to find a power vector such that the number of supported users is maximized. This feature is reflected in the following definition [20].

Definition 2.1 The target SIR, γi is said to be achievable if there exists a non-negative power vector P such that ii γ≥Γ for all i.

The definition says that the target SIR, γi is achievable if there exists power vector P such that for ( ) ηPHI ≥− , denote the eigenvalues of H by λi and the spectral radius, which also is the largest eigenvalue of H, by ii λρ max)( =H .

Properties of H (Matrix iterative analysis):

1. H is an irreducible nonnegative K×K matrix. 2. H has a positive real eigenvalue = )(Hρ . 3. For the eigenvector e corresponding to )(Hρ , e > 0. 4. )(Hρ increases when any entry of H increases.

5. If 1)( <Hρ , then I-H is nonsingular and ∑∞

=

− +++==−0

21)(k

k KHHIHHI

is convergent. Conversely, if the series on the right converges, then )(Hρ <1 6. If )(Hρ <1, then 0lim =

∞→

n

nH

7. If H ≥ 0 and α > 0, then the following are equivalent: 1- ,α)( <Hρ 2- H-Iα is nonsingular and ( ) 0α 1 >−H-I .

The following proposition can now be stated

Proposition 2.2 The target SIR, γi is said to be achievable if the dominant (also the largest) eigenvalue of H, denoted by )(Hρ , is less than or equal to one [20].


18

The case )(Hρ =1 will make γi achievable only when the receiver noise is zero, otherwise infinite transmission power would be required. Naturally, in practice there always exists an upper limit for the transmission power.

Apply the previous proposition to ( ) ηPHI ≥− and solving for P we get,

( ) ηHIP 1* −−= (2.7)

According to property No. 4 of H, which states that )(Hρ increases when any entry of H increases. It can be concluded that either the target SIR, γi or the link gain (path loss) gij increases, and thus it becomes difficult to achieve the target SIR, γi [21]. Figure 2.3 illustrates this.

4 4

2 users can be supported

1 user at most is supported

3.5 3.5

3 3

2.5 2 .5

P2 P2 2 2

1 .5 1.5

1 1

0.5 0.5

0 0 P1

2 2 P1

2.5 4 1 2.5 4 0 0.5 0 0.5 1.51.5 3 3.5 3 3.51

(a) (c)

4 4

1 user at most is supported

2 users can be supported trivial case

3.5 3.5

3 3

2.5 2.5

P2 P2

2 2

1.5 1.5

1 1

0.5 0.5

0 0 0 1 2

P1

2.5 4 2 P1

1.5 3.5 0.5 1 2.5 3 4 0 0.5 1.5 3 3.5 (d) (b)

Figure 2.3: The effect of )(Hρ and η values in the number of supported users in two user case [21]: (a) )(Hρ < 1 and η > 0; (b) )(Hρ = 1 and η > 0; (c) )(Hρ >1 and η > 0;

(d) )(Hρ = 1 and η = 0.


19

Power Control Algorithms

e.g. SIR Balancing with - Optimal removal - Stepwise removal - Sequential removal

Global link info )(GfP =

Limited link info ),( )()()1( nnn PfP Γ=+

CooperativeCentralized Distributed

Very limited link info ),( )()()1( n

in

in

i PfP Γ=+ e.g. Discrete Constrained Power Control (DCPC)

Figure 2.4: Overview of power control algorithms. There are in general three different categories of approaches to solve the power

control problem. These methods depend on the link information that is available at the computation time. The methods are shown in Figure 2.4 and consist of the centralized, cooperative, and distributed methods [20].

The centralized power control methods assume a global knowledge of the link gain matrix G and permit an instantaneous computation of the entire power vector P. Although an optimum solution is possible with this method, it has several drawbacks which make it less practical for implementation.

Due to these drawbacks, other algorithms are considered that require less link information and therefore also a more limited data flow, such as the cooperative or the distributed algorithms. However, this limited link information leads to a decrease in performance as well. The following sections provide a detailed introduction to all three methods.

2.1 Centralized Power Control

In order to find a solution to the power control problem, the first approach we

discuss is the class of centralized algorithms. In this category, the entire power vector P is controlled by a central controlling unit. This unit requires that each base station reports the current link information in order to perform the power assignments for the whole (or parts) of the network. The information of each link is stored in a global link gain matrix G which permits the computation of an optimal assignment. However, the drawbacks are a significant amount of control information, introduced delays, and the high complexity due to finding a solution for the entire network.

The centralized approach is based on Aein [22] dealing with satellite communication. Here, the term SIR balancing is introduced which leads to the formulation as an eigenvalue problem. Nettleton and Alavi [23] extended this approach to spread spectrum communication systems and showed that SIR balancing substantially improves the capacity of the system. Zander [12] discussed that centralized algorithms can be considered as the optimal solutions to power control in the sense that the interference is minimized.


20

2.1.1 Centralized SIR-Balanced Power Control A widely studied approach to transmission power control is the SIR balancing

problem, i.e., how to set the transmission powers so that all users in the system have equal SIRs. This method is applicable for circuit-switched real-time services like voice, where the data rate is fixed. The SIR balancing concept was proposed for satellite communications systems and it was shown that SIR balancing can improve the capacity of spread spectrum cellular mobile radio systems. However, SIR balancing may result in the catastrophic case, where the balanced SIR is too low for satisfactory reception for all users in the system. This problem was studied, and a power control strategy was proposed that is optimal in the sense that it minimizes the outage probability, i.e., the probability that a randomly chosen user has a SIR less than a given threshold. The use of the optimal power vector P* results to all users in the system having the same SIR. If the power control problem is not feasible, this results in the disastrous case that none of the users achieve the SIR requirement. To prevent this, a removal strategy must be employed, which removes transmitters from the channel until the power control problem has been solved. The problem is to select which transmitters to remove. An intuitive approach is to remove those transmitters that produce the largest interference, i.e., transmitters having the worst link quality. Note that a removal of a transmitter from a channel does not necessarily mean that the connection is broken, but it can be handed over to another channel [20, 24].

Consider now equation (2.6) with the main goal is to maximize the minimum SIR in all links. It can be proved that such a power control is achieved by making every transmitter’s received SIR balanced while keeping the SIR level as high as possible, see [21]. For the sake of simplicity we consider a noise-less case in the following, (i.e. η = 0), and the same target SIR value for all users, i.e. 0γγ =i for all i. If a matrix A was defined, such that H = γ0 A. Zander and Kim [21] gave a proof that the inequality

( ) 0PAI ≥− 0γ (2.8) The inequality (2.8) has a solution P ≥ 0 if and only if

( )*

01 γ

ργ =≤

A (2.9)

where )(Aρ is the dominant eigenvalue of matrix A.

The power vector satisfying equation (2.8) with equality and achieving the largest SIR γ* for all links is P*, i.e. the eigenvector corresponding to the eigenvalue )(Aρ , the eigenvalue problem is described in Appendix A.

If the maximum achievable SIR γ* lies for all links above the target SIR γ0, all links reach acceptable performance. On the other hand, if γ*< γ0, all links would drop below γ0 and SIR balancing would be catastrophic, see Figure 2.5 taken from [21]. The occurrence of such an event is an indication that the channel can not support the number of links. In such a case it is necessary to remove certain terminals in order to maximize the number of connections with sufficient SIR [20].


21

Figure 2.5: Example of SIR Balancing for eight users [21].

2.1.2 Transmitter Removal Methods

Now an overview over transmitter removal algorithms can be provided, where users are removed from the system in order to achieve a sufficient SIR balancing for all other users. In the following a subscript index was added to the values which indicates the number of users that are SIR-balanced, i.e. A(K) denotes the matrix A from equation (2.8) for K users and is thus K×K in dimension [20].

Brute-Force Algorithm

The first method was considered is by Zander [12] and can be considered the most fundamental algorithm.

Brute-Force Algorithm (BFA)

1. Determine γ* corresponding to matrix A (K).

If use the eigenvector P0*

)( γγ ≥K*

(K) and terminate. 2. Set k = 1.

While k < K, find the submatrix )(

~kK−A that will yield the highest achievable SIR )(

~kK −γ .

If 0)(~ γγ ≥−kK , then use *

)(~

kK−P and terminate, otherwise set k = k +1.


22

The Brute-Force Algorithm (BFA) is considered to be an optimum removal algorithm as it tries to find a largest square submatrix of A by removing as few MSs as possible. However, this problem without heuristics is not suitable for practical implementation.

Stepwise Removal Algorithm (SRA) In the Stepwise Removal Algorithm (SRA), see [21], the MS k is removed for which the maximum of the row and column sums is maximized.

Stepwise Removal Algorithm (SRA) 1. Determine γ* corresponding to matrix A (K).


)( γγ ≥K*

(K) and terminate.

2. Set k = 0 and )()(~

KK AA = . While k < K,

form submatrix )1(~

−−kKA from )(~

kK−A by removing MS l for which

{ } iaai ,~aa Ti

kK

jj

kK

j

Tj ∀≥

⎭⎬⎫

⎩⎨⎧

== ∑∑−

=

−

=

,~max~~,~~max11

llll AA

i.e. remove terminal , for which the maximum of the row and column sums in

l

)(~

kK−A .

If 0)1(~ γγ ≥−−kK , then use eigenvector *

)1(~

−−kKP and terminate, otherwise set k=k+1.

The SRA seeks to maximize the lower bound for γ*and shows linear complexity

in the computation of the eigenvalues. However, full knowledge of the link gain matrix is necessary in order to calculate its eigenvalues.

Stepwise Maximum-Interference Removal Algorithm (SMIRA) Another variation of a transmitter removal algorithm is given in Lee, Lin, and Su [25]. This method is called the Stepwise Maximum-Interference Removal Algorithm (SMIRA) and considers also the transmitter power for the removal process. The idea behind this method is that MSs transmitting with a high power should be removed first as they cause the highest interference.

The transmitter removal methods are not limited to centralized methods, but can also be used in combination with the distributed methods which will be presented in the following section.


23

Stepwise Maximum-Interference Removal Algorithm (SMIRA) 1. Determine γ* corresponding to matrix A (K).


)( γγ ≥K*

(K) and terminate.

2. Set k = 0, )()(~

KK AA = and )()(~

KK PP = . While k < K,

form submatrix )1(~

−−kKA from )(~

kK−A by removing MS l for which

{ } iaa~aa Tii

kK

jj

kK

j

Tj ∀≥

⎭⎬⎫

⎩⎨⎧

== ∑∑−

=

−

=

,~,max~~~,~~~max11

j lllll APAP

If 0)1(~ γγ ≥−−kK , then use eigenvector *

)1(~

−−kKP and terminate, otherwise set k=k+1.

2.2 Distributed Power Control

So far it was assumed that the link gain matrix G is known and that the power assignments can be done with the knowledge of G. However, in reality this is not feasible. Foschini and Miljanic [16] therefore suggested an iterative method which is based on the Jacobi relaxation method used in linear algebra.

Assume that we have an ideal situation in equation (2.6) with minimum transmission powers of all users [20].

( ) ηPHI =− (2.10)

It was further assumed that the receiver noise is not negligible and a solution P* >

0 exists. This implies that 1)( <Hρ and that the matrix (I - H) is non-singular. Then the solution of the power vector can be given as

(2.11) 0ηHIP ≥−= −1* )(

The Jacobi relaxation method provides an iterative solution by using two matrices

L and M such that (I - H) =L - M, where L is non-singular and iterating over for . )(nP K,1,0=n

(2.12) ,1)(1)1( ηLMPLP −−+ += nn

where (2.13) ηLMPLP 1*1* −− += Replacing the matrices L and M by I and H yields the Distributed Power Control (DPC) method for . K,1,0=n


24

(2.14) ηHPP +=+ )()1( nn

∑

∑

≠=

+

≠=

+

+==

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

K

ijji

njij

niiin

in

ini

ni

K

ijji

njij

ii

ni

Pg

PgwherePP

Pgg

P

,1

)(

)()()(

)(0)1(

,1

)(0)1(

ηγ

γγ

ηγ

(2.15)

Proposition 2.3 On the convergence of DPC, for an achievable target SIR γ0, the error vector tends to the zero vector starting with any ε*)()( PP −= nnε (0) if and only if . 1)( 1 <− MLρ

The speed of the convergence is very important, since the link attenuations are changing all the time. For the iteration in (2.12), it can be shown that the smaller the , the faster the convergence. Hence the task is to find L and M such that

and as small as possible. )( 1ML−ρ1)( 1 <− MLρ

2.2.1 Constrained Power Control

So far the transmitter power was assumed to be adjustable without limitations. In

reality, however, due to the limited transmitter power, an upper bound exists. This leads to the introduction of the following constraint [20]:

(2.16) ,maxPP0 ≤≤ where is the vector of each transmitter’s maximum power boundary.

),,( maxmax1

maxKPPP K=

The Distributed Constrained Power Control (DCPC) is given as:

K,1,0,min max)()(

0)1( =⎭⎬⎫

⎩⎨⎧

=+ nPPP in

ini

ni γ

γ (2.17)

With equation (2.17) a transmitter is limited by the maximum power when trying

to achieve the target SIR. Unfortunately, the observed user may not recover very fast from his bad link situation and transmits for a longer period with maximum power. This in turn could cause severe interference for the other users and therefore, Zander and Kim [21] recommend a more general variant of the DCPC which sets the power to a predefined value iP~ rather than the maximum value . max

iP


25

⎪⎪⎩

⎪⎪⎨

⎧

>

≤=+ ,~

,

max)()(

max)()(

)()(

)1(

in

ini

ii

in

ini

inin

i

i

ni

PPifP

PPifPP

γγγγ

γγ

(2.18)

where max~0 ii PP ≤≤ . The constrained power control algorithm equation (2.18) will converge to the solution of equation (2.10) starting with any non-negative power vector, when the system equation (2.10) has the unique solution P* within the power range in equation (2.16).

2.2.2 Distributed SIR-Balancing and Transmitter Removal

Similar like in Section 2.3.1 for the centralized method, a SIR balancing can be performed for the distributed approach as well.

Zander and Kim [21] present the Distributed Balancing Algorithm (DB) with the following iteration step.

,,1,011. )()()1( K=⎟⎟

⎠

⎞⎜⎜⎝

⎛+=+ nPP n

i

ni

ni γ

β (2.19)

where β > 0 is a constant for tuning the convergence. It is shown in [26] that

*)(*)( limlim γγ ==∞→∞→

n

n

n

nandPP

starting with any arbitrary power vector.

One problem that arises is that in DB all transmitter powers increase if not correctly balanced by the parameter β. The selection of

K,1,01

1

)(

)( ===

∑=

nP

K

i

ni

nββ

ensures a constant sum of all terminal powers.

Computing this might not be possible in a distributed way. Consider the example of section 2.2, what happens if the max power transmission of terminals is 2.5W as shown in Figure 2.6. Power vector (3.1657, 3.0235) supports both users with the minimal power consumption. In this example DCPC converges to power vector (2.5, 2.5), which supports neither of the users. No user is supported, but transmitters are consuming energy, this is called cocktail effect especially in DS-CDMA [21].

The question how to react when the target SIR is not achievable within the power range arises here as well. In congested situations when the interference level is high, some of the users should also be removed like in the centralized case, so as to support the remaining users. As previously mentioned the algorithms from section 2.3.2 can be used to perform transmitter removal in distributed power control.


26

Figure 2.6: Two-user example: Constrained power case. 2.2.3 Aiming for faster convergence The DPC algorithm was the first practical one to solve the problem of SIR

balancing in a fully distributed manner. After that many efforts have been devoted for finding algorithms with faster convergence. Faster asymptotic average rate of convergence [27] is achieved by finding an iteration matrix L-1M with smaller spectral radius ( ) -1MLρ Jäntti [27] shows that ( ) -1MLρ for the DPC algorithm is smaller than for the DB algorithm, thus the DPC algorithm has faster convergence.

For some algorithms it is difficult or even impossible to find the rate of convergence analytically, and one must resort to simulations to study the convergence, Figure 2.7 shows an example for DCPC system of 27 hexagonal cells with the cluster size N=7 and the cell radius 1 km. Terminals are moving around with mean speeds 0, 5, 20 m/s. DCPC update is done at the terminals every second with the target SIR 10 dB. Maximum peak transmission of terminals is 3 dBm; the receiver noise at the base stations is -118 dBm. Power low is assumed (α = 4) and the standard deviation for the log normal fading is set to 6 dB. One terminal is chosen, simulation runs for 50 updates (50 seconds).

As shown in Figure 2.7 the link gain matrix varies before the DCPC converges so that fast convergence is important, since the power control algorithms are in practice operating in a dynamical system with random variations. However, the convergence of the algorithms has been mainly studied in a static environment, assuming that the variations in the radio channel power gains are slow in comparison with the power control dynamics and can thus be neglected [21].

In [17] a power control algorithm is proposed with faster convergence properties than the DPC algorithm. The algorithm differs from the first-order algorithms described above in the sense that it requires the current and the previous power levels to calculate the next one. The scheme is called the Constrained Second-Order Power Control (CSOPC) Algorithm. It is described as follows.


27

Figure 2.7: SIR of a moving terminal (DCPC power update).

The Constrained Second-Order Power Control (CSOPC) Algorithm:

K,2,1,)1(,0max,min )1()()(

0)()(max)1( =⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−+= −+ nPPPP n

in

ni

nnii

ni ω

γγ

ω (2.20)

where ω(n) is called the relaxation factor, and is a decreasing sequence such that 1 < ω(1) < 2 and . 1lim )( =∞→

nn ω

Another algorithm with faster convergence properties is proposed in [28]. The

algorithm is called the Multi-Objective Distributed Power Control (MODPC) Algorithm, and is based on multi-objective optimization framework. Its convergence was shown to be faster than that of the DCPC. The MODPC algorithm is described as follows.

The Multi-Objective Distributed Power Control (MODPC) Algorithm:

K,1,0,)1()1(

,min )()(0

min)(max)1( =⎟⎟

⎠

⎞⎜⎜⎝

⎛−+−+

=+ nPP

PPP ni

ni

inii

ni γλλ

γλλ (2.21)

where is the minimum allowed transmission power of transmitter i, and miniP ]1,0[∈λ is a

weighting parameter.


28

Note that selecting λ = 0 yields the DCPC algorithm. The MODPC algorithm was extended to jointly control power and data rate [24]. A drawback of the MODPC algorithm is that for λ > 0 the algorithm converges to a smaller SIR balance than the DCPC algorithm (here it is assumed that the power control problem is feasible within the power limits). To see this, rewrite (2.21) in steady-state case, resulting in:

ii

iii P

PPP

γλλγλλ

)1()1( 0

min

−+−+

= (2.22)

0min

0 )(1

γλ

λγγ ≤−−

+= iii PP (2.23)

Therefore, unless or λ = 0, thenminii PP = 0γγ <i .

Figure 2.8 shows the simulated convergence of the DB, DCPC, CSOPC and

MODPC algorithms in a multiuser case with 80 users, averaged over 100 realizations. The CSOPC clearly outperforms the other algorithms in terms of convergence speed. The MODPC has also fast convergence, but it converges to a slightly different power vector than the other algorithms, as discussed in the previous Section. The DCPC has only slightly faster convergence than the DB algorithm [24].

Figure 2.8: Convergence of the norm of the difference between the power vector and the

optimal power vector P* of the DB, DCPC, CSOPC and MODPC algorithms in multi-user snapshot simulation (80 users) [24].


29

2.3 Cooperative Power Control

The methods by Zander [26] and Grandhi, Vijayan, and Goodman [29] described in the previous section require a normalization factor to scale the user’s power to a desired range without which no convergence can be achieved. Although both methods belong to the category of distributed power control algorithms, the computation of this normalization factor requires in both cases global link information.

To avoid this shortcoming of a global information exchange, Wong and Lam [30] propose the Cooperative Power Control algorithm, where only limited control data flows are passed among the BSs which are interconnected by a wired backbone network. The underlying network structure, which the authors refer to as control data flow structure is represented as a directed graph. The aim is to keep the information exchange due to control data traffic to a minimum.

2.3.1 Basic Cooperative Power Control The basic algorithm starts with each MS transmitting at the maximum power

level , which is then reduced until convergence is reached. At each iteration step, every BS computes its current power level based on the level from the previous iteration, its current SIR, and the SIR information it receives from its neighbors within the control data flow structure.

maxiP

Each MS i adjusts its power then according to the following rules:

,,minmax,min

)(

0)()(

)(

)()()1(

max)0(

mn

i

njNj

ni

ni

ni

ni

ni

ii

iwhere

PP

PP

Γ

⎟⎠⎞

⎜⎝⎛ ⎟

⎠⎞⎜

⎝⎛ ΓΓ

=

=

=

∈

+

γα

α (2.24)

with Ni being the set of indices of BS that send control data information to BS i according to the control data flow structure. The purpose of the parameter is to control the rate of convergence.

1≥m

2.3.2 Modified Cooperative Power Control Algorithm

This basic approach is later extended by Sung and Wong [31] with the difference

that the algorithm does not start with the maximum power and iteratively decreases the power until convergence, but instead it starts with the minimum power and monotonically adjusts the level upward until the SIRs are balanced. The advantage of this variation is that less battery power is used and that the disturbance to the balanced system by the admission of a new user is minimized.


30

,,maxmax,min

)(

0)()(

)(

)()()1(

min)0(

mn

i

njNj

ni

ni

ni

ni

ni

i

i

cwhere

PP

PP

Γ

⎟⎠⎞

⎜⎝⎛ ⎟

⎠⎞⎜

⎝⎛ ΓΓ

=

=

=

∈

+

γα

α (2.25)

Here, a constant c is additionally introduced for the convergence of the algorithm.

The condition c < 1 ensures that the limit )(lim nin P∞→ exists and therefore converges to a

fixed point. The condition c < 1 – ε for an arbitrary small value ε ensures that the fixed point achieves SIR balancing.

2.1.1 Asynchronous Cooperative Power Control

The cooperative algorithms presented so far require a synchronous operation of the power updates. An extension to asynchronous operation is presented in [31] as well. This permits that power levels can be changed in different time and rate among each link and the control data for the SIRs can be sent at a different rate than the power updating. The modified algorithm of the cooperative power control just needs to replace the synchronous SIR measurements )(n

iΓ by delayed SIR measurements )(),(~ ijdnj

nij

−Γ=Γ for some delay dij ≤ dmax bounded by the maximum delay dmax.

Convergence of the asynchronous approach to finite values is proved by Sung and Wong [31], however, it is required that the rate of convergence must be faster than the rate changes in the link gain matrix, e.g. due to shadow fading. Additionally, studies were performed that investigated the convergence behavior. When users depart from the system and all other users have high SIR values above a certain requirement γ~ (protection ratio), the SIR balancing will result in unnecessary high SIR values for the users. Since all users already had satisfying SIR levels, a further increase is not necessary. Therefore, the cooperative algorithm can be further modified to also avoid this effect:

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

Γ

≤ΓΓ

⎟⎠⎞⎜

⎝⎛ ΓΓ

=

=

=

′

′ ∈

+

.,

,,max,max

)(0

0)(

)(

0)()(

)(

)()()1(

min)0(

otherwise

ifc

where

PP

PP

m ni

ni

mn

i

njNj

ni

ni

ni

ni

ni

i

i

γ

γγ

α

α (2.26)

Here, we again use γγ ~

0 ≥ as the target SIR. With this modification the transmit power of an MS will decrease if its received SIR at the BS is higher than 0γ . Therefore, in


31

a dynamic situation with a fluctuation of users entering and leaving the system, the power levels of the users in the system will not go to infinity.

2.1 Joint Power and Rate Control

So far the same target SIR was assumed for all users. This is a valid assumption

when considering second generation systems with only a single class of users. However, in 3G systems each user will access different services with different transmission rates and error requirements. Therefore, the radio resource management needs to assign each user his own target SIR level [20].

Rate adaptation sets the data rate Ri of user i with a monotonically increasing modem-dependent function )( if γ of the SIR γi

( ).ii fR γ≤

The following two definitions are given by Zander and Kim [21] to describe if a rate vector )( maxPR is achievable for a maximum power vector Pmax.

Definition 2.4 A rate vector ),,()( 1

maxKRR K=PR is instantaneously achievable if

there exists a positive power vector max1 ),,( PP ≤= KPP K such that ( ) .ifR ii ∀≤ γ

Definition 2.5 A rate vector ),,()( **

1max

KRR K=PR* is achievable in the average sense if it may be expressed as ∑=

kkk RR ~* α where [ ] 11,0 =∈ ∑

kkk αα and where

all kR~ are instantly achievable rate vectors.

This definition implies using the set of instantly achievable rate vectors kR~ and switching between them during a fraction of time kα in order to get the average rate )( maxPR* .

There is also a constraint on the data rate. Unlike the transmission power which is bounded by the performance of the amplifier, each link requires a minimum data rate minR i . Additionally, the service provider aims at offering as much excess data as possible to his customer. This leads to another optimization problem in the context of joint power and rate control.

( )

( ) itosubject ii

K

ii

∀≥

∑minmax*

max*

RR

Rmax

P

P (2.27)


32

Work on joint power and rate control in the form of a constraint optimization problem can be found by Sampath, Kumar, and Holtzman [32]. The authors define the optimization problem as

∑∑==

K

ii

K

ii RorP

11maxmin

Subject to

Qos constraint: iPg

PgRW

iK

ijjjij

iii

i

∀≥

∑≠=

,

,1

γ

Rate constraint: iRR ii ∀≥ ,min Power constraint: iPP ii ∀<< ,0 max

Note that in this case the SIR in the QoS constraint is understood as tb IE . The proposed method is a centralized scheme, where knowledge of the link gain matrix is assumed. The authors consider the following criteria for optimization:

• Minimization of the total transmitted power, • Maximization of the sum of the transmission rates.

The given problem can be solved by linear and non-linear programming methods and

in the case that the system is not feasible, some users must be rejected or the constraints need to be relaxed [20].

Chapter 3

Case Studies

Ch. 3. Case Studies

33

Case Studies

3.1 Introduction

The downlink is the limiting link with respect to capacity of 3G systems. This

means that poor power control or inefficient users that demand more than the average power requirements (dirty users) will subsequently affect the overall capacity of DS-CDMA system [33]. For this reason the downlink system capacity is investigated and the effect “dirty users” have on the system capacity. Also the effect of imperfect power control on system capacity is studied.

3.2 The Dirty User Problem

Poor terminal design leads to the “Dirty User Problem”, where a terminal requests

more power from the base station than alternate terminals located at the same position. This dirty user causes higher interference on all other users in the cell and ultimately limits the capacity of the forward link of a DS-CDMA system. In this section we will investigate this effect and determines the performance degradation as the number of dirty users increase and/or if their power requirements were to increase. In [33] a statistical channel model including path loss and log-normal fading is developed, that utilizes a closed loop power control algorithm to compute the power required for each user, taking into account intra (same cell) as well as inter-cell (other cell) interference.

For a given Eb/It receiver requirement the number of users that can be supported is determined by [33]. Also, it has been shown that the inclusion of “dirty users” substantially reduces the capacity of the system.

3.2.1 System Model The cellular system is modeled as a set of uniformly spaced base-stations with a

number of users distributed over a 2-D space. 25 base-stations on 5×5 grid are assigned figure 3.1 shows this configuration. The distance between base stations is arbitrary set to 1km. The results will show the performance averaged over all users and all base stations. This cellular configuration best represents real situation as it suffers both intra and inter-cell interference [33].

Assuming that the path attenuation is the product of the fourth power of the distance and a log-normal random variable as used in [34]. That is the path loss between each user and the base station is proportional to 4)10/(10 −rη where r is the distance from the user to the base station and η is a Gaussian random variable with standard deviation σ = 8 dB and zero mean. As results are looking at relative performance the selection of η and σ is not critical. Values in the range of 42 ≤≤η and dBdB 104 ≤≤ σ would be acceptable.

Each user demands a particular carrier to interference ratio (C/I), this is called the target C/I and is calculated from the Eb/It requirement of the terminal as

Ch. 3. Case Studies

34

Figure 3.1: Distribution of users and base station positions.

RW

IEIC MStb

ett // )(

)arg(= (3.1)

where Eb/It is the mobile terminal information bit to total interference plus noise ratio requirement to achieve the required bit error rate, W is the bandwidth, and R is the information data rate. The carrier to interference for each mobile terminal (MS) is calculated using [33]

∑ ≠′=′ ′ ++

= K

kkk mkkmk

kmkm

MS NILpPLpp

IC

)(1)( /

/α

β (3.2)

where β is the fraction of signal power dedicated to the information data, Pk is the total transmit power of the base station to which link k is established, Lpkm is the link loss from cell k to mobile station m, α is the cell-specific orthogonality factor (where 0 = orthogonal and 1 = full interference), pkm is the power allocated to the link from the base station k to mobile station m, kI ′ is the other cell interference for base station k ′ and Nm is the noise at MS m. Without loss of generality, soft handover functionality is ignored.

Ch. 3. Case Studies

35

3.2.2 System Simulation Approach In [33] the steps used in determining the power needed by each user is described

such that each user’s carrier to interference ratio is satisfied. As the number of users increases, either the maximum power of the base station is reached or the C/I for all users cannot be reached (due to the interference present). Likewise as the Eb/It requirements increase the number of users that can be supported decreases.

Firstly set the target C/I for each user as described in equation (3.2) and determine the link loss between every user and every base station. Then iterate K times over the different cells to compute the intra-cell interference. Iterate also L times over all cells to allow the incorporation of the inter-cell interference. For each cell the new C/I is calculated as equation (3.2) and then calculate C/I∆ as

)()arg( MSett I

CIC

IC

−=∆

(3.3)

This provides the difference between the target and the actual C/I and is used for fast convergence to the target C/I as the next iteration’s power setting for each terminal is

∆

+=ICpp kmkm (3.4)

3.2.3 Numerical Results

In this section the cellular performance (capacity) is determined in terms of the

receiver Eb/It requirements. Also the capacity degradation incurred when “dirty users” are present in a cellular system is shown.

Figure 3.2 shows the average users per cell over all K = 25 cells. Here the user data rate is 32kbps with an orthogonality factor of α = 0.5 and the power dedicated to the information bits β = 0.8. Background noise is insignificant and results from 3dB to 15dB are shown. The users per cell are initialized to 5 and increase the users per cell by one until such time as equation (3.5) is true [33].

1.0.)arg( I

CIC

IC

ett>− (3.5)

When equation (3.5) is true this is an indication that convergence to the target C/I has not been achieved, and the capacity of the system has therefore been reached. As expected the result in figure 3.2 shows that the number of users that can be supported decreases exponentially with increasing Eb/It requirements.

Figure 3.3 shows the capacity degradation with the increase of dirty users in the system. Here the “clean” user Eb/It requirement is 6dB. The capacity of the system is determined using equation (3.5), taking into account the different C/I requirements for each terminal. This result is shown for different ratios between the dirty user power requirements and the normal user power requirements (i.e. 3dB means that the dirty users

Ch. 3. Case Studies

36

A

vera

ge n

umbe

r of u

sers

per

cel

l

Figure 3.2: Users that can be supported for a given Eb/It requirement.

have an Eb/It requirement 3dB larger than the normal users). The plot shows for a 3dB difference and 20% dirty users the system reduces capacity by about four users, while for a 6dB difference in power and a minimum 20% dirty users the average users per cell is reduced to 19, or more than one third reduction [33].

3.3 Power Control Imperfections The purpose of power control is to ensure that the received signal strength of all

users are equal. However, this cannot be accomplished perfectly with practical systems, resulting in capacity loss due to the nonoptimal performance of the correlation receiver under these circumstances. Practically nonidealities in power control such as finite step size, relative signal strength measurement error, synchronization error within the receiver and residual fast fading not compensated for by the power control process to be made, lead to misadjustment of the power received at the cell site. Further disturbance in power control process is due to the delay in controlling from the time the MS transmits until it receives a power control command back from the cell site and it can adjusts its power. This delay is comprised of the processing delay plus the channel propagation delay. Therefore power control imperfections must be considered in the system analysis [35].

Ch. 3. Case Studies

37

In [36, 37, and 38], the power control imperfection was assumed to be uniformly distributed. They pointed that there should be a more accurate and realistic model to determine the actual statistic of the power control error. In [39, 40, 41, 42, and 43] log normal power control imperfection was assumed. In [40], the pdf of the received power due to the combined influence of power control imperfection, the propagation statistics (such as Rayleigh fading and log normal shadowing), the dynamic range of the transmitter power control, the spatial MSs distribution was assumed to be log normal with zero logarithmic mean and standard deviation.

The imperfection in the power control system is determined by the logarithmic standard deviation of the lognormal power distribution of the received signal. In the case of perfect power control the logarithmic deviation is 0 dB. A lognormal distribution is assumed for the individual received power due to the following reasons [35]:

• It provides a mean to investigate the influence of imperfect power control

analytically and a simple relationship between the magnitude of the power control error and the system parameters can be derived.

• The received power at the cell site depends on a lot of independent factors (such

as the power control algorithm (PCA) used, speed of the adaptive power control system, spatial distribution of MSs and the propagation statistics such as fading

Figure 3.3: Capacity per cell as the fraction of dirty users increase.

Ave

rage

num

ber o

f use

rs p

er c

ell

Fraction of Dirty Users

Ch. 3. Case Studies

38

and shadowing). Each factor gives a contribution in dB to the received power. Using the central limit theorem, the logarithm of the received power is Gaussian distributed, implying that the received signal is lognormally distributed.

• In [44] data drawn from a large number of field tests conducted in widely

varying terrain in a large number of cities and in several countries have shown the received power can be closely approximated by a log normal pdf with mean and standard deviation of normal exponent equal to 7 and 2.4 dB respectively.

• This assumption was verified by simulation results predicted by [45] since the

power at any instant is the result many small incremental adjustments. It was claimed in [40] that the implicit influence of all the factors on the pdf of the average received power is investigated.

3.3.1 Performance Analysis The transmission quality specification for a CDMA cellular system may be put in

terms of Eb/It, as follows [42]:

η++

=−

ext

hg

t

b

IIeW

RB

IE

int

2 0

(3.6)

where B is the single user r.f. bandwidth, R is the information bit rate, W is the (constant) r.f. signal power to be ideally received, g0 is a zero-mean Gaussian random variable (r.v.) with variance 2

pσ which accounts for imperfect power control on the desired user, Iint is internal interference power from users inside a cell and Iext is the external interference power, η is the thermal noise power (AWGN), and 20/10ln=h . The link is in outage if the carrier-to- interference power ratio, C/I, is lower than a specified value of the protection ratio, β:

βη

<+

+==

−

WWII

eBR

IE

IC

ext

hg

t

b

int

2 0

(3.7)

β depends on channel characteristics, modulation and coding. Letting

WIIyex exthg /)(, int

2 0 +== − and Wz /η= , the outage probability may be expressed as:

∫ ∫∞ +

=

−>−=0

)(

0

)()(Przy

xyout dxxpdyypzxyPβ

β (3.8)

where )(xpx is the lognormal probability density function (p.d.f.) of the imperfect power control variable x, and )(ypy is the p.d.f. of the normalized interference power y.

Ch. 3. Case Studies

39

Based on a suggestion in [46] to resort to characteristic functions (c.f.’s), the following equivalent expression for the outage probability may be derived:

∫∞

∞−

−+= ωβωω

ωπω deXY

jP j

out )()(121

21 (3.9)

where { })exp()( xjEX ωω = , { })exp()( yjEY ωω = , and E denotes expectation. Being the internal and external interference independent, )()()( int ωωω extYYY = . In the special case of perfect power control, )exp()( ωω jX = , for more details on the derivation of the outage probability Pout refer to [42].

Following [47] that define system spectrum efficiency of a cellular system, sysη , as the ratio of the overall maximum data rate in the service area to the overall bandwidth allocated to the service:

c

ucellsys B

Rm

nn=η (3.10)

where ncell is the number of cells in the service area, nu is the maximum number of users per cell (system capacity), m is the cluster size, and Bc is the bandwidth per cell. Assuming m = 1 and fixing both R and Bc = B, then spectrum efficiency increases independently with both ncell and nu. Increase ncell with means that sysη grows proportionally with r-2, r being the cell radius. System capacity is linked to the transmission quality specification, i.e. nu = f(Pout), and to channel and system characteristics [42].

3.3.2 Numerical Results

Results were generated using total number of chips per bit = 128, It was assumed that the chip period Tc = 1 µs. The standard deviations of the received power σp were allowed to be 1, 1.4, and 2 dB. Simulation and field trial results have suggested the standard deviation of the received power level is between 1 and 2 dB [48 and 44]. The average probability of error versus the number of users has been plotted for the worst case (i.e. assuming the largest possible value of interference) in figure 3.4 for a fixed Eb/It of 12 dB for all possible values of σp, including the ideal case of σp = 0 dB. These results show that when using a correlation receiver, even slight variances in the received power levels seriously reduce capacity [41].

Capacity has been sharply reduced due to imperfect power control. Table 3.1 summarizes, for the worst and best cases (the worst case will assume the largest possible value of interference over a given interval, whereas the best case analysis will assume the smallest possible value), the capacity loss from the case of perfect power control for Eb/It = 12 dB and BER = 10-3. The capacity loss is referenced to the ideal best case for the best case of all received power level variances, and similarly for the worst case. For σp = 1 dB, capacity is reduced in the neighborhood of 15%. For σp = 1.4 dB, capacity is reduced by approximately 30%. For σp = 2 dB, capacity is reduced nearly 60%. Thus, tight power

Ch. 3. Case Studies

40

control is a necessity in CDMA system employing correlation receivers, and even standard deviations on the order of 1.4 dB can result in almost a 1/3 drop in capacity. Similar large drops in capacity have been shown if the received power levels are modeled as having uniform distributions about the mean [36].

Figure 3.4: BER versus number of users.

Table 3.1: Capacity loss for Eb/It = 12 dB and BER = 10-3.

Worst Case Best Case σp (dB) nu

Capacity Loss (%) nu

Capacity Loss (%)

0 25 - 30 - 1 21 16 27 10

1.4 17 32 22 27 2 11 56 13 57

Ch. 3. Case Studies

41

3.4 Summary

In this chapter the system capacity reduction due to users that request more power than should be required by a well designed terminal have been investigated. These users are labeled as “dirty users” as they cause the generation of excess transmit power, which is seen as interference to other users. As the downlink is the limiting link, in terms of capacity, this reduces the overall system capacity of users/km2. Realistic system parameters are utilized and the capacity loss is determined as a function of the percentage of dirty users. Results show that with only small increases in both the Eb/It requirements and the percentage of “dirty users” the capacity of the downlink can be substantially degraded [33].

Next, Imperfect power control in a CDMA system is represented. Results show that even accurate power control mechanisms have a significant loss in capacity from the case of perfect power control. Proposed power control systems have a log-normal distribution with standard deviations less than 2 dB. Even with this elaborate system, the capacity reduction will be between 10% and 30%. If less stringent power control algorithms are used and the standard deviation increases to 2 dB, then capacity drops by nearly 60% [41]. Clearly, stringent power control measures are needed to maintain high capacity levels in a CDMA system.

Chapter 4

Power Control in CDMA IS-95

Ch. 4. Power Control in CDMA IS-95

42

Power Control in CDMA IS-95

4.1 Introduction The aim in this Chapter is to give a somewhat detailed overview of power

control in CDMA IS-95 cellular communication system. The IS-95 system is the first operational commercial DS-CDMA system, and problems encountered during its operation provide valuable experience for future research work and development.

Power control for DS-CDMA according to the IS-95 standard consists of reverse link open-loop power control, reverse link closed-loop power control, and forward link power control. Reverse link open-loop power control is primarily a function of the mobile stations. The base stations take an active role in the reverse link closed-loop power control and the forward link power control.

4.2 Reverse Link Power Control

The reverse link power control affects the access and reverse traffic channels. It is used for establishing the link while originating a call and reacting to large path-loss fluctuations. The reverse link power control includes the access probes, the open-loop power control (also known as autonomous power control) and the closed-loop power control. The closed loop power control involves the inner-loop power control and the outer-loop power control.

4.2.1 Access Probes

The access channel is used to send call requests and messaging from the mobile to the base station prior to establishing a voice or data connection (see Figure 4.1) [6]. The mobile acquires the CDMA system by receiving and processing the pilot, sync, and paging channels. The paging channel provides the Access Parameters message which contains the parameters to be used by the mobile when transmitting to the base station on an access channel [3]. The access parameters are

• The access channel number • The nominal power offset (NOM_PWR) • The initial power offset step size (INIT_PWR) • The incremental power step size (PWR_STEP) • The number of access probes per access probe sequence • The time-out window between access probes • The randomization time between access probe sequences

Based on the information received on the pilot, sync, and paging channels, the mobile attempts to access the system via one of several access channels. During the access state, the mobile has not yet been assigned a forward link traffic channel (which contains the power control bits). One problem that has to be immediately solved in power control is the initial mobile transmit power. Before the mobile establishes contact with the base station, the mobile cannot be power-controlled by the base station. Thus, the natural question is when the mobile first attempts to access


43

the base station, what power level should the mobile use to transmit its request? At this point, the base station has not yet made contact with the mobile user, and the base station has no idea as to the location of the mobile user. There are two options: the first option is that the mobile can attempt to access the base station with a high transmit power. Such high power increases the probability that the base station will receive that mobile’s access request. However, the disadvantage of a high initial transmit power is that such high power represents interference to other users currently served by the cell. The second option is that the mobile can request access from the base station with a low transmit power. Such low power decreases the likelihood that the base station will receive the mobile’s access request. But the advantage is that this mobile won’t cause much interference to other users [5]. The solution as specified in the IS-95 standard is that when the mobile first attempts to access the system, it transmits a series of access probes. Access probes are a series of transmissions of progressively higher power. The mobile transmits its first access probe at a relatively low power, then it waits for a response back from the base station. After the acknowledgment time window (Ta) has expired, the mobile waits for an additional random time (RT) and increases its transmit power by a step size. The mobile tries again. The process is repeated until the mobile gets a respond from the base station. However, there is a maximum number of probes per probe sequence and a maximum number of probe sequences per access attempt. The entire process to send one message and receive an acknowledgment for the message is called an access attempt. Each transmission in the access attempt is referred to as an access probe. The mobile transmits the same message in each access probe in an access attempt. Each access probe contains an access channel preamble and an access channel capsule (see Figure 4.2). Within an access attempt, access probes are grouped into access probe sequences. Each access probe sequence consists of up to 16 access probes, all transmitted on the same access channel [3].

There are two reasons that could prevent the mobile from getting an

acknowledgment after the transmission of a probe.

1. The transmit power level might be insufficient. In this case, the incremental step power strategy helps to resolve the problem.

2. There might be a collision due to the random contention of the access channel by several mobiles. In this case, the random waiting time minimizes the probability of future collisions.

Figure 4.1: CDMA System Access.


44

Figure 4.2: Access Attempt, Probe Sequence, and Access Probe in Power Control.

Figure 4.3: A series of access probes by the mobile to access the system.

3-16 Frames 1-16 Frames

Access Preamble Message Capsule

. . . .

Acknowledgment Window (Ta)

Random Time (RT)

Probe # 1 Probe # 2

Probe # 3

Probe # 16

1 2 15 (Max.)

. . . . . .

Probe Sequence

Back-off Delay


45

For every access probe sequence, a back-off delay is generated pseudo randomly. Timing between access probes of an access probe sequence is also generated pseudo randomly. After transmitting each access probe, the mobile waits for Ta. If an acknowledgment is received, the access attempt ends. If no acknowledgment is received, the next access probe is transmitted after an additional random time (see Figure 4.2). The power difference between the current access probe and the previous access probe is called an access probe correction (see Figure 4.3). The step size for a single access probe correction is specified by the system parameter PWR_STEP [5]. If the mobile does not receive an acknowledgment within an access attempt, the attempt is considered a failure and the mobile tries to access the system at another time. If the mobile receives an acknowledgment from the base station, it remembers what power level works, and proceeds with the registration and traffic channel assignment procedures. The standard further specifies that the mobile should use the power level it receives from the base station to estimate how much to initially transmit. In other words, if the mobile sees a strong pilot signal from the base station, then it assumes that the base station is nearby and thus transmits initially at a relatively low level. If the mobile sees a weak pilot signal from the base station, then it assumes that the base station is far away and thus transmits initially at a relatively high level. From this measurement and from information on the link power budget that is transmitted during initial synchronization, the forward link path loss is estimated [49]. Assuming a similar path loss for the reverse link, the mobile uses this information to determine its transmitter power. A simplified link budget equation for the reverse link can be written Received SNR (dB) = mobile power (dBm) – net reverse losses (dB) – total reverse

link noise and interference (dBm) (4.1a) So that the mobile power to be transmitted is determined by Mobile power (dBm) = received SNR (dB) + net reverse losses (dB) + total reverse

noise and interference (dBm) (4.1b) where dBm denotes dB with respect to 1mW and the net losses on the reverse link include propagation and other losses offset by antenna gains. For the forward link, the received base station power can be written Received power (dBm) = base power (dBm) – net forward losses (dB) (4.2a) which can be solved for the net losses on the forward link: Net forward losses (dB) = base power (dBm) – received power (dBm) (4.2b)

This equation neglects the fact that the mobile measurement of received base station power is corrupted by forward link noise and interference. Substituting the net forward loss of (4.2b) in (4.1b) as an estimate of the net reverse loss and substituting a target value of the reverse link received SNR result in the equation


46

Mobile power (dBm) = target SNR (dB) + base station power (dBm) + total reverse noise and interference (dBm) – received power (dBm) (4.3a)

= constant (dB) – received power (dBm) (4.3b) If the mobile knows the transmit ERP of the base station, then the mobile would know how much it needs to transmit to compensate for that path loss. In reality, the mobile does not know the actual ERP of the base station, nor does it know how much received power is contributed by other, neighboring base stations. Therefore, a default constant is specified by the standard using generic assumptions of typical loading and base station ERPs. Specifically, from (4.3a) the initial transmit power of the mobile, pt ,initial in decibels, can be expressed using CDMA access parameters as pt, initial = - pr - K + (NOM_PWR-16×NOM_PWR_EXT) + INIT_PWR (4.4) where pt, initial = mean output transmit power (dBm), pr = mean input receive power (dBm), NOM_PWR = nominal power (dB), NOM_PWR_EXT = nominal power for extended handoff (dB), INIT_PWR = initial adjustment (dB), K = 73 for cellular (Band Class 0), and 76 for PCS (Band Class 1). The values for NOM_PWR, NOM_PWR_EXT, INIT_PWR, and the step size of a single access probe correction PWR_STEP are system parameters specified in the Access Parameters message. These are obtained by the mobile station prior to transmitting [3].

4.2.2 Open Loop Power Control In the open-loop scheme, the measured received signal strength from the base station is used to determine the transmit power for the mobile; a decrease in the average received base station signal power is a real time indication of a degradation in the mobile channel that can be caused by variations in the characteristics of the signal path, such as terrain and manmade structures that introduce “shadowing” of the signal. Assuming that the reverse link is subject to the same changes in average path loss as the forward link, under open-loop power control the mobile's average transmit power is adjusted accordingly. Thus the required amount of mobile transmitter power is inversely proportional to the amount of received forward link power as shown in figure 4.4. This provides a quick response to changes in signal conditions [2].

Figure 4.4: Effect of open-loop power control.

Pow

er

Distance from base station to mobile

Average power received by mobile

Pow

er


Average power the mobile needs to transmit

Pow

er


Average power received at base station


47

Open-loop power control is purely a mobile-controlled operation and does not involve the base station at all [5]. This open-loop process continues well after the base station has acknowledged the mobile’s access request and after the mobile starts to transmit on a traffic channel. A large dynamic range of 80 dB is allowed to provide an ability to guard against deep fades [1]. After a call is established, and as the mobile moves around within the cell, the path loss between the mobile and the base station will continue to change. As a result, the received power at the mobile will change and the open-loop power control will continue to monitor the mobile received power pr and adjust the mobile transmit power according to the following equation (4.5) [3]: pt = - pr - K + (NOM_PWR - 16×NOM_PWR_EXT) + INIT_PWR + (sum of all access probe corrections) (4.5) where the access probe corrections is the sum of all the appropriate incremental power steps prior to receiving an acknowledgment at the mobile, and pt is the continuous open-loop estimate of the mobile transmit power. The difference between (4.5) and (4.4) is that (4.5) contains an additional term specifying the sum of all access probe corrections made during the access probe transmission. The mobile station supports a total combined range of initial offset parameters, closed NOM_PWR, and access probe corrections of at least ±32 dB for mobile station operating in Band Class 0 and ±40 dB for mobile station operating in Band Class 1 [3]. It is important to note that the open-loop power control as specified in (4.5) is based on an estimate of the forward path loss. This power control is used to compensate for slow-varying and log-normal shadowing effects where there is a correlation between the forward-link and reverse-link fades. However, since the forward and reverse links are on different frequencies, the open-loop power control is inadequate and too slow to compensate for fast Rayleigh fading. Note that fast Rayleigh fading is frequency dependent and occurs over every half-wavelength (see figure 4.5). In other words, since fast Rayleigh fading is frequency dependent, we cannot use open-loop power control (which assumes forward path loss is identical to reverse path loss) to compensate for fast Rayleigh fading [49]. By design, the temporal response of the mobile to this information is nonlinear. If the pilot is suddenly received with high signal strength, the mobile transmitter power is reduced immediately, within several microseconds, on the principle that a higher received value of forward link power is a better estimate of average link loss, apart from fading. But if the measured signal strength drops, the mobile power is increased slowly, on the order of a millisecond. The reason for this procedure is that if the power is not decreased quickly when an improvement in the path is encountered, the mobile will cause an increase in interference for the other users until the problem is corrected. Similarly, if the power is increased rapidly, the path loss may in fact be less than inferred from the forward link, perhaps because the base station signal faded and the mobile signal did not, and again the mobile would cause interference for the other users. Therefore, the system accepts degradation in a single user's signal to prevent increased interference for all users. Figure 4.6 illustrates the effect of fast fading on the received mobile signal power. Figure 4.7 shows the mobile transmit power corresponding to the channel in figure 4.6 as controlled only by the open-loop nonlinear method. The dashed line in


48

Figure 4.6: Effect of fast fading in signal strength.

Figure 4.7: Mobile Transmitter power as governed by the open-loop power control only.

figure 4.7 represents the transmit power if the received signal were traced without the nonlinear filter, and the solid line represents the transmit power with the filter. Figure 4.5: With traveling through the standing wave pattern, the mobile will

experience fades once every half wavelength. Note that the standing wave pattern shown is a simple example resulting from the addition of two equally strong waves that are 180 degrees out of phase.


49

The sources of error in the open-loop power control are

• Assumption of reciprocity on the forward and reverse links • Use of total received power including power from other base stations • Slow response time ~ 30 ms to counter fast fading due to multipath

4.2.3 Closed Loop Power Control

Because the forward and reverse links are separated in frequency (45 MHz for cellular and 80 MHz for PCS), however they tend to fade independently. The correct setting of mobile transmit power cannot be derived exactly using only the base station's average signal strength as measured at the mobile; feedback from the base station on its measurement of received mobile power must be used, In addition to that fading sources in multipath require a much faster power control than the open-loop power control. The additional power adjustments required to compensate for fading losses are handled by the reverse link closed-loop power control mechanism that involves both the base station and the mobile, and has a response time of 1.25 ms for 1 dB steps and a dynamic range of 48 dB (covered in 3 frames). The quicker response time gives the closed-loop power control mechanism the ability to override the open-loop power control mechanism in practical applications. Together, two independent power control mechanisms cover a dynamic range of at least 80 dB. The closed-loop power control provides correction to the open-loop power control [3]. Once the mobile gets on a traffic channel and starts to communicate with the base station, the closed-loop power-control process operates along with the open-loop power control. In the closed-loop power control, the base station continuously monitors the reverse link and measures the link quality. If the link quality is getting bad, then the base station will command the mobile, via the forward link, to power up. If the link quality is too good, then there is excess power on the reverse link; in this case, the base station will command the mobile to power down. Ideally, FER is a good indicator of link quality. But because it takes a long time for the base station to accumulate enough bits to calculate FER, Eb/It is used as an indicator of reverse link quality. The base station sends the power-control commands to the mobile using the forward link. These power-control commands are in the form of power-control bits (PCBs). The amount of mobile power increase and power decrease per each PCB is nominally +1 dB and -1 dB. Because the closed-loop power control is meant to combat fast Rayleigh fading, the mobile’s response to these power-control commands must be very fast. For this reason, these PCBs are added to the data stream after the encoding and interleaving in order to eliminate more than 20 ms delay associated with deinterleaving and decoding [5]. Therefore, PCBs are not error protected and the probability of bit error for the power-control subchannel may be higher than that of the traffic channel if no special provision is taken. What actually happens is that bits are robbed from the traffic channel in order to send these PCBs. Figure 4.8 shows a simplified block diagram of a portion of the forward traffic channel generation. The output from the vocoder and input into the convolutional encoder is 9.6 Kbps (at full rate for Rate Set 1). The Rate 1/2 convolutional encoder doubles the baseband rate to 19.2 Kbps. Prior to spreading; the PCBs at 800 bps are multiplexed onto the baseband stream at 19.2 Kbps. The PCBs are integrated into the traffic channel by robbing selected bits from the baseband stream. This way, a separate “channel” at 800 bps (for


50

power-control purposes) exists beneath the traffic channel. The stream of PCBs at 800 bps is therefore called the power-control subchannel (PCS). These PCBs are continuously transmitted to the mobile by the base station. Note that since the rate of PCB transmission is 800 bps, a PCB (0 or 1) is sent once every (1/800) second, or 1.25 ms. A 0 bit indicates to the mobile that it should increase its mean output power level, whereas 1 indicates to the mobile to decrease its mean output power level. Both forward-link and reverse-link traffic channel frames are 20 ms in duration. Since one PCB is sent once every 1.25 ms, each traffic channel frame can be divided into (20 ms/1.25 ms) or 16 segments (see figure 4.9). These segments are called power-control groups (PCGs). Prior to transmission, the reverse traffic channel interleaver output data stream is gated with a time filter. The time filter allows transmission of some symbols and deletion of others. The duty cycle of the transmission gate varies with the transmit data rate, i.e., variable rate vocoder output, which, in turn, depends on the voice activity. Table 4.1 indicates the number of PCGs that are sent at different frame rates. The assignment of the gated-on and gated-off groups is determined by the Data Burst Randomizer (DBR) that is used to reduce reverse-link power during quieter periods of speech by pseudorandomly masking out redundant symbols produced by symbol repetition. It generates a masking pattern of 0s and 1s that randomly masks out redundant data. The masking pattern is partially determined by the vocoder rate [5]. At the base station, the reverse link receiver estimates the received signal strength by measuring Eb/It during each power group (1.25 ms).

• If the signal strength exceeds a target value, a power-down control bit 1 is sent.

• Otherwise a power-up control bit 0 is transmitted to the mobile via the power control subchannel on the forward link.

Figure 4.8: In the forward traffic channel, the PCBs at 800 bps are multiplexed

directly onto the baseband information stream at 19.2 Kbps.

Figure 4.9: Power Control Groups 1 PCG = 1.25ms

PCG = power control group

One Frame (20 ms) = 16 PCG

Gated-on PCGsGated-off PCGs


51

Table 4.1: Power Control Groups vs. Frame Rate. Frame Rate Rate (kbps) No. of PCGs Sent

Full 9.6 16 1/2 4.8 8 1/4 2.4 4 1/8 1.2 2

Since each power-control group is 1.25 ms in duration and the baseband is at a rate of 19.2 Kbps, then each power-control group contains (19.2 × 103)(1.25 × 10-3) = 24 bits. The first 16 of the 24 modulation symbols in a 1.25 ms PCG interval are possible starting positions for the power control bit. The starting position of the power control bit is determined by the values of the last four long-code chips used for scrambling in the preceding 1.25 ms period, i.e. The PCB bit position is determined by the decimal value of the four most significant bits of the decimator output where the input of the decimator is the long PN code, as illustrated in figure 4.10. Therefore, the separation between the start of consecutive power control bits is random, ranging from 9 to 39 modulation symbols. The 23rd PN code chip from the last 1.25 ms period is the most significant bit in determining the position, and 20th chip is the least significant bit. In figure 4.10, the values of the chips 23, 22, 21, 20 are 1011 = 11; thus, in this case, the power control bit starts at the 11th modulation symbol. It is important to recognize that the exact location of the PCB in the PCG is not fixed but pseudorandom. This is done to randomize the location of the power control bits to avoid any spikes due to periodic repetition [3]. Similar to the reverse link transmission, the forward link transmissions are organized in 20 ms frames. Each frame is divided into 16 PCGs. The transmission of a power control bit occurs on the forward traffic channel in the second PCG following the corresponding reverse link PCG in which the signal strength was estimated [5].

Figure 4.10: Position of the Power Control Bits.

20 21 22 23

5 31 20 21 22 23 0 1 2 3 4 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 2

1 1 0 1

1 power control bit = 2 data bits

1.25 ms = 24 scrambled traffic data bits

1/64 Long Code Used for Scrambling

These 4 bits of previous long code specified the starting point of the power Control bits value: 1011 = 11; the power control bit starts at position 11.

Not used for power control

0 2 31 4 5 6 7 8 9 10 11 12 13 14 15

1.25 ms

1 Frame (20 ms): 16 power control groups


52

This is illustrated in the example shown in Figure 4.11 For example, for PCG7, the base station measures the Eb/It. The base station compares the measured Eb/It with the threshold. If the measured Eb/It is greater than the threshold, then the base station inserts a PCB of 1 during PCG9 on the forward traffic channel. If the measured Eb/It is less than the threshold, then the base station inserts a PCB of 0 during PCG9 on the forward traffic channel. This process is repeated for every power-control group in the frame. Once the mobile receives and processes the forward link channel, it extracts the power control bits from the forward traffic channel. The power control bits then allow the mobile to fine-tune its transmit power on the reverse link. The reverse link closed-loop power control mechanism consists of two parts inner-loop power control and outer-loop power control. The inner-loop power control keeps the mobile as close to its target (Eb/It)setpoint as possible, whereas the outer-loop power control adjusts the base station target (Eb/It)setpoint for a given mobile. Based on the power control bit received from the base station, the mobile either increases or decreases transmit power on the reverse traffic channel as needed to approach the target value of (Eb/It)nom or set point that controls the long-term FER, Each power bit produces a 1 dB change in mobile power, i.e., it attempts to bring the measured Eb/It value 1 dB closer to its target value. Note that it might not succeed because It is also always changing. Therefore, further adjustments may be required to achieve the desired Eb/It. The base station, through the mobile, can directly change only Eb, not It, and the objective is the ratio of Eb to It, not any particular value for Eb or It. The base station measures Eb/It 16 times in each 20 ms frame. If the measured Eb/It is greater than the current target value of Eb/It, the base station informs the mobile to decrease its power by 1 dB. Otherwise, the base station informs the mobile to increase its transmit power by 1 dB (see Figure 4.12).

Figure 4.11: Closed-loop power control using PCBs.

Eb/It


53

The relationship between Eb/It and the corresponding FER is nonlinear and varies with vehicle speed and RF environment. Performance deteriorates with increasing vehicle speed. The best performance corresponds to a stationary vehicle where additive white Gaussian noise dominates. Thus, a single value of Eb/It is not satisfactory for all conditions. The use of a single, fixed value for Eb/It could reduce channel capacity by 30% or more by transmitting excessive, unneeded power. The value of the variable a is kept very small (see figure 4.13), so it may take 35 frames to reduce the Eb/It set point by 1 dB. Typically, the value of 100a is set at about 3 dB. The set point value is reduced by a for each consecutive frame until a frame error occurs. The set point is then increased by a relatively large amount and the process is repeated. The set point can range from 3 dB to 10 dB. A value of Eb/It ≥ 5 dB corresponds to good voice quality [3].

Since FER is a direct measure of link quality, the system is controlled using the measured FERs rather than Eb/It. FER is the key parameter in controlling and assuring a satisfactory voice quality. It is not sufficient to maintain a target Eb/It, but it is necessary to control FERs as they occur. The objective of the Reverse Outer-Loop Power Control (ROLPC) is to balance the desired FER on the reverse link and system capacity. System capacity can be controlled with the ROLPC parameters by increasing the acceptable FER. Changing FER can be accomplished by setting the ratio of down_frr to up_frr. The down_frr is calculated by the system by using the desired reverse FER (rfer) and up_frr as down_frr = (rfer × up_frr)/2 (4.6) Based on simulations, the following values for up_frr are suggested:

If (0.2% ≤ rfer ≤ 0.4%), up_frr = 6000 If (0.6% ≤ rfer ≤ 1.0%), up_frr = 5000 If (1.2% ≤ rfer ≤ 2.0%), up_frr = 3000 If (2.2% ≤ rfer ≤ 3.0%), up_frr = 1000

Figure 4.12: Target Eb/It.

Eb/It Set Point

1.25 ms

Next Eb/It

Set Point

Eb Eb

It

Time

Mobile Transmit Power (dBm)

Target Eb/It

Frame i Frame i + 1


54

Maximum

Time

3dB

10dB

Set Point Value

Minimum

Frame Error Occurs

100a

a

100a

20 ms

Figure 4.13: Set Point Value vs. Time.

The outer-loop process is not defined by the IS-95 standard, and each infrastructure manufacturer is free to implement its own outer-loop algorithms. Note that these algorithms are almost always proprietary to the manufacturer. Tables 4.2 and 4.3 lists the range and default values of different parameters for RS1 and RS2. The inner-loop power control is also responsible for detecting the mobile that fails to respond to power control and that may be causing interference to other mobiles. The base station counts the number of consecutive power decrease commands, and, if the count exceeds the specified threshold value, the base station will send a Lock until Power Cycle message to the mobile [3]. This message disables the mobile until the user turns the power off and on. Figure 4.14 gives the flow chart for the reverse link closed-loop power control.

Table 4.2: ROLPC Parameters for RS1. Parameter Range Suggested Value Description of Parameter

rfer 1 0.2-3.0% 1% Target reverse link FER (rfer) (Eb/It)nom 1 (dB) 3.5-8.0 6.5 Initial (Eb/It)set point (Eb/It)max 1 (dB) 5.5-9.5 8.5 Maximum (Eb/It)set point (Eb/It)min 1 (dB) 3.0-5.8 3.5 Minimum (Eb/It)set point

Table 4.3: ROPLC Parameters for RS2.

Parameter Range Suggested Value Description of Parameter rfer 2 0.2-6.0% 1% Target reverse link FER

(Eb/It)nom 2 (dB) 3.8-8.3 6.8 Initial (Eb/It)set point (Eb/It)max 2 (dB) 5.8-9.8 8.8 Maximum (Eb/It)set point (Eb/It)min 2 (dB) 3.0-5.8 3.8 Minimum (Eb/It)set point


55

Inner Loop (Every 1.25 ms)

Outer Loop (20 ms)

Yes

No

Initialize Eb/It Set Point to (Eb/It)nom

Measure Eb/It on PCG (1.25 ms)

(Eb/It)m > set point

Order mobile to Power up 1 dB.

One Frame Received

Order mobile to Power down 1 dB.

No. of Commands> Threshold

Send a Lock until Power Cycle

message to mobile.

Calculate new (Eb/It)set point.

Yes

NoNo

Yes

Figure 4.14: Flow Chart for Reverse Link Closed-Loop Power Control.

4.2.4 Open-Loop and Closed-Loop Implementation The mobile transmit power is therefore a function of the open-loop and closed-loop power control of the system. Equation (4.5) can be modified to include the closed-loop power correction [3]; that is,

pt = – pr – K + (NOM_PWR – 16 × NOM_PWR_EXT) + INIT_PWR + Sum of Access Probe Corrections

+ Sum of all Closed-Loop Power Control Corrections (4.7) Figures 4.15.a and 4.15.b show one implementation of the reverse-link power-control scheme. For the closed-loop power control, the base station has the entire outer loop as well as part of the inner loop; the mobile has the other part of the inner loop. For the open-loop power control, the entire open-loop portion resides in the mobile. In Figure 4.15.a, the base station receives the reverse-link signal from the mobile. The base station first demodulates the signal and estimates the FER of the reverse link. This information on the reverse-link frame quality is fed into a threshold computer, which adjusts the Eb/It threshold based on the received frame quality. At the same time, the base station also makes an Eb/It estimate of the reverse link. The Eb/It threshold and the Eb/It estimate are then compared.


56

Eb/It

Eb/It

Eb/It

Figure 4.15: (a) Reverse-link power-control functions carried out by the base station; (b) Reverse-link power-control functions carried out by the mobile.


57

If the estimate is greater than the threshold, then the link Eb/It is higher than what is needed to maintain a good frame quality; a PCB of 1 is thus sent to command the mobile to power down. If the estimate is less than the threshold, then the link Eb/It is lower than what is needed to maintain a good frame quality; a PCB of 0 is thus sent to command the mobile to power up. The PCBs are multiplexed onto the forward traffic channel and transmitted to the mobile. On the mobile side (see Figure 4.15.b), the mobile receives the forward link signal. It recovers the PCB and, based on the PCB, makes a decision to power up by 1 dB or to power down by 1 dB. The decision is the closed-loop correction. The correction is combined with the open-loop terms, and the combined result is fed to the transmitter so that it can transmit at the proper power level.

4.3 Forward Link Power Control

The purpose of the forward link power control is to reduce power for users that are either stationary, relatively close to the base station, impacted little by multipath fading and shadowing effects, or experiencing minimal other cell interference. Therefore, extra power can be given to users that are either in a more difficult environment or far away from the base station and experiencing high error rates. Forward link power control (FLPC) aims at reducing interference on the forward link. The FLPC not only limits the in-cell interference, but it is especially effective in reducing other cell/sector interference [3]. The forward link power control attempts to set each traffic channel transmit power to the minimum required to maintain the desired FER at the mobile. The mobile continuously measures forward traffic channel FER. It reports this measurement to the base station on a periodic basis. After receiving the measurement report, the base station takes the appropriate action to increase or decrease power on the measured logical channel. The base station also restricts the power dynamic range so that the transmitter power never exceeds a maximum value that would cause excessive interference or so that it never falls below the minimum value required for adequate voice quality. Since FERs are measured (not Eb/It as in the closed inner-loop strategy), this process is a direct reflection of voice quality. However, it is a much slower process. Because orthogonal Walsh codes are employed for the forward link instead of long PN codes, cochannel interference is not an urgent issue. Therefore, slow measurements do not add much degradation to system performance. Figure 4.16 is a flow chart for the FLPC process. Forward link power control is expressed in terms of parameters N, D, U, and V (see Figure 4.17), which may be adjusted to various values for the operation of an actual system. For RS1, the Power Measurement Report Message (PMRM) contains the number of error frames received and the total number of frames received during the interval covered by the report (frame counters then are reset for the next report interval). The FER is equal to the number of error frames divided by the total number of frames received in the reporting interval. The following are steps for forward link power control for RS1 (see Figure 4.17).


58

Set (ffer)T and Timer

Measure ffer (ffer)m

(ffer)m < (ffer)T Timer Has Expired

Report Measurement

Repeat Process

Yes Yes

No No

Figure 4.16: Flow Chart for Forward Link Power Control.

Figure 4.17: Forward Link Power Control for RS1.

Action by Mobile

• Mobile keeps track of the number of error frames in a period of length pwr_rep_frame.

• If error frames > a specified number, the mobile sends a PMRM containing:

♦ Total number of frames in pwr_rep_frame ♦ Number of error frames in pwr_rep_frame ♦ FER

• If error frames < a specified number, a PMRM is not sent. • After sending a PMRM, the mobile waits for a period pwr_rep_delay before

starting a new period.

V (dB)

D (dB)

N Frames

Traffic ChannelDigital Gain

FER < fer_small

Time

U (dB)

FER Too High fer_small < FER < fer_big

PMRM Not Received

FER Too HighFER > fer_big

Key ParametersN ~ 80 framesD ~ 0.25 dBU ~ 1.0 dBV ~ 2.0 dB


59

Action by Base Station

• On receiving the PMRM, the base station compares the reported FER as follows and adjusts traffic channel power.

♦ FER < fer_small → reduce power by D ♦ fer_small < FER < fer_big → increase power by U ♦ FER > fer_big → increase power by V

• If no PMRM is received

♦ Base station starts a timer fpc_step. ♦ When timer expires, power level is reduced by D. ♦ The timer resets after it expires or after receipt of a PMRM.

• Digital gain is never set below min_gain or above max_gain. • If flpc_enable = 0, digital gain is set to nom_gain.

For RS2, 1 bit per reverse link-frame (the E or erasure bit) is added to inform the base station whether or not the last forward link frame was received without error at the mobile. This allows more rapid and precise control of forward link power than the scheme used for RS1. The following are steps for forward link power control for RS2 (see figure 4.18). Forward Link Power Control with RS2

• Uses erasure indicator bit instead of PMRM • Much faster than RS1 implementation

♦ Forward link power control could change every 2 frames; thus, its response is very fast.

• Process.

♦ In each frame, the mobile sends an erasure indicator bit showing whether the previous forward frame had an erasure bit or not.

♦ If an erasure is indicated by the mobile (i.e. Erasure Bit True), the base station increases traffic channel digital gain by up_adj.

♦ If no erasure is indicated by the mobile (i.e. Erasure Bit False), the base station decreases traffic channel digital gain by dn_adj.

Figure 4.18: Forward Link Power Control for RS2.

Traffic Channel

Digital Gain

Time

Bad Traffic Frame Received withErasure Bit Unknown

Good Traffic Frame Received with Erasure Bit

False

20 ms

up_adj

Good Traffic Frame Received with Erasure Bit True

dn_adj


60

Table 4.4 and 4.5 list the values of the parameters for forward link power control for RS1 and RS2, respectively.

Table 4.4: Forward Link Power Control Parameters for RS1.

Parameters Range Suggested Value Description

FER 0.2–3% 1% target forward FER

fer_small 0.2–5% 2% lower forward link FER threshold minimum PMRM FER required to increase gain by U

fer_big 2–10% 6% upper forward link FER threshold minimum PMRM FER required to increase gain by V

min_gain 34–50 40 minimum traffic channel digital gain max_gain 50–108 80 maximum traffic channel digital gain nom_gain 34–108 57 nominal traffic channel digital gain

fpc_step 20–5000 ms 1600 ms forward power control timer value which determines

when gain is decreased by D

Table 4.5: Forward Link Power Control Parameters for RS2.

Parameters Range Suggested Value Description

FER 0.2–6% 1% target forward FER up_adj 1–50 15 gain increase when forward erasure is observed dn_adj — N/A gain decrease when no forward erasure is observed

min_gain 30–50 30 minimum traffic channel digital gain max_gain 50–127 127 maximum traffic channel digital gain nom_gain 40–108 80 nominal traffic channel digital gain

4.4 Power control in soft handover

Handover in wireless cellular systems is needed when a mobile user moves

from the coverage area from one cell into that of another cell. In the FDMA and TDMA systems, the handovers are typically hard handovers, meaning that the connection to the original cell is terminated before the connection to the new cell is established. In CDMA systems, due to the universal frequency reuse, a mobile user can be simultaneously connected to several cells. Thus, when a mobile moves from one cell to another, it can establish connection to the new cell before the connection to the old cell is terminated. In this case, the mobile is said to be in soft handover. This is beneficial, since the mobile user can at each time instant use only enough transmission power to be able to reach one of the base stations to which it is connected. This way the average transmission power is lower than without soft handover, and less interference is produced to the other users. However, soft handover increases the radio resource usage in the downlink [24].

Power control has special implications during soft handover. In IS-95 CDMA, power control in soft handover works as follows. In uplink closed-loop power control, the mobile station receives power control commands from all the base stations in the active set (the set of base stations involved in the soft handover at a given time). It then combines these commands, and based on the combined command, it adjusts its transmission power. The basic principle is that if any of the base stations sends a power-down-command, the mobile station decreases its transmission power. The transmission power is increased only if the mobile station receives a power-up-


61

command from all the base stations in the active set, this algorithm is indicated in figure 4.19 (0 means Power Up and 1 means Power down) [50].

In downlink closed-loop power control, the same power control command sent from a mobile station is received by all base stations in the active set. Due to errors in the reception of the power control command, the base station powers can start drifting apart. This is very undesirable, as it destroys the balance between up- and downlink power levels. A typical way to deal with the power drifting problem is a scheme called power balancing, where each base station in the active set periodically correct their transmission powers towards a reference level set by the network [24].

Figure 4.19: Flowchart for uplink transmit power control scheme during soft hand over.

COR = 0 COR

Uplink TPCB

From BSA

Uplink TPCB

From BSB

Uplink TPCB

From BSX

Decrease MS transmit power

Increase MS transmit power

COR = 1

Set of BS’s involved in the active set of MS

Chapter 5

Adaptive step-size power control

Ch. 5. Adaptive step-size power control 62

Adaptive step-size power control

5.1 Introduction The transmit power update step size can be either fixed (fixed step size algorithm)

or made adaptive to the channel variations. A specific example of the adaptive step size approach is the inverse algorithm (i.e., DCPC defined in the previous chapter). Fixed step size algorithms are easy to implement, and need much less bandwidth on the forward link. This is because only the sense of power change (i.e., up or down) needs to be conveyed to the mobile, which can be achieved by sending a simple 1-b command, which we assume can be in error with probability rp .

Figure 5.1 shows a performance comparison between the fixed step size algorithm, an adaptive delta-modulation algorithm, and the inverse algorithm. A step size of 1 dB is used in the fixed step size algorithm. An update rate of 800 Hz, a vehicle speed of 30 km/h (corresponding to a Doppler frequency of 25 Hz, considering a carrier frequency of 900 MHz), and a return channel error rate rp of 0.0 are used. As expected, the performance of the inverse algorithm is found to be superior to that of the fixed step size algorithm. For example, for the above set of parameters, the inverse algorithm needs 3.5 dB less Eb/N0 than the fixed step size algorithm to achieve 10-2 BER. Inverse algorithm implementations, however, would need additional bandwidth on the return channel to carry the power-control step size, in addition to the power up/down command. In practice, because of the increased complexity and bandwidth requirements, inverse algorithms are rarely used [9].

A compromise would be to use an adaptive delta-modulation algorithm that will be introduced in this chapter. It is a new scheme for adapting the power control step size based on the received ON-OFF power control commands in a decision feedback power control scenario. This scheme can be used in power control for increasing its performance without any increase in the signaling bandwidth used for feeding back the power control commands. The proposed method is called the adaptive step (AS) method. The method is combined with the FSPC and DCPC algorithms to construct a new power control algorithm, the Adaptive Step Power Control (ASPC) algorithm.

5.1.1 Problem setup

Consider the DCPC and FSPC algorithms. For a particular user, these algorithms are described by (all variables in decibel scale) { })()(,min)1( max tetpptp δ+=+ (5.1) and { }))(()(,min)1( max tesigntpptp δ+=+ (5.2) respectively, where δ is the power control step size and e(t) = γt(t) - γ(t) is the power control misadjustment.


Figure 5.1: Comparison of the BER performance of fixed step size, adaptive delta modulation, and inverse algorithms [9].

It is clear that the DCPC algorithm belongs to the class of information feedback

(IFB) algorithms and the FSPC algorithm to the class of decision feedback (DFB) algorithms, where In IFB real-valued commands are fed back, while in DFB only the sign of the command is fed back [24]. The latter class is used in DSCDMA systems in practice, since the power update rate is relatively high, and thus the number of bits per power control command must be low so that the power control signaling would not consume too much radio resources. For example, in UMTS the power update rate is 1500 Hz and only up-down commands are used so that only one bit is needed for the command transmission. Note that if δ = 1, then e(t) in the DCPC case can be regarded as the power update adjustment that would guarantee that e(t+1) = 0 if the channel were static and all other users in the system did not update their powers.

The idea of the proposed scheme is to allow the use of an IFB-type algorithm, like the DCPC algorithm, while still employing decision feedback. Thus, the adaptive step size can be thought as a reconstruction of e(t), constructed from the received power control commands u(t), u(t -1), . . ., where u(t)∈{-1,1}, t = 0, 1, 2, . . ..


5.2 Adaptation method The adaptation method proposed here is referred to as the Adaptive Step (AS) method. Let e(t) = γt(t) - γ(t) and u(t) = sign(e(t)). Define

[ ] { }1,1,)1()(121),( −∈−+= xtutxuxta (5.3)

Note that

−≠−=

=)1()(,0)1()(,1

)1,(tutuiftutuif

ta (5.4)

and

−≠−=

=−)1()(,1)1()(,0

)1,(tutuiftutuif

ta (5.5)

The AS method can be described by ),()1(~)1,()(~ tutetate eδ+−= (5.6) where )(~ te is the reconstruction of e(t) and eδ is a parameter controlling the speed of the update.

While not readily seen from (5.6), the idea of the adaptation method is very intuitive: if the two latest commands have the same sign, the reconstruction of e(t) is updated by eδ to the direction of the last command u(t) so as to increase the step size of the next power update. If the two latest commands have different signs, a zero crossing must have happened in the signal e(t), and the reconstruction also crosses zero.

5.3 The Adaptive Step Power Control (ASPC) algorithm

The ASPC algorithm is simply the combination of the FSPC algorithm, the AS method, and the DCPC algorithm. Considering uplink, the base station generates the commands u(t)∈{-1,1} as in the FSPC algorithm, the commands are transmitted to the mobile station, which applies AS to generate a reconstruction )(~ te of the power control misadjustment, and then updates its power as in the DCPC algorithm, but using the reconstructed value instead of the true e(t). This is described by { })(~)(,min)1( max tetpptp δ+=+ (5.7)

Figure 5.2 shows a flowchart of the ASPC algorithm [24].


Figure 5.2: Flowchart of the ASPC algorithm.

5.4 Modifications The performance of the AS method naturally depends on the selection of the parameter eδ . If too small eδ is selected, then the reconstruction cannot track the actual misadjustment e(t). This can happen for example during a deep fade in the radio channel. On the other hand, if eδ is too big, then the advantage of the “fine-tuning” provided by the adaptation method to the power control algorithm is significantly reduced. To circumvent these problems, some modifications are proposed to the standard AS method. All these modifications aim to make the parameter eδ to adapt to various conditions.

5.4.1 AS with asymmetric update step sizes

From closed loop power control point of view, the situation where the SIR is below the target is more serious than vice versa. An intuitive way to allow a more rapid recovery from these situations is to use a larger update parameter when receiving positive commands (increase power) than when receiving negative commands (decrease power). Mathematically this can be put as follows. Let up

eδ and downeδ be the update parameters in

the positive and negative directions, respectively.


Define

[ ] { }1,1,2)1()(41),( −∈+−+= bxtutuxtb (5.8)

The asymmetric AS (AS-A) is [ ] )()1,()1,()1,()1(~)1,()(~ tutatbtbtetate e

downe

upeAA δδδ −+−++−= (5.9)

5.4.2 AS with gradually increasing update step size

The convergence of the ASPC algorithm also depends heavily on the selection of eδ . In a situation where the power control misadjustment is large, it would be better to apply a larger eδ to speed up the convergence. This can be done by increasing eδ gradually when receiving consecutive commands that have the same sign. Mathematically, the Gradual AS (AS-G) is

)()1,(1)1(~)1,()(~1

1

0

tuktatetatesn

m

m

kmeGG

−++−= ∑ ∏

=

−

=

δδ (5.10)

where ns is a parameter that limits the maximum increase of the update parameter, so that after receiving ns + 1 consecutive commands with the same sign, the update parameter is no longer increased. δm, m = 1, 2,…, ns are weighting factors defining the fraction of eδ

that is to be added to the update parameter when receiving the mth command with the same sign.

A drawback of this method is that it can lead to high overshoot in the reconstructed signal. Therefore, it is be better to set ns to a relatively low value. In simulation experiments, ns = 2 seemed to be a good compromise between overshoot limitation and tracking speed.

5.4.3 AS with variable update step size

Yet another intuitive method to adapt the update parameter is described here. Consider the FSPC algorithm in (5.2). Since the power control step δ (not to be confused with eδ ) is fixed, the best situation is achieved when the commands (power updates) generated by the FSPC algorithm are consecutive +1’s and -1’s, since in this case the power control misadjustment e(t) oscillates between the opposite sides of the origin at consecutive samples. The amplitude of this oscillation depends on the step size δ. Now, consider that we could decrease the step size applied at the transmitter, while maintaining the consecutive up-down command flow. In this case the amplitude of the oscillation of the power control misadjustment would be decreased. If the continuous up-down command flow breaks, the step size could be increased again. This can be done with ASPC and the following modification to the AS method. This modification is called the Variable Gain AS (AS-VG). It is described by


),()()1(~)1,()(~ tuttetate eVGVG δ+−= (5.11) )1()()1()( −+−= tututt VGee δδδ (5.12)

where VGδ controls the rate of change of the update parameter )(teδ , which is now time-varying. The idea behind this method is that the update parameter is decreased every time the two most recent power control commands have different signs, otherwise it is increased. In this way the algorithm tries to find the smallest update step size that still leads to consecutive up-down power control command flow. To prevent the update step size to grow too large, it should be limited. A limit of 1 dB was used in all the simulations.

5.4.4 Modified ASPC algorithms

The modifications described above can be applied in power control in the same way as the AS method is used in the ASPC algorithm. The modified ASPC algorithms are thus called the ASPCA, ASPC-G and ASPC-VG algorithms that use the corresponding step size adaptation methods, all theses algorithms have been tried using simulink simulation program that will be described in chapter 6.

5.5 Analysis on the convergence speed

The reason for adapting the step size in the first place is to make the transmission power to change faster if the consecutive TPC commands have the same sign. One can propose the following general adaptive power control algorithm for this purpose as )()1(~)()(~ tdtetcte +−= , (5.13) )(~)()1( tetptp +=+ (5.14)

Depending on the choice of c(t) and d(t) one can achieve different speeds of increase of the power control update step size. The FSPC algorithm and the proposed algorithms can be fitted in this general framework as shown in Table 5.1.

Table 5.1: General framework for the proposed power control algorithms.

PCA c(t) d(t) FSPC 0 δu(t) ASPC a(t,1) δeu(t)

ASPC-A a(t,1) [ ] edowne

upe tatbtbta δδδ )1,()1,()1,()1,( −+−+

ASPC-G a(t,1) )()1,(11

1

0

tuktasn

m

m

kme

−+∑ ∏

=

−

=

δδ

ASPC-VG a(t,1) ∑=

−+t

kVGe kuku

1)1()()0( δδ


Consider the case when the TPC command is positive starting from time t = 0, i.e., u(t) = 1, t = 0, 1, …. Table 5.2 shows the rate of change of p(t) with the different algorithms in this special case.

In the case of FSPC algorithm, the speed of change in the transmission power is linear, while for the proposed algorithms it is either quadratic or cubic. Figure 5.3 shows the power evolution graphically with the following parameters that were selected using simulation experiments to give reasonable performance:

201.0

,2,1,11.0

3.0

1.01

==

===

=

==

s

VG

m

downe

upe

e

n

mδδδ

δ

δδ

K

(5.15)

Figure 5.3: Power evolution with various algorithms in the case p(0) = 0, u(t) = 1, t = 0, 1, 2, ….


Table 5.2: Convergence of power with the proposed power control algorithms.

PCA p(t) Change rate FSPC δtp +)0( Linear

ASPC 2

)1()0( ++

ttp eδ Quadratic

ASPC-A 2

)1()0( −++

tttp upee δδ Quadratic

ASPC-G

+>+−−−

+

+

++−−+

−−++

+++

+≤−++

+

1),1(2

)1)((2

)1()1()1(

)1)1((6

)2)(1(2

)0(

1),(62

)1()0(

3

3

smsess

ssmeses

ssme

sse

sme

e

ntifnntnt

nnnnt

nn

nnp

ntifttttp

δδ

δδδ

δδ

δ

δδδ

Cubic

Quadratic

ASPC-VG )12

)2)(1(()(6

)0( 3 −−++

+−+ tttttp eVG δ

δ Cubic

5.6 Simulation results

The simulation program is implemented in MATLAB. It has seven cells in a

hexagonal pattern, where the cell radius is 50 m and base station height is 15 m. The users are uniformly distributed over the seven cells. The chip rate is 3.84 Mchip/s as in UMTS, which gives a processing gain of 19.3 dB if channel coding gain is ignored. The target (Eb/It) is 6 dB for every user. In the beginning of the simulation, the users are assigned velocities randomly between vmin = 0 km/h and vmax = 30 km/h and a random direction of movement. These are not changed during simulation. Ideal handovers are assumed in the sense that each user is connected to the base station with the least channel attenuation at all times. The sampling rate of the simulator matches the sampling rate of the power control, which is 1.5 kHz in WCDMA.

The radio link attenuation is modeled as a product of three variables the large scale propagation loss that depends on the distance between the transmitter and the receiver, log-normal shadowing with a mean of 0 dB and standard deviation of 8 dB, and motion induced Rayleigh-distributed multipath fading generated by Jakes’ model. It is assumed that the receivers are able to combine two equal-strength paths with independent multipath fading. The simulation parameters are summarized in Table 5.3.

Note that with cell radius of 50 m, the assumption of the receiver being able to combine two equal strength paths is not realistic, since the difference of the distances of these two paths should exceed the length that a radio wave propagates within the time of


one chip duration. For a chip rate of 3.84 Mchips/s, this length is about 78 m. Also the base station height of 15 m is not realistic. The selection of these parameters was not done by the author, as the channel model was imported from another simulator. However, the simulation scenarios were selected so that the mobile powers stayed within the minimum and maximum power limits and the system was always feasible. Some simulation examples demonstrating the properties and performance of the ASPC algorithms are given here.

5.6.1 Error tracking

Figure 5.4 shows an example of the power control misadjustment tracking performance of the ASPC, ASPC-A, ASPC-G and ASPC-VG algorithms for a slowly moving (5 km/h) user. This case was simulated with the simulator described previously. The parameters were selected as in (5.15). These parameters were selected by trial and error to give good results in the simulation experiments.

It is seen that the ASPC reconstruction follows the actual misadjustment to some extent, although it is quite coarse. While the actual misadjustment follows somewhat smooth, secondorder- type curves, the reconstruction behaves more like a sawtooth wave. If the actual misadjustment stays at one side from zero long times, the reconstruction eventually deviates far from the actual value. Nevertheless, every time a zero-crossing occurs on the actual misadjustment, the reconstruction also immediately crosses zero, thus rapidly decreasing the deviation from the actual value. The parameter eδ obviously has a great effect on the performance, and it should be selected according to the fading rate. This is a drawback of the ASPC algorithm, and it motivates to investigate the modifications proposed above, where this parameter is adaptive. Considering the modifications, it is seen that the ASPC-A algorithm is able to reduce the amplitude of the e(t) deviation in the positive direction (SIR is below SIR target) around sample number 75. Both the ASPC-G and ASPC-VG algorithms, however, do this more effectively and also reduce the deviation to the negative direction around sample number 100.

Table 5.3: Simulation parameters.

Parameter Value number of users (N) 80

number of cells (NBS) 7 data rate (Rb) 45 kb/s chip rate (Rc) 3.84 Mchip/s

Eb/It target 6 dB base station height 15 m

path loss exponent (d) 4 shadowing standard deviation (σs) 8 dB

shadowing decorrelation distance (D) 45 m max transmitter power (pmax) 21 dBm min transmitter power (pmin) -50 dBm

thermal noise power (η) 10-12 W power control update rate (fp) 1500 Hz

carrier frequency (fc) 1950 MHz


Figure 5.4: Example of the power control misadjustment tracking performance of the ASPC algorithms (mobile speed 5 km/h).


5.6.2 Convergence in two-user case The power control problem in two-user case was discussed in Section 2.2. The

two-user case is simulated here to demonstrate some interesting properties of the ASPC algorithms. The simulation was done with the following link gains:

⋅⋅⋅⋅

=

=

−−

−−

68

94

2221

1211

1025.61052416.11082253.4100.1

gggg

G

The system load as measured by )(Hρ was set to )(Hρ = 0.95. The initial

powers of the users were p1 = 5dBm and p2 = 12dBm. These values were selected so that the initial point in the power plane is outside the feasible region. The high load makes the feasible region very narrow. The parameters were δ = 1 for FSPC, eδ = 0.1 for ASPC, and

VGδ = 0.01 for ASPC-VG. Figure 5.5 shows the convergence of the power vector to the optimal power vector

p* with the DCPC, FSPC, ASPC and ASPC-VG algorithms. The two diagonal curves in the figures are the power requirement limits as in (2.4) (cf. Figure 2.2). The DCPC algorithm converges to the optimal point as expected. The FSPC algorithm does not converge but oscillates between the two points, since the feasibility region is too narrow for the applied step size (1 dB). Both the ASPC and ASPC-VG algorithms converge to the neighborhood of the optimal point, and start oscillating around it. The oscillation is considerably smaller than with FSPC. Also, the oscillation with ASPC-VG is smaller than with ASPC. Note also that during the convergence, the ASPC algorithms stay very near to the feasible region, while the DCPC algorithm has relatively large oscillations outside the feasible region. The result of this feature is clearly seen in Figure 5.6, as discussed below.

Figure 5.6 shows the convergence of SIR to SIR target, measured by )()(

1

1

ttt

γγ and

2)()(

2

2 +ttt

γγ for users 1 and 2, respectively. The offset by 2 for user 2 is for separating the

curves in the figures. Here an interesting feature of the ASPC algorithms is clearly visible: the oscillation of SIR around the SIR target during the transient phase is considerably smaller with the ASPC algorithms than with the DCPC algorithm, even though the ASPC algorithms utilize decision feedback and the DCPC algorithm uses information feedback. Also, the ASPC-VG algorithm is able to finally reduce the oscillation much more than the ASPC algorithm, since the adaptive step size is gradually decreasing due to the consecutive up-down commands.

Figure 5.7 shows the convergence of the power vector towards the optimal power vector, as measured by the norm *pp − . Figure 5.8 shows the same curves on top of each other for easier comparison. It is seen that the ASPC-VG algorithm gets very close to the convergence speed of DCPC. Finally, Figure 5.9 shows the convergence in a multiuser case with 80 users. Similar behavior is observed as in the two-user case,


although the convergence of the DCPC algorithm is in this case much faster than with the ASPC-VG algorithm.

Figure 5.5: Comparison of the convergence of the algorithms for two users and static channel.


Figure 5.6: Convergence of the SIR to SIR target in two-user snapshot simulation. The graphs of user 2 in the figures are offset vertically by 2 for better illustration.


Figure 5.7: Convergence of the norm of the difference between the power vector and the optimal power vector p* with the DCPC, FSPC, ASPC and ASPC-VG

algorithms in two-user snapshot simulation.


Figure 5.8: Power convergence comparison in two-user snapshot simulation.

5.6.2.1 A note on the convergence of the ASPC-VG algorithm

For the ASPC-VG algorithm in the static-channel case it sometimes might happen that the parameter updating algorithm (5.12) starts oscillating without converging to a small value. Figure 5.10 shows an example of this case. The adaptive step-size, power control commands, and deviation of SIR from SIR target are shown for user 1 in the figure. It is seen that the power vector oscillates between four points around the optimal point, causing a continuous (1, 1, -1, -1) pattern for the power control commands. As a result, also (5.12) starts to oscillate between two points and this “deadlock” situation is maintained forever [24]. Thus, some means for detecting this deadlock situation might be needed, e.g., by detecting the (1, 1, -1, -1) pattern from the received power control commands. However, this situation is not very likely to sustain long times in a real dynamic environment with random changes in the channel gains.


5.6.3 Performance of the ASPC algorithms Figures 5.11, 5.12 and 5.13 show the empirical cumulative distribution functions

(CDF) of the ASPC algorithm and its modifications ASPC-A, ASPC-G and ASPC-VG, compared to FSPC and DCPC with loop delay of 1 TPC, with vmin = 0 km/h and vmax = 5, 15 and 30 km/h, respectively. The parameters for the algorithms were the same as in Section 5.6.1. It is seen that the ASPC method is most effective with low mobile speeds in terms of outage probability. The ASPC-A and ASPC-G algorithms are able to reduce the outage probability with a slight degradation in the variance of SIR (or Eb/It) around the target. The best compromise seems to be the ASPC-VG algorithm, which has very good performance at wide range of mobile speeds due to its ability to adapt the update parameter according to various conditions.

Figure 5.9: Power convergence comparison in multi-user snapshot simulation (80 users).


Figure 5.10: Example of a “deadlock” situation with the ASPC-VG algorithm.

Figure 5.11: Empirical CDF of Eb/It, mobile speeds from 0 to 5 km/h.


5.7 Summary

The ASPC algorithm and its modifications clearly have some interesting properties. Compared to the FSPC algorithm, they are able to significantly decrease the variance of the power control misadjustment without any increase in power control signaling; only one bit is still needed for the power control feedback command. The ASPC-VG algorithm is particularly interesting in its ability to improve the convergence speed of ASPC even close to that of the DCPC algorithm.

As mentioned earlier, the ASPC algorithm and its modifications are combinations of the FSPC and DCPC algorithms with the proposed step-size adaptation methods. These methods could of course be combined with any other algorithms.

The ASPC algorithm was shown to perform very well at slow mobile speeds, but the performance deteriorates at higher speeds due to the fixed update step size. From the proposed modifications, the ASPC-VG algorithm is most efficient, and works well also with high mobile speeds.

Chapter 6

Simulink Simulation Model

Ch. 6. Simulink Simulation Model 81

Simulink Simulation Model

6.1 Introduction Designing cellular handsets and base stations is a challenging task. Some of the largest challenges include the design of complex link-layer control logic, digital signal processing (DSP), and analog/mixed-signal components. Some of these functions can be designed and optimized independently, due to the limited scope of the components involved. But many functions, such as power control, involve several different components and therefore need system-level design tools to adequately simulate and test them [7].

Power control, also known as transmit power control (TPC), is a significant design problem in modern CDMA cellular networks. Power control comprises the techniques and algorithms used to manage and adjust the transmitted power of base stations and handsets. It also serves several purposes; including reducing co-channel interference, managing voice quality, maximizing cell capacity, and minimizing handset mean transmit power.

Power control algorithms monitor voice quality statistics and received power levels that are functions of both the physical layer’s forward and reverse link characteristics. These algorithms involve the transmission of power adjustment commands to each mobile phone over the forward traffic channel’s power control subchannel. They also involve link-layer operations such as the transmission of system overhead messages on the access channel.

Successful optimization of any power control algorithm design requires the simulation of many components. This optimization can be achieved with system-level design, which allows the simulation of the physical and link layers of entire communication systems.

With graphical block-diagram and state-machine system-level design tools, we can quickly specify a top-level architecture for the whole system that matches the conceptual design and perform global optimizations by trying many different solutions. Block diagrams let us accurately model the concurrency of the multiple components and the complex timing relationships present in any real system. Here, we use Simulink as a system-level design tool to design and simulate different power control algorithms of IS-95 CDMA.

The bock-diagram shown in figure 6.1 is built to simulate IS-95 Reverse Traffic Channel Open and Closed Loop Power Control. It consists of three main blocks Base Station, Mobile and Channel. With the control logic, reverse traffic channel, and forward traffic channel in place, we can run simulations to test the algorithm. Here, we will add a channel with three Raleigh fading multipaths (direct path, path with delay of 2 µSecs and path with delay of 14.5 µSecs -3dB gain) at a Doppler frequency of 40 Hz plus AWGN at -84 dBm.


Figure 6.1: IS-95 Reverse Traffic Channel Open and Closed Loop Power Control model.


6.2 Open-loop power control

In open-loop power control, the mobile’s transmit power is determined by measuring the received signal strength of the base station and estimating the forward link path loss. Assuming a similar path loss for the reverse link, the mobile uses this information to determine its transmitter power.

The first time a handset transmits, it will do so on its access channel as a reply to a message on the paging channel, or to place an outgoing call. Due to the near-far problem and the risk of interfering with other mobiles in the cell, the handset initially transmits at a low power. It then makes successive attempts (or probes) to be heard, gradually increasing its power each time until the base station detects the message and acknowledges it.

The handset’s initial mean output power is a function of the base station’s received power plus system parameters in the initial access parameters message sent on the paging channel. These parameters include nominal power (Nom_Pwr), initial power (Init_Pwr), step increase in power between access probes (Pwr_Step), and the number of access probes allowed in a sequence (Num_Step). The formula is given in (6.1).

Mean Output Power (dBm) = – Mean Input Power – 73 (dB) + Nom_Pwr (dB) +

Init_Pwr (dB) (6.1)

When designers start to create a complex system in this manner, system-level design tools allow them to begin at a high level and progressively add detail and fidelity to the design. For example, engineers can start designing a link-layer protocol without the physical layer in place, and then add that layer after testing their protocol. As another example, engineers can design the channel coding operations with a simple additive white Gaussian noise (AWGN) channel and then add a realistic fading channel later. Engineers can also design these components in parallel. In our example, we will start with the control logic for the power control algorithm without the channel.

Figure 6.2 and 6.3 illustrates a state machine describing the control logic of Base Station Controller and Mobile Controller that would typically be coded in software on a microcontroller. Graphical state machine design tools allow the description of system states, substates, and events that cause the transitions between them. This can greatly clarify the description of complex algorithms. Parameters values used in each state machine as specified in [3] are shown in Table 6.1. We can compare system states with system signals.

Figure 6.3 highlights two system states, the first is the system access superstate it contains two substates and the second is the reverse traffic channel control state and it contains one substate. Arrows are used to describe transitions between states and the labels on the arrows show the event that causes the transition.

Data processing can be included in the body of the state or after the transition label. In Figure 6.3, when the mobile first enters the access_probe substate of the system access state, it:

• Sets the transmit power using the formula • Enables the transmitter


• Starts a timer • Waits in the Access_Probe substate.

If the mobile’s power level is sufficient for reception at the base station, the base

station transmits an acknowledgement on the paging channel. This message on the paging channel, labeled as the event BS_Response, triggers the system to leave the system access superstate, disable the transmission on the access channel, and move to the reverse traffic channel control state below.

If a reply is not received, the Time_Out event generated by the timer causes the system to leave the Access_Probe substate, increase the Sum_Access_Probe_Correction variable by Pwr_Step, and increase its Num_Access_Probes counter by one. The system then reenters the Access_ Probe state, where the new value of the Sum_Access_Probe_Correction variable is used to modify the transmit power. It repeats this operation until the base station replies or the maximum allowed number of access probes Num_Step is exceeded.

In Figure 6.3, we see that when the Num_Step threshold is reached (Num_Access_Probes≥Num_Step), the system enters the wait state. Here, the access transmission is disabled, the probe power correction and probe count variables are reset, and the mobile starts its timer to wait for a random period given by another system parameter.

Once the mobile begins to transmit on the reverse traffic channel and receive on the forward traffic channel, a fast, closed-loop power control algorithm is employed. Here, the base station measures the handset’s received signal power and commands it to increase (PCB=0 if Eb/N0≤Target Eb/N0) or decrease (PCB=1 if Eb/N0>Target Eb/N0) as shown in Figure 6.3 by the Power_Control_Misadjust value which will be generated using different types of power control algorithms so that the reverse traffic channel meets a specified FER. Example minimum quality levels are a 1% to 2% FER and a maximum of three to four consecutive frame errors.

Figure 6.2: Base Station Controller State Machine.


Figure 6.3: Mobile Controller State Machine.

Table 6.1: Mobile Controller state machine parameters values

Variable Parameter Description Value

Input_Power Input Power -40 (dB) Init_Pwr Initial Power 10 (dB)

Nom_Pwr Nominal Power 5 (dB) Pwr_Step Power Step 5 (dB) Num_Step No. of access probes per access probe sequence 8

Access Threshold - -20 (dB) Eb/N0 Measured Eb/N0 -

Target Eb/N0 - 4 (dB) PCG_Clock Power Control Group Clock Period 1.25 mSec MS_Clock Mobile Station Clock Period 0.5 mSec


6.3 Closed-loop power control

Closed-loop control involves both the forward and reverse traffic channels, so successful optimization of the algorithm requires the simultaneous simulation of both these physical layer channels. To add the physical layer to a design, we can use libraries of pre-built blocks for DSP and communication operations provided with block-diagram system level tools.

Closed-loop power control can be further subdivided into inner and outer loops. In the outer loop, the base station starts with a target FER and a target bit energy-to-noise spectral density ratio (Eb/N0) required to achieve the target FER. The base station then continually measures the FER and adjusts the threshold Eb/N0 accordingly.

6.4 Base station algorithm

Both the forward and reverse traffic channels are subdivided into 20 ms frames.

Each frame is further subdivided into 16 power control groups (PCGs) lasting 1.25 ms. In the inner loop, the base station measures the received Eb/N0 of each mobile for every PCG and compares it to the target threshold calculated by the outer loop. If the Eb/N0 is less than the target, the base station commands the mobile to increase its transmit power. If the received power is higher than the target, the base station commands the mobile to decrease its power.

The base station communicates these commands to the mobile via the power control subchannel of the forward traffic channel. This subchannel transmits by inserting power control bits into the traffic channel at the PCG rate using a technique called “symbol puncturing.” The bits are inserted after the long code scrambling, just before Walsh code spreading. There are 24 symbols in one PCG in the forward traffic channel and therefore 24 possible locations for the power bit. The location changes with every PCG and is specified by the last 4 bits of the long PN code in the previous frame.

The handset extracts the power control bits using the same long PN code bits. If a 1 bit is received, the mobile reduces its transmit power by the estimated error value. If a 0 bit is received, the mobile increases its transmit power by the new estimated error value. Now the mobiles uses the formula in (6.2) to calculate its transmit power.

Mean Output Power (dBm) = - Mean Input Power – 73 (dB) + Num_Pwr (dB) + Init_Pwr

(dB) + sum of all access probe corrections (dB) + the sum of all closed-loop power control corrections (dB) (6.2)

The reverse traffic channel control state is shown in figure 6.3, which adjusts its

transmitted power as a function of the power bit. On entering the traffic channel control state from the System_Access state, the traffic channel is enabled. In the conversation substate, the transmit power is set using the previously mentioned formula. On every PCG clock event, the system exits the substate and looks at the value of the Error then Power_ Control_ Misadjust variable is incremented by that amount. The system then returns to the conversation substate, where the new value of the Power_ Control_ Misadjust variable is used.


6.5 System simulations In this section we will apply different power control algorithms that are mentioned in the previous chapters (Fixed Step Size Power Control “FSPC”, Adaptive Step Size Power Control “ASPC”, AS with Asymmetric update step sizes “AS-A”, AS with gradually increasing update step size “AS-G”, and AS with variable update step size “AS-VG”) on our simulation model and see how it affects on updating mobile transmitted power (MS_Tx_Power), measured Eb/N0 at the base station and its convergence to (Target Eb/N0), and Variation of S/N. To prevent the update step size to grow too large, a limit of 1 dB was used in all the simulations.

6.5.1 Fixed Step Size Power Control “FSPC” algorithm

In FSPC on every PCG clock event, the system exits the substate and looks at the value of the power bit stored in Error. If the value of the Rx_Power_Bit equals 0; the Power_Control_Misadjust variable is incremented by 1 dB. If the value equals 1, the Power_Control_Misadjust variable is decremented by 1 dB. The system then returns to the conversation substate, where the new value of the Power_Control_Misadjust variable is used, so we convert received PC commands (Rx_Power_Bit) from unipolar 0 and 1 to bipolar 1 and -1 respectively at the entry of mobile controller as shown in figure 6.4.

Figure 6.4: Mobile Station model using FSPC.


Figure 6.5: Received Eb/N0, Threshold, and mobile transmitted power for FSPC

algorithm. Figure 6.5 shows the mobile received Eb/N0, and the Eb/N0 threshold. The lower

axis shows the mobile transmitted power. The next axis shows a frame rate clock where each edge marks the start of a frame, the value of the power bit sent on the power control subchannel, and the PCG rate clock.

Due to fading, the received Eb/N0 varies. Whenever Eb/N0 is greater than the threshold, the base station sets the power control bit to 1 and the mobile correspondingly decreases its transmit power. Whenever Eb/N0 is less than the threshold, the base station sets the power control bit to 0 and the mobile correspondingly increases its transmit power. These power adjustments ensure that the mobile maintains an acceptable FER while minimizing its transmission power.


6.5.2 Adaptive Step Size Power Control “ASPC” algorithm

As discussed in the previous chapter we will use equation (5.7) and apply it to our simulation model for ASPC algorithm, the model is the same as the one shown in figure 6.4 except that the unipolar to bipolar converter is replaced by the block diagram shown in figure 6.6. The enable shown here is to make this subsystem only enabled during the conversation state. The Tx_Power_Update variable is applied to Error input variable of the mobile controller shown in figure 6.3. Note the saturation block used here to limit output to 1 dB. Figure 6.7 shows the effects produced by applying the ASPC algorithm. In figure 6.7 it is clear that now MS_Tx_Power increased and decreased quadratically with 1.0=eδ not linearly as in the FSPC so it oscillates closely around Target_Eb/N0.

6.5.3 AS with asymmetric update step sizes “AS-A”

According to equation (5.8) and (5.9) the model in figure 6.4 is the same with the

unipolar to bipolar converter is replaced by the block diagram shown in figure 6.8. Figure 6.9 shows the effects produced by applying the AS-A algorithm. We can notice that MS_Tx_Power quadratically increased with larger update step sizes than when decreased ( 1.03.0 == down

eupe and δδ ).

6.5.4 AS with gradually increasing update step sizes “AS-G”

According to equation (5.10) the model in figure 6.4 is the same with the unipolar

to bipolar converter is replaced by the block diagram shown in figure 6.10. Figure 6.11 shows the effects produced by applying the AS-G algorithm. We can notice that MS_Tx_Power cubically increased and decreased faster than ASPC with ( 21 == sm nandδ ).

6.5.5 AS with variable update step size “AS-VG” According to equation (5.11) and (5.12) the model in figure 6.4 is the same with

the unipolar to bipolar converter is replaced by the block diagram shown in figure 6.12. Figure 6.13 shows the effects produced by applying the AS-VG algorithm. We can notice that MS_Tx_Power cubically increased and decreased faster than ASPC with ( 01.0=VGδ ). Note also that after 200 mSecs of time, we start receiving consecutive 1’s and 0’s of power control bits which results in a reduction of the amplitude of Eb/N0 oscillations around Target_Eb/N0 which, in turn, reduces MS_Tx_Power oscillations around optimal value to even less than 0.01 dB. If compared to FSPC with the same situation MS_Tx_Power will continue to oscillate with amplitude of oscillations equal to 1 dB.

The variance of Eb/N0 for all the previous cases is shown in figure 6.14, before t = 25 mSecs there was no access for the mobile on the network after that time mobile has been accessed and power control algorithm has been started as BS assign a traffic channel for it, so as shown in figure 6.14 variance of Eb/N0 start to decrease very rapidly for all cases which is a good indication for the effect of power control on the system then after t = 1 Sec it starts to saturate around a specific value. Figure 6.15 is a zoomed version of


figure 6.14 showing the variance in the period from 1.9 to 2 Secs. As shown ASPC, AS-A and AS-G have approximately the same variance with ASPC having the lowest value, on the other hand both FSPC and AS-VG have variance lower than the previous group by about 25 with AS-VG giving the smallest variance value.

Figure 6.6: Block diagram of ASPC algorithm.

Figure 6.7: Received Eb/N0, Threshold, and mobile transmitted power for ASPC algorithm.


Figure 6.8: Block diagram of AS-A algorithm.

Figure 6.9: Received Eb/N0, Threshold, and mobile transmitted power for AS-A

algorithm.


Figure 6.10: Block diagram of AS-G algorithm.

Figure 6.11: Received Eb/N0, Threshold, and mobile transmitted power for AS-G algorithm.


Figure 6.12: Block diagram of AS-VG algorithm.

Figure 6.13: Received Eb/N0, Threshold, and mobile transmitted power for AS-VG algorithm.


Figure 6.14: Variance of Eb/N0 for FSPC, ASPC, AS-A, AS-G, and ASVG before and after access intervals.

Figure 6.15: Variance of Eb/N0 for FSPC, ASPC, AS-A, AS-G, and ASVG when the mobile is in the conversation state.

Chapter 7

Conclusion and Future Work

Ch. 7. Conclusion and Future Work

95

Conclusion and Future Work

Power control is of utmost importance in CDMA cellular communication systems. Such systems are used in the 3rd generation cellular networks, such as UMTS in Europe. These systems are targeted for a large number of subscribers and high-speed wireless multimedia services. The increasing bandwidth demands and the growing number of users call for efficient radio resource management, and thus power control, as an important part of radio resource management, needs to be carefully considered.

In this thesis new closed-loop power control algorithms have been developed for CDMA cellular communication systems. The task of closed-loop power control is to keep the signal-to-interference (SIR) ratios at the receivers at their target values. The target values are set by outer loop power control in order to keep the frame error rates at an acceptable level with minimum possible transmission powers.

Since in CDMA all users share simultaneously the same frequency band, they all interfere with one another. Therefore, the minimization of transmission powers leads to increase in capacity. The driving idea of the proposed algorithms is the minimization of the variance of the SIRs at the receivers, while keeping them at the target values. The variance minimization leads to reduction of the required SIR targets, and thus smaller transmission powers. A detailed overview of power control in CDMA cellular systems has been given in the thesis.

The proposed adaptive step-size algorithms are very attractive from implementation viewpoint due to their simplicity and excellent performance with slow-speed mobility. A drawback of the basic ASPC algorithm is that it is only applicable for slowly moving mobiles, and its performance dramatically degrades with increasing speed. Several modifications of the ASPC algorithm were proposed, and shown to be able to enhance the high-mobile-speed performance of the basic ASPC.

The performances of the proposed algorithms were investigated through extensive computer simulations. The reference algorithms were the distributed constrained power control (DCPC) algorithm in the IFB case, and the fixed-step power control (FSPC) algorithm in the DFB case. The simulations indicated that significant performance improvements can be achieved with the proposed algorithms in comparison to the reference algorithms. In the DFB case, the performance gains come with zero increase in power control signaling, i.e., using only one-bit power control commands as in the FSPC algorithm. This is interesting considering practical implementations of CDMA cellular networks.

Of the adaptive step methods, the AS-VG method the related ASPC-VG algorithm seem to be the best compromise, giving acceptable performance at low-speed mobility, and superior performance at high-speed mobility.

Clearly the proposed adaptive algorithms can improve the closed-loop power

control performance using only local information. In some cases a part of the link gain matrix may be, at least partially, known. In [27, 51] a method called block power control is proposed, which utilizes the partially known link gain matrices. An interesting extension of the adaptive algorithms proposed in this thesis would be to apply similar

Ch. 7. Conclusion and Future Work

96

ideas in block power control using multivariable self-tuning controllers, where the user interactions within a block could be taken into account in the system model.

Interesting future studies could include the extension of the proposed adaptive algorithms to jointly control power and data rate, as well as handovers.

The convergence of the AS methods was studied in the thesis by simulations. However, analytical convergence proofs are not yet available, and remain open problems.

97

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Appendix A

101

Appendix A Eigenvalues and Eigenvectors

A.1 Eigenvalues and Eigenvectors Many applications of linear algebra are concerned with systems of n linear

equation in n unknowns that are expressed in the form

xAx λ= (A.1) where λ is scalar. Such systems are really homogeneous linear systems [52].

The system (A.1) can be rewritten as, 0=− Axxλ , or by inserting an identity

matrix and factoring, as

0)( =− xAIλ (A.2) The problem of interest for linear system (A.2) is to determine those values of λ for which the system has a nontrivial solution; such a value of λ is called an eigenvalue of A. If λ is an eigenvalue of A, then the nontrivial solutions of (A.2) are called the eigenvector of A corresponding to λ. The linear system (A.2) has a nontrivial solution if and only if det 0)( =− AIλ (A.3) This is called the characteristic equation of A. The eigenvalues of A can found by solving this equation for λ. Multiplication by A maps each eigenvector x of A (if any) onto the same line through the origin as x. Depending on the sign and the magnitude of the eigenvalue λ corresponding to x, the linear operator xAx λ= compresses or stretches x by a factor of A, with a reversal of direction in the case where A is negative, see figure A.1.

(a) 10 << λ (b) 1>λ (c) 01 <<− λ (d) 1−≤λ

Figure A.1: Direction and magnitude of Ax with respect to λ.

x

λx

λx

x

λx

x x

λx

Appendix A

102

Let’s see an example and apply it for the SIR balancing problem discussed in chapter 2 that’s shown in Figure 2.5, consider a two user case with uplink receiver noise η = 0, target SIR 0γ =14 dB and link gain matrix

=

0625.00039.00123.01

G

We need to find the largest minimum SIR γ* that can be achieved in both BSs, and

the transmitter powers the terminals should use to reach this SIR level P*. The matrix A is given by

==

00625.00123.001 A

0

Hγ

The characteristic of A is

00.000770625.0

0123.0)det( 2 =−=

−−

=− λλ

λλ AI

The eigenvalues of A are 02778.02,1 ±=λ , and the spectral radius 02778.0)( =Aρ .

Therefore, according to equation (2.2), dB1636*21 ===Γ=Γ γ .

By definition the eigenvector P* of A corresponding to λ = 0.02778 becomes

=

−

−=−

00

02778.00625.00123.002778.0

)(2

1

PP

PIA λ

which has a solution

P*= c

0.91380.4061

where c is a constant. We can see that using the power vector P* we have successful SIR balancing where 0

*21 γγ >=Γ=Γ as shown in figure 2.5.

If we have a triangular matrix

=

33

2322

131211

000

aaaaaa

A

Since the determinant of a triangular matrix is the produce of the elements on the

main diagonal, we obtain

Appendix A

103

))()((00

0)det( 332211

33

2322

131211

aaaa

aaaaa

AI −−−=−−−−−−

=− λλλλ

λλ

λ

Thus the characteristic equation of A is,

0))()(( 332211 =−−− aaa λλλ

and the eigenvalues of A are

333222111 ,, aaa === λλλ Which are the elements on the main diagonal of A. Theorem (1)

If A is an nn× triangular (upper triangular, lower triangular, or diagonal), then the eigenvalues of A are the elements on the main diagonal of A. Powers of a Matrix Once the eigenvalues and eigenvectors of a matrix A are found, it is a simple matter to find the eigenvalues and eigenvectors of any positive integer power of A; for example if λ is an eigenvalue of A and x is a corresponding eigenvector, then

xxAxxAAxAxA 22 )()()()( λλλλλ =====

which shows that λ2 is an eigenvalue of A2 and x is a corresponding eigenvector. In general, we have the following result. Theorem (2) If k is a positive integer, λ is an eigenvalue of a matrix A, and x is a corresponding eigenvector, then λk is an eigenvalue of Ak and x is a corresponding eigenvector. Eigenvalues and Invertibility The next theorem establishes a relationship between the eigenvalues and the invertibility of a matrix. Theorem (3) A square matrix A is invertible if and only if λ = 0 is not an eigenvalue of A.

Appendix A

104

A.2 Diagonalization

A square matrix A is called diagonalizable if there is an invertible matrix P such that P-1AP is a diagonal matrix; the matrix P is said to diagonalize A.

Theorem (4) If A is an nn× matrix, then the following are equivalent.

(a) A is diagonalizable. (b) A has n linearly independent eigenvectors.

Method of diagonalizing Step 1. Find n linearly independent eigenvectors of A, say p1, p2, …, pn. Step 2. Form the matrix P having p1, p2, …, pn as its column vectors.

Step 3. The matrix P-1AP will then be diagonal with λ1, λ 2, …, λ n as its successive diagonal entries, where λi is the eigenvalue corresponding to pi, for i = 1, 2, …, n

Computing Powers of a Matrix If A is an nn× matrix and P is an invertible matrix, then,

PAPAIAPPAPAPPPAPP 2111121 )( −−−−− ===

More generally, for any positive integer k

PAPAPP kk 11 )( −− =

It follows from this equation that if A is diagonalizable, and P-1AP = D is a diagonal matrix, then

kkk DAPPPAP == −− )( 11

Solving this equation for Ak yields

1−= PPDA kk

This last equation expresses the kth power of A in terms of the kth power of the diagonal matrix D. But Dk is easy to compute; for example, if

=

nd

dd

D

...00..........00...0

2

1

then

=

kn

k

k

k

d

dd

D

...00..........00...0

2

1

الملخص العربى

النفاذ المتعدد بالتقسيم الكودى هو منظومة نفاذ متعدد محدودة بالتداخل، فنتيجة إلشتراك آل المستخدمين

فى اإلرسال على نفس التردد، یعتبر التداخل المولد ذاتيآ بالمنظومة أهم عامل فى تحدید سعة المنظومة وجودة

مشعة من آل مستخدم إلى أدنى مستوى للحد من التداخل، ومع ذلك اإلتصال، ولذلك فمن الواجب خفض القدرة ال

یجب أن تكون القدرة آافية لإلبقاء على القدر المطلوب للنسبة بين قدرة اإلشارة وقدرة الضجيج وبالتالى جودة

اإلتصال، وتتحقق السعة القصوى عندما تكون النسبة بين قدرة اإلشارة وقدرة الضجيج لكل مستخدم فى أدنى

. مستوى مطلوب لألداء المقبول لقناة اإلتصال

تتغير بيئة تردد الرادیو بإستمرار مع تحرآات الجهاز المحمول وذلك نتيجة؛ الخفوت السریع و البطئ،

والهدف من الضبط الفعال للقدرة هو الحد من القدرة المشعة على آلتا . التداخل الخارجى، الحجب، وعوامل أخرى

حفاظ على جودة الوصلة تحت آل الظروف، ومن المميزات اإلضافية إطالة العمر اإلفتراضى الوصلتين مع ال

إن التصميم األمثل الناجح ألى خوارزم .لبطاریة الجهاز المحمول وإطالة عمر مكبرات القدرة لمحطات المحمول

المنظومة مما یسمح ضبط القدرة یحتاج إلى محاآاة عدة مكونات، ویمكن تحقيق هذا الهدف بتصميم مستویات

.بمحاآاة آل من الطبقة الملموسة و طبقة الوصلة لمنظومات اإلتصاالت

لنفاذ المتعدد ا تامنظوم القدرة فى جدیدة لضبط حلقية مغلقة خوارزمات إقتراح تتناول هذه الرسالة

ادئ نظم التحكم للتوليف الذاتى قد تم إفتراض خوارزمات متكيفة تقوم على مبو. لإلتصاالت الخلویة بالتقسيم الكودى

الحلقية جد مشكلة أخرى لضبط القدرةاتو حيث ت و، و التداخل للتغلب على التغيرات العشوائية لقنوات الرادیو

لموارد الرادیو مما یضطرنا إلستخدام تغذیة عكسية للتحكم محدودة إلستهالك إشارات التحكم الشاملة نتيجة المغلقة

الحلقية المغلقة فى حالة التغذیة العكسية محدودة رض طریقة جدیدة لتحسين أداء ضبط القدرة تم ع،المدى الترددى

.إقتراح خوارزمات لضبط القدرة مبنية على هذه الطریقة الجدیدة و،المدى الترددى

التحليل و المحاآاة بالكمبيوتر بإستخدام حزم برامجتم تقييم أداء الخوارزمات المقترحة من خاللولقد

)Matlab( ،من الدراسات السابقة فى هذا الموضوعمعروفة جيدًا خوارزمات مع محاآاةمقارنة نتائج ال و ،

. تحسن ملحوظ فى أداء الخوارزمات المقترحةإحراز وأظهرت النتائج

-:ق و بيانها آالتالى و الرسالة تقع فى سبعة فصول عدا المراجع و الملح

و ، لضبط قدرة اإلرسال بهالنفاذ المتعدد بالتقسيم الكودى هو مقدمة عامة عن مدى إحتياج شبكات االفصل األول

.عرض تصنيفات متعددة لتقنيات ضبط القدرة

آما یقدم أیضًا عرض . یشتمل هذا الفصل على صياغة لمشكلة ضبط القدرة بصورة ریاضيةالفصل الثانى

.لخوارزمات معروفة جيدًا من دراسات سابقة فى هذا الموضوع

یقدم هذا الفصل دراسة لتأثير وجود مستخدمين غير فعالين داخل الشبكة وآذلك تأثير األخطاء الواردة الفصل الثالث

.فى نظام ضبط القدرة على سعة الشبكة و آفائتها

. )CDMA IS-95(شبكة النفاذ المتعدد بالتقسيم الكودى یتضمن هذا الفصل تفاصيل ضبط القدرة فى الفصل الرابع

یقدم هذا الفصل تفاصيل الخوارزمات المقترحة لضبط القدرة الحلقية المغلقة فى حالة التغذیة الفصل الخامس

آما یقدم تقييم ألداء الخوارزمات المقترحة من خالل التحليل و . العكسية محدودة المدى الترددى بصورة متكيفة

مع خوارزمات معروفة جيدًا من محاآاةمقارنة نتائج ال و،)Matlab(اآاة بالكمبيوتر بإستخدام حزم برامج المح

.الدراسات السابقة فى هذا الموضوع

. ونتائجه)Simulink(یستعرض هذا الفصل شرحًا مفصًال لبرنامج المحاآاة المستخدم الفصل السادس

.إقتراحات ألعمال مستقبلية یمكن أجرائها فى هذا المجالیشتمل هذا الفصل خاتمة مع الفصل السابع

جامعة بنها املعهد العاىل للتكنولوجيا ببنها

نائب رئيس اجلامعة للدراسات العليا والبحوث على تشكيل جلنة املناقشة واحلكم من / وافق األستاذ الدكتور -: السادة

أستاذ اإلتصاالت عبد احلليم عبد النىب ذكرى/ األستاذ الدكتور -١

جامعة عني مشس-كلية اهلندسة

رئيس قسم هندسة اإللكترونيات و اإلتصاالت حممد السعيد نصر/ األستاذ الدكتور -٢ جامعة طنطا–كلية اهلندسة

بصوت واحد-عن جلنة األشراف و

رئيس قسم تكنولوجيا اهلندسة الكهربية صالح غازى رمضان/ األستاذ الدكتور -٣ جامعة بنها– جيا ببنهاواملعهد العاىل للتكنول

إستشارى شركة زد تى إى عبد العزيز حممود البسيوىن/ الدكتور -٤

للحصول على درجة املاجيستري ىف حامت حممد حممد زكريا رضوان/ لفحص الرسالة املقدمة من املهندس

.تكنولوجيا اهلندسة الكهربية

الدراسات العليا وكيل املعهد للدراسات العليا

علم الدين عادل / م .د.أ

الضبط األمثل لقدرة اإلرسال فى شبكات النفاذ التقسيم الكودىالمتعدد ب

رسالة إلى مقدمة

جيا ببنها والمعهد العالى للتكنول آجزء من متطلبات الحصول على درجة الماجستير

فى

تكنولوجيا الهندسة الكهربية

من

حاتم محمد محمد زآریا. م

:یعتمد من لجنة الممتحنين

) ( عبد الحليم عبد النبى ذآرى /د.أ -١ جامعة عين شمس–آلية الهندسة

محمد السعيد نصر/د.أ -٢ ) ( رئيس قسم هندسة اإللكترونيات و اإلتصاالت الكهربية

جامعة طنطا–آلية الهندسة

و عن لجنة اإلشراف

) ( صالح غازى رمضان / د.أ -٣ رئيس قسم تكنولوجيا الهندسة الكهربية

بنها–المعهد العالى للتكنولوجيا

) ( عبدالعزیز محمود البسيونى / د-٤ القاهرة –إستشارى شرآة زد تى إى

للتكنولوجيا ببنها، جامعة بنهاالمعهد العالى جمهوریة مصر العربية

٢٠٠٦

الضبط األمثل لقدرة اإلرسال فى شبكات النفاذ المتعدد بالتقسيم الكودى

رسالة إلى مقدمة

جيا ببنهاوالمعهد العالى للتكنول آجزء من متطلبات الحصول على درجة الماجستير

فى

تكنولوجيا الهندسة الكهربية من

حاتم محمد محمد زآریا.م

تحت إشراف صالح غازى رمضان/ د.أ لمعهد العالى للتكنولوجيا ببنهاا

عبدالعزیز محمود البسيونى/ د إستشارى شرآة زد تى إى

أیمن مصطفى حسن/ د المعهد العالى للتكنولوجيا ببنها

المعهد العالى للتكنولوجيا ببنها، جامعة بنها جمهوریة مصر العربية

٢٠٠٦

optimal power control in cdma mobile networks - bu benha/electrical... · optimal power control in...

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