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  • Power Control in Wireless

    Cellular Networks

  • Power Control in

    Wireless Cellular


    Mung Chiang

    Electrical Engineering Department, Princeton University

    Prashanth Hande

    Electrical Engineering Department, Princeton University

    Tian Lan

    Electrical Engineering Department, Princeton University

    Chee Wei Tan

    Electrical Engineering Department, Princeton University

    Boston Delft

  • Foundations and Trends R in Networkingsample

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    The preferred citation for this publication is , Power Control in Wireless CellularNetworks, Foundation and Trends R in sample, vol x, no y, pp 1156, 2008

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    ISBN: 1-933019-09-3c 2008

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    Foundations and Trends R in Networking sample will publish

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  • Foundations and TrendsR in NetworkingsampleVol. x, No y (2008) 1156c 2008

    Power Control in Wireless Cellular Networks

    Mung Chiang1, Prashanth Hande2, Tian

    Lan3 and Chee Wei Tan4





  • Abstract

    Transmit power in wireless cellular networks is a key degree of freedom

    in the management of interference, energy, and connectivity. Power

    control in both uplink and downlink of a cellular network has been

    extensively studied, especially over the last 15 years, and some of the

    results have enabled the continuous evolution and significant impact of

    the digital cellular technology.

    This monograph provides a comprehensive survey of the models,

    algorithms, analysis, and methodologies in this vast and growing lit-

    erature. It starts with a taxonomy of the wide range of power control

    problem formulations, and progresses from the basic formulation to

    more sophisticated ones. When transmit power is the only set of opti-

    mization variables, algorithms for fixed SIR are presented first, before

    turning to their robust versions and joint SIR and power optimization.

    This is followed by opportunistic and non-cooperative power control.

    Then joint control of power together with beamforming pattern, base

    station assignment, spectrum allocation, and transmit schedule is sur-

    veyed one by one.

    Throughout the monograph, we highlight the use of mathematical

    language and tools in the study of power control, including optimiza-

    tion theory, control theory, game theory, and linear algebra. Practical

    implementations of some of the algorithms in operational networks are

    discussed in the concluding chapter. As illustrated by the open prob-

    lems presented at the end of most chapters, in the area of power control

    in cellular networks, there are still many under-explored directions and

    unresolved issues that remain theoretically challenging and practically


  • Contents

    1 Introduction 3

    1.1 Overview 3

    1.2 Notation 6

    1.3 Taxonomy of Problem Formulations 6

    1.4 Convexity and Decomposability Structures 16

    2 Power Control with Fixed SIR 21

    2.1 Introduction 21

    2.2 Distributed Power Control 22

    2.3 Standard Interference Function 24

    2.4 Canonical Power Control 26

    2.5 Extensions 28

    2.6 Open Problems 32

    3 Transients, Robustness, and Admission 33

    3.1 Introduction 33

    3.2 SIR Invariant Region 34


  • 3.3 Power Control with Active Link Protection 37

    3.4 Robust Distributed Power Control 38

    3.5 Open Problems 46

    4 Power Control with Variable SIR 49

    4.1 Introduction 49

    4.2 SIR Feasibility Region 51

    4.3 Joint SIR Assignment and Power Control 53

    4.4 Open Problems 60

    5 Opportunistic Power Control 61

    5.1 Introduction 61

    5.2 Opportunistic Throughput Maximization in Uplink 62

    5.3 Opportunistic Utility Maximization in Downlink 63

    5.4 Open Problems 69

    6 Non-cooperative Power Control 71

    6.1 Introduction 71

    6.2 Fixed-SIR Power Control as Game 74

    6.3 Linear Pricing Game 76

    6.4 Energy-efficiency Utility Game: Single-carrier 77

    6.5 Energy-efficiency Utility Game: Multi-carrier 80

    6.6 Game with Network Pricing and BS Assignment 84

    6.7 Open Problems 87

    7 Joint PC and Beamforming 89

    7.1 Introduction 89

    7.2 Uplink with Fixed SIR 92

    7.3 Uplink with Variable SIR 96

    7.4 Uplink-downlink Duality 100

    7.5 Open Problems 104

    8 Joint PC and BS Assignment 105

  • 8.1 Introduction 105

    8.2 Joint PC and BS Assignment 108

    8.3 Joint PC, Beamforming, and BS Assignment 111

    8.4 Open Problems 112

    9 Joint PC and Spectral-Temporal Scheduling 115

    9.1 Introduction 115

    9.2 Joint PC and Bandwidth Allocation 116

    9.3 Joint PC and Scheduling 119

    9.4 Joint PC, Beamforming, and Bandwidth Allocation 125

    9.5 Open Problems 128

    10 Industry Adoption 131

    10.1 Introduction 131

    10.2 Power Control in 2G Networks 132

    10.3 Power Control and Scheduling in 3G/4G Networks 135

    10.4 Power Control in WiFi Networks 139

    10.5 Open Issues 139

    References 143

  • Contents


  • 1


    1.1 Overview

    Transmission powers represent a key degree of freedom in the design of

    wireless networks. In both cellular and ad hoc networks, power control

    helps with several functionalities:

    Interference management : Due to the broadcast nature ofwireless communication, signals interfere with each other.

    This problem is particularly acute in interference-limited sys-

    tems, such as CDMA systems where perfect orthogonality

    among users are difficult to maintain. Power control helps

    ensure efficient spectral reuse and desirable user experience. Energy management : Due to limited battery power in mo-

    bile stations, handheld devices, or any nodes operating on

    small energy budget, energy conservation is important for

    the lifetime of the nodes and even the network. Power con-

    trol helps minimize a key component of the overall energy

    expenditure. Connectivity management : Due to uncertainty and time-

    variation of wireless channels, even when there is neither


  • 4 Introduction

    signal interference nor energy limitation, the receiver needs

    to be able to maintain a minimum level of received signal

    so that it can stay connected with the transmitter and esti-

    mate the channel state. Power control helps maintain logical

    connectivity for a given signal processing scheme.

    To define a scope that allows an in-depth treatment within 150

    pages, we will focus on power control in cellular networks in this mono-

    graph, emphasizing primarily its use in interference management while

    occasionally touching upon energy and connectivity management. Most

    of the treatment is devoted to uplink transmission from mobile station

    (MS) to base station (BS), although extensions to downlink transmis-

    sion from a BS to MSs are sometimes discussed as well. In many for-

    mulations uplink problems are more difficult to solve, although there

    are exceptions like joint power control and beamforming, and in other

    formulations uplink and downlink problems present in


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