Algorithmes d'adaptation pour la couche physique de systèmes multi-porteuses.

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Mahmood, Asad (2008) Algorithmes d'adaptation pour la couche physique de systèmes multi-porteuses. Doctorat Electronique et Telecommunications, LEI, ENSTA.

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Résumé

The main objective of our thesis was to reduce the complexity of the existing adaptive algorithms for multi-carrier systems, both, from a theoretical/algorithmic perspective as well as taking advantage from the adaptive nature of the state-of-the-art under-lying implementation platforms. To reach this objective, adaptation was performed both from an algorithmic as well as an architectural point of view. From an algorithmic perspective, an insight into the inherent pattern, which exists in the optimal bit-allocation procedure and based upon this pattern the design of a Novel Optimal Discrete Bit Loading algorithm was performed which has a complexity significantly lower than existing algorithms for discrete bit-loading

Then optimizing the parameter of allocated power, theoretical developments for an optimal power-allocation including the Peak-Power Constraint and the design of a novel algorithm for Peak-Power Constrained Optimal Power Allocation was performed which involves a complexity significantly lower than the classical method of Iterative- Water-filling, which is conventionally employed for such constrained power allocations. Then, targeting channel coding, a proposal of the design and optimization of Finite-Length Irregular LDPC Codes, was made based on the Wave-Quantization methodology. Finally, a methodology to tune the hardware resources of a flexible underlying architecture (e.g. FPGA) at run-time based upon the needs of the channel and system is proposed. This results in the use of the link-adaptation algorithms at those ranges of Doppler-frequencies/user-mobility, which are not possible to operate upon, otherwise.

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Table des Matières

Contents

Contents iii

Acknowledgements vii

Notations x

Acronyms xiii

Publications xv

Long Summary in French xvi

List of Figures xxxvii

List of Tables xli

1 Introduction 1

1.1 Adaptive Communication Systems - Resource Allocation - 1

1.2 Resource Allocation in Single and Multicarrier Physical Layer - 2

1.3 Problem Definition - 5

1.4 Our Contributions and Thesis Presentation - 7

2 Bit-Loading Algorithm for Multicarrier Systems 11

2.1 Introduction - 11

2.2 Types of the Bit-Loading Problem - 13

2.2.1 Rate Maximization - 13

2.2.2 Margin Maximization - 15

2.3 State of the Art on Discrete Bit-Loading Algorithms - 16

2.3.1 Greedy Approach based techniques - 17

iv CONTENTS

2.3.2 Approximation techniques - 18

2.3.3 Mathematical Analysis/Optimization methods based techniques . 19

2.3.4 Subcarrier Bit-Incremental Energy Relationship - 20

2.4 3dB-Subgroup Classification of Subcarriers - 21

2.4.1 Gap Approximation - 21

2.4.2 Bit-Incremental Energy Relationship and 3-dB subgroup Classifi-

cation - 22

2.5 3dB-Subgroup allocation methodology - 24

2.5.1 Allocation Rythm across Different Steps of Bit-Allocation - 25

2.5.2 Allocation Rythm Within a Single Step of Bit-Allocation - 26

2.5.2.1 Initial allocation - 27

2.5.2.2 Final Allocation - 28

2.6 Optimal Allocation with Peak Power/Energy Per Subcarrier Constraint . 31

2.7 Simulation and Results - 33

2.7.1 Simulation Scenario - 33

2.7.2 Bit-Allocation Profile - 34

2.7.3 Total Energy Improvement Factor - 35

2.7.4 Complexity Comparison - 37

2.7.4.1 Expected Algorithm Complexity - 37

2.7.4.2 Exact Number of Execution Cycles on a Processor . . . 39

2.7.4.3 SimpleScalar Tool For Execution-Based Algorithm Com-

plexity Analysis - 39

2.7.4.4 Comparison of Number of Execution-Cycles - 40

2.8 Conclusion - 41

3 Optimal Power Allocation Algorithm for Peak-Power Constrained Mul-

ticarrier Systems 45

3.1 Introduction - 45

3.2 State of the Art on Power Allocation Schemes - 49

3.2.1 Works on Theoretical Foundations - 50

3.2.2 Works on BER-Optimal Power Allocation - 50

3.2.3 Works Related to Power Allocation with Peak-Peak Constraint . . 52

3.2.4 Iterative Waterfilling Algorithm - 53

CONTENTS v

3.3 Using Lagrange Multipliers for Convex Optimization - 55

3.3.1 Lagrangian Problem Formulation - 57

3.3.2 Duality and Karush-Kuhn-Tucker Conditions - 59

3.4 BER-Optimized Power Allocation - 61

3.4.1 BER minimization problem - 61

3.4.2 BER-Optimized Power Allocation with Peak-Power Constraint . . 62

3.4.3 Computationally Efficient Algorithm for Peak-Energy Constrained

Energy Allocation - 64

3.5 Conclusion - 74

4 Simplistic Algorithm for Irregular LDPC Codes Optimization Based on

Wave Quantification 77

4.1 Background and Problem Definition - 77

4.1.1 LDPC History, Representation and Types - 78

4.1.2 LDPC Codes Construction and Encoding - 80

4.1.3 LDPC Codes Decoding - 81

4.1.3.1 Belief Propagation - 82

4.1.4 Irregular LDPC Codes - 84

4.1.4.1 Irregularity - 84

4.1.4.2 Wave-Effect - 85

4.1.4.3 Design of Irregular LDPC Codes - 86

4.2 State of the Art on Irregular LDPC Codes Optimization and Construction 87

4.2.1 Works Related to Irregularity Profile Optimization - 87

4.2.2 Works Related to Finite Length Codes Construction - 88

4.2.3 Works Related to Hard Decoding for Irregular LDPC - 90

4.2.4 Open Problem in Finite Length Irregular LDPC Code Design . . 91

4.3 Majority-Based (MB) Hard-Decoding Algorithm for Irregular LDPC Codes 92

4.3.1 Gallager A and Gallager B Hard-Decoding Algorithms - 92

4.3.2 Concept and Algorithm for MB Hard Decoding - 94

4.3.2.1 Important Characteristics of MB Hard-Decoding Algo-

rithms - 95

4.4 Simplifying the MB Hard-Decoding Analysis for Irregular LDPC Codes . 97

4.4.1 Hard-Decoding Analysis for Irregular LDPC Codes - 97

vi CONTENTS

4.4.2 Modified Representation of Gallager’s Equation in the form of Deltas

(s) - 99

4.4.3 Classical Calculation Method of Updating pn

i in Irregular Graphs 100

4.4.4 Sum of Products of Combinations (SPC) based Calculation Method

of Updating pn

i in Irregular Graphs - 102

4.5 Wave-Effect Quantization Methodology for Design/Construction of Irreg-

ular LDPC Codes - 106

4.5.1 The Pyramid Effect - 106

4.5.2 Neighborhood - 107

4.5.3 Greedy Irregularity Construction (GIC) Algorithm - 109

4.6 Conclusion - 113

5 Algorithm-Architecture Co-Optimization for Delay-Constrained Link-

Adaptation Algorithms 115

5.1 Introduction - 115

5.2 State of the Art - 120

5.2.1 From Theoretical Perspective - 120

5.2.2 From Implementation Perspective - 121

5.3 Tools (SimpleScalar) and Techniques (Genetic Algorithms) Employed . . 122

5.3.1 SimpleScalar Tool and the Design Space of the Superscalar Archi-

tecture - 122

5.3.2 Genetic Algorithms for Design Space Exploration - 124

5.3.2.1 Population - 127

5.3.2.2 Fitness - 127

5.3.2.3 Selection of the Fittest - 127

5.3.2.4 Crossover - 127

5.3.2.5 Mutation - 128

5.4 Algorithm - Architecture Co-Optimization for Delay Constrained Link-

Adaptive Systems - 128

5.5 Conclusion - 134

6 Conclusion 135

Bibliography 141

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