Muck, Markus (2006) Systèmes multiporteuses à postfixes pseudo aléatoires. PhD thesis Électronique et communications , ENST - COMELEC Communication et Electronique, ENST p.176.

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Abstract

Dans le contexte de cette thèse, un nouveau schéma de modulation est proposé en introduisant une séquence déterministe pondérée par un scalaire pseudo aléatoire: Pseudo Random Postfix OFDM (PRP-OFDM). Il est proposé de remplacer l’extension cyclique du Cyclic Prefix OFDM (CP-OFDM) classique par un postfixe connu à l’émetteur et au récepteur [1–26].

Grâce à la nature déterministe de cette séquence, le récepteur peut exploiter sa connaissance afin d’estimer la réponse impulsionnelle du canal de propagation par une approche semi-aveugle d’ordre un. Ceci permet d’éviter l’introduction des séquences d’apprentissage ou des symboles pilotes. L’efficacité spectrale du système est donc améliorée par rapport à des architectures classiques comme le CP-OFDM, Zero-Padded OFDM(ZP-OFDM), etc. Par la suite, plusieurs algorithmes sont proposés. Ceux-ci permettent d’effectuer une estimation du canal dans un contexte statique et dans un contexte de mobilité. En delà, la dérivation d’une séquence de postfixe optimisée est présentée. Ensuite, les études sont étendues à un raffinement de la synchronisation temporelle et fréquentielle d’une estimation initiale approximative. Après, une utilisation optimale des codes LDPC (Low Density Parity Check) est discutée dans le contexte de l’OFDM: il est montré comment il faut attribuer des mots de codes LDPC à des porteuses OFDM en prenant en compte une connaissance préalable du canal de propagation à l’émetteur. Le schéma de modulation PRP-OFDM est une de plusieures propositions dans le contexte du projet européen IST-BroadWay [14–20, 29] et plus récemment par IST-WINNER [21–24, 30]: IST-WINNER est un projet IP (Integrated Project) du 6ème framework qui cible l’étude des systèmes candidats pour la prochaine génération de la communication sans file (4ème génération). Concernant l’optimisation des codes LDPC pour une utilisation avec l’OFDM, les résultats de cette thèse ont été présentés a la standardisation de IEEE802.11n; ils sont actuellement en considération pour l’adoption dans la norme [31, 32]. Efin, le dernier chapitre présente les conclusions des travaux de recherche de cette thèse, ainsi que de futurs axes de recherche.

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Table of content

1 General Introduction 1

2 Orthogonal Frequency Division Multiplexing 5

2.1 History and recent evolutions of Orthogonal Frequency Division Multiplexing - 5

2.2 Filter-Bank based representation of Orthogonal Frequency Division Multiplexing and

definition of Pseudo Random Postfix OFDM - 7

2.2.1 Definition of the CP-OFDM modulator - 7

2.2.2 Definition of the PRP-OFDMmodulator - 8

2.3 Discrete representation of the sampled signal in the receiver - 9

2.3.1 Symbol reconstruction in absence of a channel - 9

2.3.2 Symbol reconstruction in presence of multi-path propagation - 11

2.3.3 Discrete Transceiver Architectures - 13

2.4 Impact of synchronization impairments - 17

2.4.1 Frequency offset - 17

2.4.2 Time Offset - 17

2.4.3 Sampling frequency offset - 18

2.5 Strengths and weaknesses of OFDM - 19

2.6 Example of an OFDM system - 20

2.7 Conclusion - 22

3 Pseudo Random Postfix OFDM: channel estimation and equalization 23

3.1 Introduction - 23

3.2 Notations and PRP-OFDMmodulator - 24

3.3 Order one semi-blind channel estimation based on PRP-OFDM postfixes only - 26

3.3.1 Channel estimation in a time-invariant environment - 26

3.3.2 Channel estimation in a time-variant environment (presence of Doppler) - 31

3.4 Order one semi-blind channel estimation based on PRP-OFDM postfixes and preambles 35

3.5 Symbol Recovery: Equalization - 37

3.5.1 Zero Forcing equalizers - 38

3.5.2 Minimum Mean Square Error equalizers - 38

3.6 Symbol Recovery: Metric derivation - 39

3.6.1 Metric derivation - 40

3.6.2 Low-complexity metric proposal - 40

3.7 Low complexity receiver architecture - 41

3.8 Simulation results - 42

3.8.1 Mean Square Error of Pseudo-Random-Postfix OFDM based channel estimates . 44

3.8.2 Simulation results for BRAN-A channel model - 45

3.8.3 Simulation results for BRAN-C channel model - 49

xxxvi CONTENTS

3.8.4 Simulation results for BRAN-E channel model - 52

3.8.5 Simulation results for BRAN-A channel model (uncoded) - 54

3.9 Conclusion - 56

4 Pseudo Random Postfix OFDM: Postfix Design 57

4.1 Introduction - 57

4.2 Notations and PRP-OFDMmodulator - 58

4.3 PRP-OFDM Postfix Design Constraints - 59

4.3.1 Regulatory constraints - 59

4.3.2 System implementation constraints - 61

4.3.3 Base-band design constraints - 62

4.3.4 Conclusion: resulting postfix design constraints - 63

4.4 Iterative derivation of a suitable postfix - 63

4.4.1 Spectral flatness - 64

4.4.2 Out-of-band radiation - 64

4.4.3 Clipping - 65

4.5 Example of Postfix design - 65

4.6 Conclusion - 66

5 Synchronization Refinement with Pseudo Random Postfix OFDM 75

5.1 Introduction - 75

5.2 Notations and PRP-OFDMmodulator - 76

5.3 Time synchronization aspects - 77

5.3.1 Refinement in the AWGN context - 78

5.3.2 Refinement in presence of ISI - 80

5.4 Frequency Offset Estimation - 82

5.5 Simultaneous presence of Time and Frequency Offsets - 84

5.6 Performance illustration for 5GHz WLAN - 86

5.7 Conclusion - 86

6 Pseudo RandomPostfix Orthogonal Frequency DivisionMultiplexing formultiple antennas

systems 89

6.1 Introduction - 89

6.2 MTMR PRP-OFDMmodulation and demodulation - 90

6.3 Order-one MIMO channel estimation - 91

6.3.1 Static context : minimum dimension circular diagonalization - 92

6.3.2 Static context : carrier grid adaptation - 94

6.3.3 Doppler Context - 96

6.4 Examples of transceiver designs - 96

6.4.1 ZP-OFDM based decoding approach - 97

6.4.2 Decoding based on diagonalization of pseudo-circulant channel matrices - 98

6.5 Simulation results - 99

6.6 Conclusion - 101

7 Iterative Interference Suppression 105

7.1 Introduction - 105

7.2 Notations and PRP-OFDMmodulator - 106

7.3 Channel estimation - 107

7.3.1 Standard channel estimation - 107

CONTENTS xxxvii

7.3.2 The new iterative channel estimation - 108

7.3.3 Practical considerations related to Iterative Interference Suppression - 110

7.4 Simulation Results - 111

7.5 Conclusion - 112

8 Low Density Parity Check (LDPC) Coding for OFDM 117

8.1 Introduction - 117

8.2 Notations and definitions - 118

8.3 LDPC Code optimization with known and time-invariant channel - 122

8.3.1 Properties of the Gaussian Approximation applied to the analysis of message

passing decoding - 123

8.3.2 Direct interpretation of the message passing update equation - 125

8.3.3 Second order approximation of the message passing update equation - 126

8.3.4 An algorithm for LDPC code word mapping onto OFDM carriers - 128

8.4 Simulation results - 130

8.5 Conclusion - 131

9 Conclusion 133

A Proof of Diagonalization Properties of Pseudo circulant matrices 135

B Biased and unbiased MMSE equalizers 137

B.1 Biased MMSE equalizer - 137

B.2 Unbiased MMSE equalizer - 138

C Complexity Considerations 141

C.1 The complexity of basic operations - 141

C.2 The complexity of Fast Fourier Transformation (FFT) algorithms - 141

C.3 PRP-OFDM Complexity Evaluation - 142

C.3.1 Generic Complexity Evaluation - 143

C.3.2 Numerical Examples - 143

C.4 Conclusion - 143

D Modeling of the channel evolution in a Doppler context 145

D.1 Modeling time-variant channels - 145

D.2 Auto-Regressive model of first order - 146

D.3 Moving Average model - 147

E Permutation product theorem for correlation and channel matrices 149

F Complex derivation 151

List of tables 153

List of figures 154

Bibliography 163

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