Wireless Communications Over Rapidly Time-Varying

Channels

Edited by

Franz Hlawatsch

Gerald Matz

AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO

SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO

ELSEVIER Academic Press is an imprint of Elsevier

Contents

Preface xiii About the Editors xv Contributing Authors xvii Notations and Symbols xix Abbreviations xxv

CHAPTER 1 Fundamentals of Time-Varying Communication Channels 1 1.1 Introduction 1 1.2 The Physics of Time-Varying Channels 2

1.2.1 Wave Propagation 2 1.2.2 Multipath Propagation and Time Dispersion 2 1.2.3 Doppler Effect and Frequency Dispersion 4 1.2.4 Path Loss and Fading 6 1.2.5 Spatial Characteristics 6

1.3 Deterministic Description 7 1.3.1 Delay-Doppler Domain - Spreading Function 7 1.3.2 Delay-Scale Domain - Delay-Scale Spreading Function 9 1.3.3 Time-Frequency Domain - Time-Varying Transfer Function 10 1.3.4 Time-Delay Domain - Time-Varying Impulse Response 11 1.3.5 Extension to Multiantenna Systems 12

1.4 Stochastic Description 14 1.4.1 WSSUS Channels 15 1.4.2 Extension to Multiantenna Systems 20 1.4.3 Non-WSSUS Channels 23

1.5 Underspread Channels 29 1.5.1 Dispersion-Underspread Property 30 1.5.2 Correlation-Underspread Property 32 1.5.3 Approximate Eigenrelation 33 1.5.4 Time-Frequency Sampling 37 1.5.5 Approximate Karhunen-Loeve Expansion 38

1.6 Parsimonious Channel Models 40 1.6.1 Basis Expansion Models 41 1.6.2 Parsimonious WSSUS Models 44 1.6.3 Parsimonious Non-WSSUS Models 46

1.7 Measurement 48 1.7.1 Spread-Spectrum-Like Channel Sounding 48 1.7.2 Multicarrier Channel Sounding 52

V

vi Contents

1.7.3 Extension to Multiantenna Systems 54 1.7.4 Measurement of Second-Order Statistics 55

1.8 Conclusion 59 Acknowledgment 59 References 59

CHAPTER 2 Information Theory of Underspread WSSUS Channels 65 2.1 The Role of a System Model 65

2.1.1 A Realistic Model 65 2.1.2 A Brief Literature Survey 66 2.1.3 Capacity Bounds Answering Engineering-Relevant Questions 68

2.2 A Discretized System Model 69 2.2.1 The Channel Model 69 2.2.2 Discretization of the Continuous-Time Input-Output Relation 71

2.3 The Large-Bandwidth Regime: Diagonalized I/O Relation 82 2.3.1 Power Constraints 83 2.3.2 Definition of Noncoherent Capacity 84 2.3.3 A Coherent-Capacity Upper Bound 84 2.3.4 An Upper Bound on Capacity that Is Explicit in Сн(г, v) 84 2.3.5 A Lower Bound on Capacity 88 2.3.6 A Numerical Example 90 2.3.7 Extension to the Multiantenna Setting 92 2.3.8 Numerical Examples 94

2.4 The Large-Bandwidth Regime: I/O Relation with Interference 97 2.4.1 A Lower Bound on Capacity 97 2.4.2 Numerical Examples 104

2.5 The High-SNR Regime 106 2.5.1 A Lower Bound on Capacity 106 2.5.2 Numerical Examples 108

2.6 Conclusions 110 References 112

CHAPTER 3 Algebraic Coding for Fast Fading Channels 117 3.1 Introduction 117

3.1.1 Fading Channel Model 118 3.1.2 System Model 118

3.2 Product Distance Based Code Design 119 3.2.1 Signal Space Diversity and Product Distance 119 3.2.2 Lattice Constellations 122

Contents vii

3.3 Lattices 122 3.3.1 First Definitions 122 3.3.2 Sublattices and Equivalent Lattices 125

3.4 Algebraic Number Theory 127 3.4.1 Algebraic Number Fields 127 3.4.2 Integral Basis and Canonical Embeddings 130

3.5 Algebraic Lattices 132 3.6 Ideal Lattices 135 3.7 Algebraic Rotations with High Product Distance 137

3.7.1 Z" Ideal Lattices 137 3.7.2 Rotated ^"-Lattice Codes 138 3.7.3 A Simple Two-Dimensional Rotation Based on the Golden Number... 139 3.7.4 The Cyclotomic Construction 140

3.8 Sphere Decoding 144 3.8.1 The Sphere Decoder Algorithm 145 3.8.2 The Sphere Decoder with Fading 150

3.9 Performance of Rotated Constellations 150 3.10 Conclusions 151

References 152

CHAPTER 4 Estimation of Time-Varying Channels-A Block Approach 155 4.1 Introduction 155 4.2 System and Channel Model 156

4.2.1 System Model 156 4.2.2 BEM Channel Model 158

4.3 Channel Estimation Based on a Single Block 160 4.3.1 Introduction 160 4.3.2 Channel Estimation Data Model 161 4.3.3 Channel Estimators 166 4.3.4 Channel Identifiability 170 4.3.5 Simulation Results 174

4.4 Channel Estimation Based on Multiple Blocks 180 4.4.1 Introduction 180 4.4.2 Data Model and BEM for Multiple OFDM Symbols 183 4.4.3 Channel Identifiability Based on Multiple Blocks 184 4.4.4 Simulation Results 186

4.5 Extension to MIMO Systems 189 4.5.1 Introduction 189 4.5.2 Single-Carrier System 189 4.5.3 OFDM System 190

4.6 Adaptive Channel Estimation 192

viii Contents

4.7 Conclusions 194 References 194

CHAPTER 5 Pilot Design and Optimization for Transmission over Time-Varying Channels 199

5.1 Introduction 199 5.2 Pilot Design: A Framework 200

5.2.1 Modeling of Pilot-Assisted Transmission 200 5.2.2 Transceiver Architectures 202 5.2.3 Performance Criteria 203

5.3 Optimal TDM Pilot Insertion Pattern in Single Carrier Systems 204 5.3.1 Channel Model 205 5.3.2 Periodic TDM Pilot Placement 205 5.3.3 Receiver Structure 206 5.3.4 Optimization Criteria 208 5.3.5 Optimal TDM Pilot Placement 209 5.3.6 Bibliographical Notes 213

5.4 Alternative Pilot Insertion Strategy - Superimposed Training 214 5.4.1 Kaiman Tracking with Superimposed Training 214 5.4.2 Superimposed versus TDM Schemes: Performance Comparison 216 5.4.3 Bibliographical Notes 218

5.5 Resource Allocation: Amount of Training and Power Optimization 220 5.5.1 Cutoff Rate Analysis 220 5.5.2 Bibliographical Notes 224

5.6 Pilot Design for MIMO Channels 224 5.7 Pilot Design for Wideband Systems 225

5.7.1 OFDMA Systems 225 5.7.2 CDMA Systems 227 5.7.3 Ultra Wideband 227

5.8 Conclusion 227 Acknowledgment 228

5.A The Kaiman Filter for TDM Training 228 5.B Proof of Proposition 5.1 228 5.C Proof of Lemma 5.1 230 5.D Proof of Theorem 5.1 231

References 233

CHAPTER 6 Equalization of Time-Varying Channels 237 6.1 Introduction 237 6.2 System Model 239

6.2.1 Basic Assumptions 239 6.2.2 The Structure of the Effective Channel Matrix Q 240

Contents ix

6.3 Coherent Equalization 245 6.3.1 Coherent Equalization Criteria 245 6.3.2 Coherent Equalization Tools 247 6.3.3 Coherent Equalization for Time-Frequency Concentrated

Modulation/Demodulation 256 6.3.4 Coherent Equalization of Single-Carrier Modulation/Demodulation ... 259

6.4 Noncoherent Equalization 260 6.4.1 Noncoherent System Model 261 6.4.2 Noncoherent Equalization Criteria 262 6.4.3 Noncoherent Equalization Tools 265 6.4.4 Noncoherent Equalization for Single-Carrier

Modulation/Demodulation 270 6.4.5 Noncoherent Equalization for Time-Frequency Concentrated

Modulation/Demodulation 272 6.5 Conclusion 273 6.A Derivation of Posterior LLR Expression (6.36) 274 6.B Derivation of the Noncoherent MLSD Expression (6.73) 274 6.С Explanation of EM Recursion (6.91) 275 6.D Info EM(B) Algorithms for Noncoherent Equalization 276

References 277

CHAPTER 7 OFDM Communications over Time-Varying Channels 285 7.1 OFDMSystems 285

7.1.1 System Model 286 7.1.2 Effects of Rapidly Time-Varying Channels 291 7.1.3 MIMO-OFDM 297

7.2 ICI Mitigation Techniques 299 7.2.1 Linear Equalization 299 7.2.2 Nonlinear Equalization 306 7.2.3 Transmitter Preprocessing 313 7.2.4 Extension to MIMO-OFDM 317

7.3 Time-Varying Channel Estimation 318 7.3.1 Basis Expansion Model of LTV Channels 319 7.3.2 Training-Based Channel Estimation 320 7.3.3 Iterative Channel Estimation and Turbo Equalization 324 7.3.4 Impact of Channel Estimation on BER Performance 325 7.3.5 Channel Estimation in MIMO-OFDM 325

7.4 Concluding Remarks 327 7.4.1 System and Application Aspects 327 7.4.2 Open Issues 328 References 329

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CHAPTER 8 Multiuser MIMO Receiver Processing for Time-Varying Channels 337 8.1 Introduction 337 8.2 Multiuser MIMO Systems 338 8.3 Tools for Complexity Reduction 341

8.3.1 Iterative Approximation of the MAP Detector 341 8.3.2 Reduced-Rank Model for the Time-Varying Channel 343 8.3.3 The Krylov Subspace Method 345 8.3.4 Sphere Decoding 348

8.4 Iterative Multiuser MIMO Time-Varying Channel Estimation 352 8.4.1 Signal Model 352 8.4.2 Reduced-Rank LMMSE Channel Estimator 353 8.4.3 Comparison of the Slepian and Fourier Bases 354 8.4.4 Krylov Approximation of the Reduced-Rank LMMSE Channel

Estimator 355 8.5 Linear Joint Antenna Multiuser Detection 355

8.5.1 Multiuser Detection in Chip Space 355 8.5.2 Multiuser Detection in User Space 356

8.6 Nonlinear Detection 358 8.6.1 Exploiting the Reduced-Rank Channel Model 358 8.6.2 Soft Sphere Decoding 361 8.6.3 Computational Complexity 362

8.7 Simulation Results 364 8.7.1 Bit Error Rate Comparison 364 8.7.2 Computational Complexity Comparison 366

8.8 Conclusions 368 Acknowledgments 369

8.A Computation of the Log-Likelihood Ratio (8.44) 369 References 371

CHAPTER 9 Time-Scale and Dispersive Processing for Wideband Time-Varying Channels 375

9.1 Introduction 375 9.1.1 Need for Wideband Channel Characterizations 375 9.1.2 Examples of Wideband Dispersive Channel Characteristics 377 9.1.3 Chapter Organization 380

9.2 Narrowband Channel Characterization 381 9.2.1 Narrowband Spreading Function 381 9.2.2 Discrete Channel Characterization and Finite Approximations 381

9.3 Wideband Delay-Scale Channel Characterization 383 9.3.1 Narrowband and Wideband Conditions 383 9.3.2 Wideband Spreading Function 384

Contents xi

9.3.3 Discrete Delay-Scale Channel Characterization 384 9.3.4 Finite Approximations 386 9.3.5 Multipath-Scale Diversity 387 9.3.6 Time-Scale Rake Receiver 389

9.4 Wideband Dispersive Channel Characterization 392 9.4.1 Dispersive Time-Frequency Structures 392 9.4.2 Dispersive Spreading Function and Unitary Warping Relations 393 9.4.3 Discrete Dispersive Channel with Physical Limitations 394 9.4.4 Generalized Time-Frequency Rake Receiver 395

9.5 Underwater Wireless Communication Channels 396 9.5.1 Shallow Water Environment Model 396 9.5.2 Time-Frequency Characteristics of Shallow Water Environments 398 9.5.3 Mode Separation in Time-Frequency 398 9.5.4 Dispersion Diversity Receiver Design 400 9.5.5 Numerical Simulations for Shallow Water Communications 403

9.6 Application Example 405 9.7 Conclusions 410

References 411

Index 417