Wireless Communications – Algorithmic Techniques

Giorgio M. Vitetta is a Full Professor of Telecommunications at the Department of Information Engineering of the University of Modena and Reggio Emilia. He received the Dr. Ing. Degree in Electronic Engineering (cum Laude) in 1990 and the Ph. D. degree in 1994, both from the University of Pisa, Italy. Desmond Taylor is the Tait Professor of Communications at the University of Canterbury. He gained his PhD in Electrical Engineering from McMaster University in Canada. He specializes in Digital Communication Systems. He is the director of journals for the IEEE Communications Society. Philippa Martin is a lecturer in Electrical Engineering at the University of Canterbury. Her research interests include coded modulation, error correction coding and decoding, reduced complexity decoding algorithms, iterative processing, space-time coding, detection and decoding, and combined equalization and decoding. Fabrizio Pancaldi received his Dr. Ing. Degree in Electronic Engineering (cum laude) and a Ph. D. degree in 2006, both from the University of Modena and Reggio Emilia, Italy. He is currently a Research Fellow and lectures in Telecommunication Networks.

Preface xi List of Acronyms xiii 1 Introduction 1 1.1 Structure of a Digital Communication System 3 1.2 Plan of the Book 7 1.3 Further Reading 8 Part I MODULATION AND DETECTION 2 Wireless Channels 11 2.1 Introduction 11 2.2 Mathematical Description of SISO Wireless Channels 16 2.2.1 Input--Output Characterization of a SISO Wireless Channel 16 2.2.2 Statistical Characterization of a SISO Wireless Channel 23 2.2.3 Reduced-Complexity Statistical Models for SISO Channels 36 2.3 Mathematical Description and Modeling of MIMO Wireless Channels 44 2.3.1 Input--Output Characterization of a MIMO Wireless Channel 45 2.3.2 Statistical Characterization of a MIMO Wireless Channel 50 2.3.3 Reduced-Complexity Statistical Modeling of MIMO Channels 57 2.4 Historical Notes 57 2.4.1 Large-Scale Fading Models 58 2.4.2 Small-Scale Fading Models 60 2.5 Further Reading 64 3 Digital Modulation Techniques 65 3.1 Introduction 65 3.2 General Structure of a Digital Modulator 65 3.3 Representation of Digital Modulated Waveforms on an Orthonormal Basis 68 3.4 Bandwidth of Digital Modulations 70 3.5 Passband PAM 74 3.5.1 Signal Model 74 3.5.2 Constellation Selection 76 3.5.3 Data Block Transmission with Passband PAM Signals for Frequency-Domain Equalization 79 3.5.4 Power Spectral Density of Linear Modulations 80 3.6 Continuous Phase Modulation 86 3.6.1 Signal Model 86 3.6.2 Full-Response CPM 89 3.6.3 Partial-Response CPM 93 3.6.4 Multi-h CPM 98 3.6.5 Alternative Representations of CPM Signals 100 3.6.6 Data Block Transmission with CPM Signals for Frequency-Domain Equalization 107 3.6.7 Power Spectral Density of Continuous Phase Modulations 110 3.7 OFDM 116 3.7.1 Introduction 116 3.7.2 OFDM Signal Model 122 3.7.3 Power Spectral Density of OFDM 131 3.7.4 The PAPR Problem in OFDM 135 3.8 Lattice-Based Multidimensional Modulations 137 3.8.1 Lattices: Basic Definitions and Properties 137 3.8.2 Elementary Constructions of Lattices 144 3.9 Spectral Properties of a Digital Modulation at the Output of a Wireless Channel 146 3.10 Historical Notes 149 3.10.1 Passband PAM Signaling 149 3.10.2 CPM Signaling 151 3.10.3 MCM Signaling 152 3.10.4 Power Spectral Density of Digital Modulations 153 3.11 Further Reading 154 4 Detection of Digital Signals over Wireless Channels: Decision Rules 155 4.1 Introduction 155 4.2 Wireless Digital Communication Systems: Modeling, Receiver Architecture and Discretization of the Received Signal 156 4.2.1 General Model of a Wireless Communication System 156 4.2.2 Receiver Architectures 157 4.3 Optimum Detection in a Vector Communication System 159 4.3.1 Description of a Vector Communication System 159 4.3.2 Detection Strategies and Error Probabilities 159 4.3.3 MAP and ML Detection Strategies 162 4.3.4 Diversity Reception and Some Useful Theorems about Data Detection 167 4.4 Mathematical Models for the Receiver Vector 168 4.4.1 Extraction of a Set of Sufficient Statistics from the Received Signal 169 4.4.2 Received Vector for PAM Signaling 177 4.4.3 Received Vector for CPM Signaling 181 4.4.4 Received Vector for OFDM Signaling 184 4.5 Decision Strategies in the Presence of Channel Parameters: Optimal Metrics and Performance Bounds 188 4.5.1 Signal Model and Algorithm Classification 188 4.5.2 Detection for Transmission over of a Known Channel 189 4.5.3 Detection in the Presence of a Statistically Known Channel 198 4.5.4 Detection in the Presence of an Unknown Channel 205 4.6 Expectation--Maximization Techniques for Data Detection 207 4.6.1 The EM Algorithm 207 4.6.2 The Bayesian EM Algorithm 210 4.6.3 Initialization and Convergence of EM-Type Algorithms 213 4.6.4 Other EM Techniques 213 4.7 Historical Notes 214 4.8 Further Reading 216 5 Data-Aided Algorithms for Channel Estimation 217 5.1 Channel Estimation Techniques 218 5.1.1 Introduction 218 5.1.2 Feedforward Estimation 219 5.1.3 Recursive Estimation 222 5.1.4 The Principle of Per-Survivor Processing 227 5.2 Cram'er--Rao Bounds for Data-Aided Channel Estimation 228 5.3 Data-Aided CIR Estimation Algorithms in PATs 235 5.3.1 PAT Modeling and Optimization 235 5.3.2 A Signal Processing Perspective on PAT Techniques 238 5.4 Extensions to MIMO Channels 244 5.4.1 Channel Estimation in SC MIMO PATs 244 5.4.2 Channel Estimation in MC MIMO PATs 245 5.5 Historical Notes 245 5.6 Further Reading 247 6 Detection of Digital Signals over Wireless Channels: Channel Equalization Algorithms 249 6.1 Introduction 249 6.2 Channel Equalization of Single-Carrier Modulations: Known CIR 250 6.2.1 Channel Equalization in the Time Domain 250 6.2.2 Channel Equalization in the Frequency Domain 281 6.3 Channel Equalization of Multicarrier Modulations: Known CIR 286 6.3.1 Optimal Detection in the Absence of IBI and ICI 287 6.3.2 ICI Cancelation Techniques for Time-Varying Channels 289 6.3.3 Equalization Strategies for IBI Compensation 292 6.4 Channel Equalization of Single Carrier Modulations: Statistically Known CIR 292 6.4.1 MLSD 292 6.4.2 Other Equalization Strategies with Frequency-Flat Fading 299 6.5 Channel Equalization of Multicarrier Modulations: Statistically Known CIR 301 6.6 Joint Channel and Data Estimation: Single-Carrier Modulations 302 6.6.1 Adaptive MLSD 302 6.6.2 PSP MLSD 303 6.6.3 Adaptive MAPBD/MAPSD 305 6.6.4 Equalization Strategies Employing Reference-Based Channel Estimators with Frequency-Flat Fading 306 6.7 Joint Channel and Data Estimation: Multicarrier Modulations 307 6.7.1 Pilot-Based Equalization Techniques 308 6.7.2 Semiblind Equalization Techniques 310 6.8 Extensions to the MIMO Systems 311 6.8.1 Equalization Techniques for Single-Carrier MIMO Communications 311 6.8.2 Equalization Techniques for MIMO-OFDM Communications 314 6.9 Historical Notes 315 6.10 Further Reading 319 Part II INFORMATION THEORY AND CODING SCHEMES 7 Elements of Information Theory 323 7.1 Introduction 323 7.2 Capacity for Discrete Sources and Channels 323 7.2.1 The Discrete Memoryless Channel 324 7.2.2 The Continuous-Output Channel 325 7.2.3 Channel Capacity 326 7.3 Capacity of MIMO Fading Channels 330 7.3.1 Frequency-Flat Fading Channel 330 7.3.2 MIMO Channel Capacity 332 7.3.3 Random Channel 335 7.4 Historical Notes 337 7.5 Further Reading 338 8 An Introduction to Channel Coding Techniques 339 8.1 Basic Principles 339 8.2 Interleaving 341 8.3 Taxonomy of Channel Codes 343 8.4 Taxonomy of Coded Modulations 344 8.5 Organization of the Following Chapters 346 8.6 Historical Notes 346 8.7 Further Reading 347 9 Classical Coding Schemes 349 9.1 Block Codes 349 9.1.1 Introduction 349 9.1.2 Structure of Linear Codes over GF(q) 350 9.1.3 Properties of Linear Block Codes 352 9.1.4 Cyclic Codes 357 9.1.5 Other Relevant Linear Block Codes 369 9.1.6 Decoding Techniques for Block Codes 371 9.1.7 Error Performance 388 9.2 Convolutional Codes 390 9.2.1 Introduction 390 9.2.2 Properties of Convolutional Codes 394 9.2.3 Maximum Likelihood Decoding of Convolutional Codes 408 9.2.4 MAP Decoding of Convolutional Codes 413 9.2.5 Sequential Decoding of Convolutional Codes 419 9.2.6 Error Performance of ML Decoding of Convolutional Codes 422 9.3 Classical Concatenated Coding 432 9.3.1 Parallel Concatenation: Product Codes 432 9.3.2 Serial Concatenation: Outer RS Code 434 9.4 Historical Notes 435 9.4.1 Algebraic Coding 435 9.4.2 Probabilistic Coding 438 9.5 Further Reading 439 10 Modern Coding Schemes 441 10.1 Introduction 441 10.2 Concatenated Convolutional Codes 442 10.2.1 Parallel Concatenated Coding Schemes 442 10.2.2 Serially Concatenated Coding Schemes 444 10.2.3 Hybrid Concatenated Coding Schemes 445 10.3 Concatenated Block Codes 445 10.4 Other Modern Concatenated Coding Schemes 446 10.4.1 Repeat and Accumulate Codes 446 10.4.2 Serial Concatenation of Coding Schemes and Differential Modulations 447 10.5 Iterative Decoding Techniques for Concatenated Codes 448 10.5.1 The Turbo Principle 448 10.5.2 SiSo Decoding Algorithms 455 10.5.3 Applications 459 10.5.4 Performance Bounds 465 10.6 Low-Density Parity Check Codes 468 10.6.1 Definition and Classification 468 10.6.2 Graphic Representation of LDPC Codes via Tanner Graphs 468 10.6.3 Minimum Distance and Weight Spectrum 471 10.6.4 LDPC Code Design Approaches 472 10.6.5 Efficient Algorithms for LDPC Encoding 477 10.7 Decoding Techniques for LDPC Codes 478 10.7.1 Introduction to Decoding via Message Passing Algorithms 478 10.7.2 SPA and MSA 481 10.7.3 Technical Issues on LDPC Decoding via MP 489 10.8 Codes on Graphs 494 10.9 Historical Notes 501 10.10 Further Reading 503 11 Signal Space Codes 505 11.1 Introduction 505 11.2 Trellis Coding with Expanded Signal Sets 505 11.2.1 Code Construction 506 11.2.2 Decoding Algorithms 517 11.2.3 Error Performance 518 11.3 Bit-Interleaved Coded Modulation 520 11.3.1 Code Construction 520 11.3.2 Decoding Algorithms 521 11.3.3 Error Performance 522 11.4 Modulation Codes Based on Multilevel Coding 524 11.4.1 Code Construction for AWGN Channels 524 11.4.2 Multistage Decoder 528 11.4.3 Error Performance 529 11.4.4 Multilevel Codes for Rayleigh Flat Fading Channels 530 11.5 Space-Time Coding 531 11.5.1 ST Coding for Frequency-Flat Fading Channels 531 11.5.2 ST Coding for Frequency-Selective Fading Channels 561 11.6 Historical Notes 565 11.7 Further Reading 566 12 Combined Equalization and Decoding 567 12.1 Introduction 567 12.2 Noniterative Techniques 568 12.3 Algorithms for Combined Equalization and Decoding 571 12.3.1 Introduction 571 12.3.2 Turbo Equalization from a FG Perspective 575 12.3.3 Reduced-Complexity Techniques for SiSo Equalization 580 12.3.4 Turbo Equalization in the FD 583 12.3.5 Turbo Equalization in the Presence of an Unknown Channel 585 12.4 Extension to MIMO 586 12.5 Historical Notes 588 12.5.1 Reduced-Complexity SiSo Equalization 588 12.5.2 Error Performance and Convergence Speed in Turbo Equalization 588 12.5.3 SiSo Equalization Algorithms in the Frequency Domain 589 12.5.4 Use of Precoding 589 12.5.5 Turbo Equalization and Factor Graphs 589 12.5.6 Turbo Equalization for MIMO Systems 589 12.5.7 Related Techniques 590 12.6 Further Reading 590 Appendix A Fourier Transforms 591 Appendix B Power Spectral Density of Random Processes 593 B.1 Power Spectral Density of a Wide-Sense Stationary Random Process 593 B.2 Power Spectral Density of a Wide-Sense Cyclostationary Random Process 594 B.3 Power Spectral Density of a Bandpass Random Process 595 Appendix C Matrix Theory 597 Appendix D Signal Spaces 601 D.1 Representation of Deterministic Signals 601 D.1.1 Basic Definitions 601 D.1.2 Representation of Deterministic Signals via Orthonormal Bases 602 D.2 Representation of Random Signals via Orthonormal Bases 606 Appendix E Groups, Finite Fields and Vector Spaces 609 E.1 Groups 609 E.2 Fields 611 E.2.1 Axiomatic Definition of a Field and Finite Fields 611 E.2.2 Polynomials and Extension Fields 612 E.2.3 Other Definitions and Properties 616 E.2.4 Computation Techniques for Finite Fields 620 E.3 Vector Spaces 622 Appendix F Error Function and Related Functions 625 References 629 Index 713