Wireless Communications – Principles, Theory and Methodology

Table of Contents:
1 Introduction 1 1.1 Resources for Wireless Communications 3 1.2 Shannon s Theory 4 1.3 Three Challenges 5 1.4 Digital Modulation vs Coding 6 1.5 Philosophy to Combat Interference 7 1.6 Evolution of Processing Strategy 8 1.7 Philosophy to Exploit 2-Dimensional Random Fields 9 1.8 Cellular: Concept, Evolution and 5G 9 1.9 The Structure of This Book 11 1.10 Repeatedly Used Abbreviations and Math Symbols 12 2 Mathematical Background 17 2.1 Introduction 18 2.2 Congruence Mapping and Signal Spaces 18 2.3 Estimation methods 23 2.3.1 Maximum Likelihood Estimation 24 2.3.2 Maximum A Posteriori (MAP) Estimation 25 2.4 Commonly Used Distributions in Wireless 25 2.4.1 Chi-square Distributions 25 2.4.2 Gamma Distributions 30 2.4.3 Nakagami Distributions 30 2.4.4 Wishart Distribution 31 2.5 The Calculus of Variations 32 2.6 Two Inequalities for Optimization 34 2.6.1 Inequality for Rayleigh quotient 34 2.6.2 Hadamard Inequality 34 2.7 Q-function 35 2.8 The CHF Method and Its Skilful Applications 37 2.8.1 Gil-Pelaez s Lemma 37 2.8.2 Random Variables in Denominators 37 2.8.3 Parseval s theorem 38 2.9 Matrix Operations and Differentiation 38 2.9.1 Decomposition for a Special Determinant 38 2.9.2 Higher-Order Derivations 38 2.9.3 Kronecker Product 39 3 Channel Characterization 45 3.1 Introduction 46 3.2 Large-Scale Propagation Loss 47 3.2.1 Free-Space Propagation 48 3.2.2 Average Large-Scale Path Loss in Mobile 48 3.2.3 Okumura s Model 49 3.2.4 Hata s Model 51 3.2.5 JTC Air Model 52 3.3 Log-Normal Shadowing 52 3.4 Multipath Characterization for Local Behavior 53 3.4.1 An Equivalent Bandwidth 53 3.4.2 Temporal Evolution of Path Coefficients 59 3.4.3 Statistical Description of Local Fluctuation 60 3.4.4 Complex Gaussian Distribution 60 3.4.5 Nakagami Fading 61 3.4.6 Clarke-Jakes Model 62 3.5 Composite Model to Incorporate Multipath and Shadowing 63 3.6 Example to Illustrate the Use of Various Models 64 3.6.1 Static Design 64 3.6.2 Dynamic Design 65 3.6.3 Large-Scale Design 66 3.7 Generation of Correlated Fading Channels 66 3.7.1 Rayleigh Fading with Given Covariance Structure 66 3.7.2 Correlated Nakagami Fading 67 3.7.3 Complex Correlated Nakagami Channels 72 3.7.4 Correlated Log-Normal Shadowing 73 3.7.5 Fitting a Lognormal Sum 75 3.8 Summary 76 4 Digital Modulation 83 4.1 Introduction 84 4.2 Signals and Signal Space 84 4.3 Optimal MAP and ML Receivers 86 4.4 Detection of Two Arbitrary Waveforms 88 4.5 MPSK 91 4.5.1 BPSK 92 4.5.2 QPSK 93 4.5.3 MPSK 96 4.6 M-ary QAM 101 4.7 Noncoherent Scheme-Differential MPSK 103 4.7.1 Differential BPSK 104 4.7.2 Differential MPSK 104 4.7.3 Connection to MPSK 105 4.8 MFSK 105 4.8.1 BFSK with Coherent Detection 105 4.9 Non-Coherent MFSK 108 4.10 Bit Error Probability vs Symbol Error Probability 109 4.10.1 Orthogonal MFSK 109 4.10.2 Square M-QAM 109 4.10.3 Gray-Mapped MPSK 110 4.11 Spectral Efficiency 113 4.12 Summary of Symbol Error Probability for Various Schemes 114 5 Minimum Shift Keying 121 5.1 Introduction 122 5.2 MSK 123 5.3 de Buda s Approach 123 5.3.1 The Basic Idea and Key Equations 124 5.4 Properties of MSK Signals 125 5.5 Understanding MSK 127 5.5.1 MSK as FSK 127 5.5.2 MSK as Offset PSK 128 5.6 Signal Space 128 5.7 MSK Power Spectrum 130 5.8 Alternative Scheme-Differential Encoder 131 5.9 Transceivers for MSK Signals 134 5.10 Gaussian Shaped MSK 136 5.11 Massey s Approach to MSK 136 5.11.1 Modulation 136 5.11.2 Receiver Structures and Error Performance 138 5.12 Summary 139 6 Channel Coding 143 6.1 Introduction and Philosophical Discussion 144 6.2 Preliminary of Galois Fields 146 6.2.1 Fields 146 6.2.2 Galois Fields 146 6.2.3 The Primitive Element of GF(q) 146 6.2.4 Construction of GF(q) 147 6.3 Linear Block Codes 149 6.3.1 Syndrome Test 151 6.3.2 Error-Correcting Capability 154 6.4 Cyclic Codes 157 6.4.1 The Order of Elements: A Concept in GF(q) 157 6.4.2 Cyclic codes 159 6.4.3 Generator, Parity-Check and Syndrome Polynomial 160 6.4.4 Systematic Form 162 6.4.5 Syndrome and Decoding 163 6.5 Golay Code 164 6.6 BCH Codes 165 6.6.1 Generating BCH Codes 166 6.6.2 Decoding BCH Codes 167 6.7 Convolutional Codes 170 6.7.1 Examples 170 6.7.2 Code Generation 171 6.7.3 Markovian Property 172 6.7.4 Decoding with Hard-Decision Viterbi Algorithm 175 6.7.5 Transfer Function 177 6.7.6 Choice of Convolutional Codes 180 6.7.7 Philosophy behind Decoding Strategies 182 6.7.8 Error Performance of Convolutional Decoding 186 6.8 Trellis Coded Modulation 189 6.9 Summary 192 7 Diversity Techniques 201 7.1 Introduction 202 7.2 Idea Behind Diversity 204 7.3 Structures of Various Diversity Combiners 205 7.3.1 MRC 206 7.3.2 EGC 207 7.3.3 SC 207 7.4 PDFs of Output SNR 208 7.4.1 MRC 208 7.4.2 EGC 209 7.4.3 SC 210 7.5 Average SNR Comparison For Various Schemes 211 7.5.1 MRC 211 7.5.2 EGC 212 7.5.3 SC 213 7.6 Methods for Error Performance Analysis 214 7.6.1 The Chain Rule 214 7.6.2 The CHF Method 215 7.7 Error Probability of MRC 215 7.7.1 Error Performance in Non-Diversity Rayleigh fading 216 7.7.2 MRC in i.i.d. Rayleigh Fading 217 7.7.3 MRC in Correlated Rayleigh Fading 219 7.7.4 Pe for Generic Channels 221 7.8 Error Probability of EGC 221 7.8.1 Closed Form Solution to Order-3 EGC 222 7.8.2 General EGC error performance 224 7.8.3 Diversity Order of EGC 225 7.9 Average Error Performance of SC in Rayleigh fading 226 7.9.1 Pure SC 226 7.9.2 Generalized SC 228 7.10 Performance of Diversity MDPSK Systems 229 7.10.1 Non-Diversity MDPSK in Rayleigh Fading 229 7.10.2 Remarks on Use of the Chain Rule 232 7.10.3 Linear Prediction to Fit the Chain Rule 233 7.10.4 Alternative Approach for Diversity MDPSK 234 7.11 Non-Coherent MFSK with Diversity Reception 235 7.12 Summary 237 8 Processing Strategies for Wireless Systems 247 8.1 Communication Problem 248 8.2 Traditional Strategy 249 8.3 Paradigm of Orthogonality 249 8.4 Turbo Processing Principle 250 9 Channel Equalization 255 9.1 Introduction 256 9.2 The channel Capacity of ISI Channels 257 9.3 Pulse Shaping for ISI-Free Transmission 257 9.4 ISI and Equalization Strategies 258 9.5 Zero-Forcing Equalizer 259 9.5.1 Orthogonal Projection 259 9.5.2 ZFE 261 9.5.3 Equivalent Discrete ZFE Receiver 263 9.6 MMSE Linear Equalizer 267 9.7 Decision-Feedback Equalizer 270 9.8 SNR Comparison and Error Performance 272 9.9 An Example 273 9.10 Spectral Factorization 274 9.11 Summary 276 10 Channel Decomposition Techniques 283 10.1 Introduction 285 10.2 Channel Matrix of ISI Channels 285 10.3 Idea of Channel Decomposition 286 10.4 QR-Decomposition Based THP Equalizer 287 10.5 The GMD Equalizer 289 10.6 OFDM for Time-Invariant Channel 289 10.6.1 Channel SVD 290 10.6.2 OFDM: A Multicarrier Modulation Technique 291 10.6.3 PAPR and Statistical Behavior of OFDM 293 10.6.4 Combatting PAPR 295 10.7 CP and Circulant Channel Matrix 295 10.8 OFDM Receiver 298 10.9 Channel Estimation 299 10.10 Coded OFDM 299 11 Turbo Codes and Turbo Principle 309 11.1 Introduction and Philosophical Discussion 311 11.2 Two-Device Mechanism for Iteration 313 11.3 Turbo Codes 315 11.3.1 A Turbo Encoder 315 11.3.2 RSC versus NRC 315 11.3.3 Turbo Codes with Two Constituent RSC Encoders 319 11.4 BCJR Algorithm 320 11.5 Turbo Decoding 324 11.6 Illustration of Turbo-Code Performance 325 11.7 EXIT Charts 327 11.8 Convergence and Fixed Points 332 11.9 Statistics of LLRs 332 11.9.1 Mean and Variance of LLRs 332 11.9.2 Mean and Variance of Hard Decision 333 11.10 Turbo Equalization 333 11.11 Turbo CDMA 337 11.12 Turbo IDMA 339 11.13 Summary 340 12 Multiple Access Channels 349 12.1 Introduction 351 12.2 Typical MA Schemes 352 12.3 User Space of Multiple Access 355 12.3.1 User Spaces for TDMA 355 12.3.2 User Space for CDMA 356 12.3.3 User Space for MC-CDMA 357 12.3.4 User Space for OFDMA 358 12.3.5 Unified Framework for Orthogonal Multi-Access Schemes 360 12.4 Capacity of Multiple-Access Channels 361 12.4.1 Flat Fading 361 12.4.2 Frequency-Selective Fading 363 12.5 Achievable MI by Various MA Schemes 363 12.5.1 AWGN Channel 364 12.5.2 Flat Fading MA Channels 366 12.6 CDMA-IS-95 368 12.7 Processing Gain of Spreading-Spectrum 373 12.8 IS-95 Down-Link Receiver and Performance 373 12.9 IS-95 Uplink Receiver and Performance 381 12.103GPP-LTE Uplink 382 12.11M-Sequences 385 12.11.1 PN sequences of a shorter period 386 12.11.2 Conditions for M-Sequence Generators 386 12.11.3 Properties of M-Sequence 387 12.11.4 Ways to Generate PN sequences 389 12.12 Walsh Sequences 392 12.13 CAZAC Sequences for LTE-A 392 12.14 Non-Orthogonal MA Schemes 394 12.15 Summary 395 13 Wireless MIMO Systems 405 13.1 Introduction 407 13.2 Signal Model and Mutual Information 407 13.3 Capacity with CSIT 408 13.4 Ergodic Capacity without CSIT 410 13.4.1 i.i.d. MIMO Rayleigh channels 410 13.4.2 Ergodic Capacity for Correlated MIMO channels 411 13.5 Capacity: Asymptotic Results 413 13.5.1 Asymptotic Capacity with Large MIMO 413 13.5.2 Large SNR Approximation 414 13.6 Optimal Transceivers with CSIT 417 13.6.1 Optimal Eigenbeam Transceiver 417 13.6.2 Distributions of the Largest Eigenvalue 418 13.6.3 Outage Performance 420 13.6.4 Average Mutual Information of MIMO-MRC 420 13.6.5 Symbol Detection Probability 421 13.7 Receivers without CSIT 422 13.8 Optimal Receiver 422 13.9 Zero-Forcing MIMO Receiver 423 13.10 MMSE Receiver 425 13.11 V-BLAST 428 13.12 Space-Time Block Codes 429 13.13 Alamouti s Codes 430 13.14 General Space-Time Codes 433 13.14.1 Exact Pairwise Pe 434 13.15 Information Lossless Space-Time Codes 435 13.16 Multiplexing Gain vs. Diversity Gain 436 13.16.1 Two Frameworks 437 13.16.2 Derivation of the DMT 438 13.16.3 Available DF for Diversity 439 13.17 Summary 443 14 Cooperative Communications 453 14.1 A Historical Review 455 14.2 Relaying 455 14.3 Cooperative Communications 457 14.3.1 Cooperation Protocols 457 14.3.2 Diversity Analysis 460 14.3.3 Resource Allocation 462 14.4 Multiple-Relay Cooperation 463 14.4.1 Multi-Relay over Frequency Selective Channels 463 14.4.2 Optimal Matrix Structure 467 14.4.3 Power Allocation 468 14.5 Two-Way Relaying 473 14.5.1 Average Power Constraints 476 14.5.2 Instantaneous Power Constraint 478 14.6 Multi-Cell MIMO 479 14.7 Summary 480 15 Cognitive Radio 489 15.1 Introduction 491 15.2 Spectrum Sensing for Spectrum Holes 492 15.3 Matched Filter vs. Energy Detector 492 15.4 Detection of Random Primary Signals 496 15.4.1 Energy Based Detection 497 15.4.2 Maximum Likelihood Ratio Test 499 15.4.3 Eigenvalue Ratio Test 501 15.5 Detection with Estimated Noise Variance 501 15.5.1 LRT with 2n 501 15.5.2 LRT without Noise-Level Reference 502 15.6 Cooperative Spectrum Sensing 503 15.6.1 Gaussian Signals in Nakagami Fading 504 15.6.2 A General Configuration 505 15.7 Standardization of CR Networks 507 Index