Digital Communication over Fading Channels

MARVIN K. SIMON, PhD, is Principal Scientist at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena. MOHAMED-SLIM ALOUINI, PhD, is Associate Professor in the Department of Electrical and Computer Engineering of the University of Minnesota, Minneapolis.

Preface xxv

Nomenclature xxxi

Part 1 Fundamentals

Chapter 1 Introduction 3

1.1 System Performance Measures 4

1.1.1 Average Signal-to-Noise Ratio (SNR) 4

1.1.2 Outage Probability 5

1.1.3 Average Bit Error Probability (BEP) 6

1.1.4 Amount of Fading 12

1.1.5 Average Outage Duration 13

1.2 Conclusions 14

References 14

Chapter 2 Fading Channel Characterization and Modeling 17

2.1 Main Characteristics of Fading Channels 17

2.1.1 Envelope and Phase Fluctuations 17

2.1.2 Slow and Fast Fading 18

2.1.3 Frequency-Flat and Frequency-Selective Fading 18

2.2 Modeling of Flat-Fading Channels 19

2.2.1 Multipath Fading 20

2.2.1.1 Rayleigh 20

2.2.1.2 Nakagami-q (Hoyt) 22

2.2.1.3 Nakagami-n (Rice) 23

2.2.1.4 Nakagami-m 24

2.2.1.5 Weibull 25

2.2.1.6 Beckmann 28

2.2.1.7 Spherically-Invariant Random Process Model 30

2.2.2 Log-Normal Shadowing 32

2.2.3 Composite Multipath/Shadowing 33

2.2.3.1 Composite Gamma/Log-Normal Distribution 33

2.2.3.2 Suzuki Distribution 34

2.2.3.3 K Distribution 34

2.2.3.4 Rician Shadowed Distributions 36

2.2.4 Combined (Time-Shared) Shadowed/Unshadowed Fading 37

2.3 Modeling of Frequency-Selective Fading Channels 37

References 39

Chapter 3 Types of Communication 45

3.1 Ideal Coherent Detection 45

3.1.1 Multiple Amplitude-Shift-Keying (M-ASK) or Multiple Amplitude Modulation (M-AM) 47

3.1.2 Quadrature Amplitude-Shift-Keying (QASK) or Quadrature Amplitude Modulation (QAM) 48

3.1.3 M-ary Phase-Shift-Keying (M-PSK) 50

3.1.4 Differentially Encoded M-ary Phase-Shift-Keying (M-PSK) 53

3.1.4.1 π/4-QPSK 54

3.1.5 Offset QPSK (OQPSK) or Staggered QPSK (sqpsk) 55

3.1.6 M-ary Frequency-Shift-Keying (M-FSK) 56

3.1.7 Minimum-Shift-Keying (MSK) 58

3.2 Nonideal Coherent Detection 62

3.3 Noncoherent Detection 66

3.4 Partially Coherent Detection 68

3.4.1 Conventional Detection 68

3.4.1.1 One-Symbol Observation 68

3.4.1.2 Multiple-Symbol Observation 69

3.4.2 Differentially Coherent Detection 71

3.4.2.1 M-ary Differential Phase-Shift-Keying (M-DPSK) 71

3.4.2.2 Conventional Detection (Two-Symbol Observation) 73

3.4.2.3 Multiple-Symbol Detection 76

3.4.3 π/4-Differential QPSK (π/4-DQPSK) 78

References 78

Part 2 Mathematical Tools

Chapter 4 Alternative Representations of Classical Functions 83

4.1 Gaussian Q-Function 84

4.1.1 One-Dimensional Case 84

4.1.2 Two-Dimensional Case 86

4.1.3 Other Forms for One- and Two-Dimensional Cases 88

4.1.4 Alternative Representations of Higher Powers of the Gaussian Q-Function 90

4.2 Marcum Q-Function 93

4.2.1 First-Order Marcum Q-Function 93

4.2.1.1 Upper and Lower Bounds 97

4.2.2 Generalized (mth-Order) Marcum Q-Function 100

4.2.2.1 Upper and Lower Bounds 105

4.3 The Nuttall Q-Function 113

4.4 Other Functions 117

References 119

Appendix 4A. Derivation of Eq. (4.2) 120

Chapter 5 Useful Expressions for Evaluating Average Error Probability Performance 123

5.1 Integrals Involving the Gaussian Q-Function 123

5.1.1 Rayleigh Fading Channel 125

5.1.2 Nakagami-q (Hoyt) Fading Channel 125

5.1.3 Nakagami-n (Rice) Fading Channel 126

5.1.4 Nakagami-m Fading Channel 126

5.1.5 Log-Normal Shadowing Channel 128

5.1.6 Composite Log-Normal Shadowing/Nakagami-m Fading Channel 128

5.2 Integrals Involving the Marcum Q-Function 131

5.2.1 Rayleigh Fading Channel 132

5.2.2 Nakagami-q (Hoyt) Fading Channel 133

5.2.3 Nakagami-n (Rice) Fading Channel 133

5.2.4 Nakagami-m Fading Channel 133

5.2.5 Log-Normal Shadowing Channel 133

5.2.6 Composite Log-Normal Shadowing/Nakagami-m Fading Channel 134

5.2.7 Some Alternative Closed-Form Expressions 135

5.3 Integrals Involving the Incomplete Gamma Function 137

5.3.1 Rayleigh Fading Channel 138

5.3.2 Nakagami-q (Hoyt) Fading Channel 139

5.3.3 Nakagami-n (Rice) Fading Channel 139

5.3.4 Nakagami-m Fading Channel 140

5.3.5 Log-Normal Shadowing Channel 140

5.3.6 Composite Log-Normal Shadowing/Nakagami-m Fading Channel 140

5.4 Integrals Involving Other Functions 141

5.4.1 The M -PSK Error Probability Integral 141

5.4.1.1 Rayleigh Fading Channel 142

5.4.1.2 Nakagami-m Fading Channel 142

5.4.2 Arbitrary Two-Dimensional Signal Constellation Error Probability Integral 142

5.4.3 Higher-Order Integer Powers of the Gaussian Q-Function 144

5.4.3.1 Rayleigh Fading Channel 144

5.4.3.2 Nakagami-m Fading Channel 145

5.4.4 Integer Powers of M -PSK Error Probability Integrals 145

5.4.4.1 Rayleigh Fading Channel 146

References 148

Appendix 5A. Evaluation of Definite Integrals Associated with Rayleigh and Nakagami-m Fading 149

5a.1 Exact Closed-Form Results 149

5a.2 Upper and Lower Bounds 165

Chapter 6 New Representations of Some Probability Density and Cumulative Distribution Functions for Correlative Fading Applications 169

6.1 Bivariate Rayleigh PDF and CDF 170

6.2 PDF and CDF for Maximum of Two Rayleigh Random Variables 175

6.3 PDF and CDF for Maximum of Two Nakagami-m Random Variables 177

6.4 PDF and CDF for Maximum and Minimum of Two Log-Normal Random Variables 180

6.4.1 The Maximum of Two Log-Normal Random Variables 180

6.4.2 The Minimum of Two Log-Normal Random Variables 183

References 185

Part 3 Optimum Reception and Performance Evaluation

Chapter 7 Optimum Receivers for Fading Channels 189

7.1 The Case of Known Amplitudes, Phases, and Delays—Coherent Detection 191

7.2 The Case of Known Phases and Delays but Unknown Amplitudes 195

7.2.1 Rayleigh Fading 195

7.2.2 Nakagami-m Fading 196

7.3 The Case of Known Amplitudes and Delays but Unknown Phases 198

7.4 The Case of Known Delays but Unknown Amplitudes and Phases 199

7.4.1 One-Symbol Observation—Noncoherent Detection 199

7.4.1.1 Rayleigh Fading 201

7.4.1.2 Nakagami-m Fading 206

7.4.2 Two-Symbol Observation—Conventional Differentially Coherent Detection 211

7.4.2.1 Rayleigh Fading 214

7.4.2.2 Nakagami-m Fading 217

7.4.3 N s -Symbol Observation—Multiple Differentially Coherent Detection 217

7.4.3.1 Rayleigh Fading 218

7.4.3.2 Nakagami-m Fading 218

7.5 The Case of Unknown Amplitudes, Phases, and Delays 219

7.5.1 One-Symbol Observation—Noncoherent Detection 219

7.5.1.1 Rayleigh Fading 220

7.5.1.2 Nakagami-m Fading 221

7.5.2 Two-Symbol Observation—Conventional Differentially Coherent Detection 221

References 222

Chapter 8 Performance of Single-Channel Receivers 223

8.1 Performance Over the AWGN Channel 223

8.1.1 Ideal Coherent Detection 224

8.1.1.1 Multiple Amplitude-Shift-Keying (M-ASK) or Multiple Amplitude Modulation (M-AM) 224

8.1.1.2 Quadrature Amplitude-Shift- Keying (QASK) or Quadrature Amplitude Modulation (QAM) 225

8.1.1.3 M-ary Phase-Shift-Keying (m-psk) 228

8.1.1.4 Differentially Encoded M-ary Phase-Shift-Keying (M-PSK) and π/4-QPSK 234

8.1.1.5 Offset QPSK (OQPSK) or Staggered QPSK (SQPSK) 235

8.1.1.6 M-ary Frequency-Shift-Keying (m-fsk) 236

8.1.1.7 Minimum-Shift-Keying (MSK) 237

8.1.2 Nonideal Coherent Detection 237

8.1.3 Noncoherent Detection 242

8.1.4 Partially Coherent Detection 242

8.1.4.1 Conventional Detection (One-Symbol Observation) 242

8.1.4.2 Multiple-Symbol Detection 244

8.1.5 Differentially Coherent Detection 245

8.1.5.1 M-ary Differential Phase-Shift-Keying (M-DPSK) 245

8.1.5.2 M-DPSK with Multiple-Symbol Detection 249

8.1.5.3 π/4-Differential QPSK (π/4-DQPSK) 250

8.1.6 Generic Results for Binary Signaling 251

8.2 Performance Over Fading Channels 252

8.2.1 Ideal Coherent Detection 252

8.2.1.1 Multiple Amplitude-Shift-Keying (M-ASK) or Multiple Amplitude Modulation (M-AM) 253

8.2.1.2 Quadrature Amplitude-Shift- Keying (QASK) or Quadrature Amplitude Modulation (QAM) 254

8.2.1.3 M-ary Phase-Shift-Keying (m-psk) 256

8.2.1.4 Differentially Encoded M-ary Phase-Shift-Keying (M-PSK) and π/4-QPSK 258

8.2.1.5 Offset QPSK (OQPSK) or Staggered QPSK (SQPSK) 262

8.2.1.6 M-ary Frequency-Shift-Keying (m-fsk) 262

8.2.1.7 Minimum-Shift-Keying (MSK) 267

8.2.2 Nonideal Coherent Detection 267

8.2.2.1 Simplified Noisy Reference Loss Evaluation 273

8.2.3 Noncoherent Detection 281

8.2.4 Partially Coherent Detection 282

8.2.5 Differentially Coherent Detection 284

8.2.5.1 M-ary Differential Phase-Shift- Keying (M-DPSK)—Slow Fading 285

8.2.5.2 M-ary Differential Phase-Shift- Keying (M-DPSK)—Fast Fading 290

8.2.5.3 π/4-Differential QPSK (π/4-DQPSK) 294

8.2.6 Performance in the Presence of Imperfect Channel Estimation 294

8.2.6.1 Signal Model and Symbol Error Probability Evaluation for Rayleigh Fading 295

8.2.6.2 Special Cases 297

References 301

Appendix 8A. Stein’s Unified Analysis of the Error Probability Performance of Certain Communication Systems 304

Chapter 9 Performance of Multichannel Receivers 311

9.1 Diversity Combining 312

9.1.1 Diversity Concept 312

9.1.2 Mathematical Modeling 312

9.1.3 Brief Survey of Diversity Combining Techniques 313

9.1.3.1 Pure Combining Techniques 313

9.1.3.2 Hybrid Combining Techniques 315

9.1.4 Complexity–Performance Tradeoffs 316

9.2 Maximal-Ratio Combining (MRC) 316

9.2.1 Receiver Structure 317

9.2.2 PDF-Based Approach 319

9.2.3 MGF-Based Approach 320

9.2.3.1 Average Bit Error Rate of Binary Signals 320

9.2.3.2 Average Symbol Error Rate of M-PSK Signals 322

9.2.3.3 Average Symbol Error Rate of M-AM Signals 323

9.2.3.4 Average Symbol Error Rate of Square M-QAM Signals 324

9.2.4 Bounds and Asymptotic SER Expressions 326

9.3 Coherent Equal Gain Combining 331

9.3.1 Receiver Structure 331

9.3.2 Average Output SNR 332

9.3.3 Exact Error Rate Analysis 333

9.3.3.1 Binary Signals 333

9.3.3.2 Extension to M-PSK Signals 339

9.3.4 Approximate Error Rate Analysis 340

9.3.5 Asymptotic Error Rate Analysis 342

9.4 Noncoherent and Differentially Coherent Equal Gain Combining 342

9.4.1 DPSK, DQPSK, and BFSK Performance (Exact and with Bounds) 343

9.4.1.1 Receiver Structures 343

9.4.1.2 Exact Analysis of Average Bit Error Probability 346

9.4.1.3 Bounds on Average Bit Error Probability 352

9.4.2 M-ary Orthogonal FSK 353

9.4.2.1 Exact Analysis of Average Bit Error Probability 356

9.4.2.2 Numerical Examples 364

9.4.3 Multiple-Symbol Differential Detection with Diversity Combining 367

9.4.3.1 Decision Metrics 367

9.4.3.2 Average Bit Error Rate Performance 368

9.4.3.3 Asymptotic (Large N s) Behavior 371

9.4.3.4 Numerical Results 372

9.5 Optimum Diversity Combining of Noncoherent Fsk 375

9.5.1 Comparison with the Noncoherent Equal Gain Combining Receiver 377

9.5.2 Extension to the M-ary Orthogonal FSK Case 378

9.6 Outage Probability Performance 379

9.6.1 MRC and Noncoherent EGC 379

9.6.2 Coherent EGC 380

9.6.3 Numerical Examples 381

9.7 Impact of Fading Correlation 389

9.7.1 Model A: Two Correlated Branches with Nonidentical Fading 390

9.7.1.1 Pdf 390

9.7.1.2 Mgf 392

9.7.2 Model B: D Identically Distributed Branches with Constant Correlation 392

9.7.2.1 Pdf 393

9.7.2.2 Mgf 393

9.7.3 Model C: D Identically Distributed Branches with Exponential Correlation 394

9.7.3.1 Pdf 394

9.7.3.2 Mgf 394

9.7.4 Model D: D Nonidentically Distributed Branches with Arbitrary Correlation 395

9.7.4.1 Mgf 395

9.7.4.2 Special Cases of Interest 396

9.7.4.3 Proof that Correlation Degrades Performance 397

9.7.5 Numerical Examples 399

9.8 Selection Combining 404

9.8.1 MGF of Output SNR 405

9.8.2 Average Output SNR 406

9.8.3 Outage Probability 409

9.8.3.1 Analysis 409

9.8.3.2 Numerical Example 410

9.8.4 Average Probability of Error 411

9.8.4.1 BDPSK and Noncoherent BFSK 411

9.8.4.2 Coherent BPSK and BFSK 413

9.8.4.3 Numerical Example 415

9.9 Switched Diversity 417

9.9.1 Dual-Branch Switch-and-Stay Combining 419

9.9.1.1 Performance of SSC over Independent Identically Distributed Branches 419

9.9.1.2 Effect of Branch Unbalance 433

9.9.1.3 Effect of Branch Correlation 436

9.9.2 Multibranch Switch-and-Examine Combining 439

9.9.2.1 Classical Multibranch SEC 440

9.9.2.2 Multibranch SEC with Post-selection 443

9.9.2.3 Scan-and-Wait Combining 446

9.10 Performance in the Presence of Outdated or Imperfect Channel Estimates 456

9.10.1 Maximal-Ratio Combining 457

9.10.2 Noncoherent EGC over Rician Fast Fading 458

9.10.3 Selection Combining 461

9.10.4 Switched Diversity 462

9.10.4.1 SSC Output Statistics 462

9.10.4.2 Average SNR 463

9.10.4.3 Average Probability of Error 463

9.10.5 Numerical Results 464

9.11 Combining in Diversity-Rich Environments 466

9.11.1 Two-Dimensional Diversity Schemes 466

9.11.1.1 Performance Analysis 468

9.11.1.2 Numerical Examples 469

9.11.2 Generalized Selection Combining 469

9.11.2.1 I.I.D. Rayleigh Case 472

9.11.2.2 Non-I.I.D. Rayleigh Case 492

9.11.2.3 I.I.D. Nakagami-m Case 497

9.11.2.4 Partial-MGF Approach 502

9.11.2.5 I.I.D. Weibull Case 510

9.11.3 Generalized Selection Combining with Threshold Test per Branch (T-GSC) 512

9.11.3.1 Average Error Probability Performance 515

9.11.3.2 Outage Probability Performance 520

9.11.3.3 Performance Comparisons 524

9.11.4 Generalized Switched Diversity (GSSC) 531

9.11.4.1 GSSC Output Statistics 531

9.11.4.2 Average Probability of Error 532

9.11.5 Generalized Selection Combining Based on the Log-Likelihood Ratio 532

9.11.5.1 Optimum (LLR-Based) GSC for Equiprobable BPSK 533

9.11.5.2 Envelope-Based GSC 536

9.11.5.3 Optimum GSC for Noncoherently Detected Equiprobable Orthogonal Bfsk 536

9.12 Post-detection Combining 537

9.12.1 System and Channel Models 537

9.12.1.1 Overall System Description 537

9.12.1.2 Channel Model 537

9.12.1.3 Receiver 539

9.12.2 Post-detection Switched Combining Operation 539

9.12.2.1 Switching Strategy and Mechanism 539

9.12.2.2 Switching Threshold 540

9.12.3 Average BER Analysis 540

9.12.3.1 Identically Distributed Branches 542

9.12.3.2 Nonidentically Distributed Branches 542

9.12.4 Rayleigh Fading 543

9.12.4.1 Identically Distributed Branches 544

9.12.4.2 Nonidentically Distributed Branches 547

9.12.5 Impact of the Severity of Fading 548

9.12.5.1 Average BER 550

9.12.5.2 Numerical Examples and Discussion 552

9.12.6 Extension to Orthogonal M-FSK 552

9.12.6.1 System Model and Switching Operation 552

9.12.6.2 Average Probability of Error 555

9.12.6.3 Numerical Examples 562

9.13 Performance of Dual-Branch Diversity Combining Schemes over Log-Normal Channels 566

9.13.1 System and Channel Models 566

9.13.2 Maximal-Ratio Combining 568

9.13.2.1 Moments of the Output SNR 568

9.13.2.2 Outage Probability 570

9.13.2.3 Extension to Equal Gain Combining 571

9.13.3 Selection Combining 571

9.13.3.1 Moments of the Output SNR 572

9.13.3.2 Outage Probability 575

9.13.4 Switched Combining 575

9.13.4.1 Moments of the Output SNR 576

9.13.4.2 Outage Probability 581

9.14 Average Outage Duration 584

9.14.1 System and Channel Models 585

9.14.1.1 Fading Channel Models 585

9.14.1.2 GSC Mode of Operation 585

9.14.2 Average Outage Duration and Average Level Crossing Rate 586

9.14.2.1 Problem Formulation 586

9.14.2.2 General Formula for the Average LCR of GSC 586

9.14.3 I.I.D. Rayleigh Fading 589

9.14.3.1 Generic Expressions for GSC 589

9.14.3.2 Special Cases: SC and MRC 590

9.14.4 Numerical Examples 591

9.15 Multiple-Input/Multiple-Output (MIMO) Antenna Diversity Systems 594

9.15.1 System, Channel, and Signal Models 594

9.15.2 Optimum Weight Vectors and Output SNR 595

9.15.3 Distributions of the Largest Eigenvalue of Noncentral Complex Wishart Matrices 596

9.15.3.1 CDF of S 596

9.15.3.2 PDF of S 598

9.15.3.3 PDF of Output SNR and Outage Probability 599

9.15.3.4 Special Cases 600

9.15.3.5 Numerical Results and Discussion 601

References 604

Appendix 9A. Alternative Forms of the Bit Error Probability for a Decision Statistic that Is a Quadratic Form of Complex Gaussian Random Variables 619

Appendix 9B. Simple Numerical Techniques for Inversion of Laplace Transform of Cumulative Distribution Functions 625

9b.1 Euler Summation-Based Technique 625

9b.2 Gauss–Chebyshev Quadrature-Based Technique 626

Appendix 9C. The Relation between the Power Correlation Coefficient of Correlated Rician Random Variables and the Correlation Coefficient of Their Underlying Complex Gaussian Random Variables 627

Appendix 9D. Proof of Theorem 9.1 631

Appendix 9E. Direct Proof of Eq. (9.438) 632

Appendix 9F. Special Definite Integrals 634

Part 4 Multiuser Communication Systems

Chapter 10 Outage Performance of Multiuser Communication Systems 639

10.1 Outage Probability in Interference-Limited Systems 640

10.1.1 A Probability Related to the CDF of the Difference of Two Chi-Square Variates with Different Degrees of Freedom 640

10.1.2 Fading and System Models 643

10.1.2.1 Channel Fading Models 643

10.1.2.2 Desired and Interference Signals Model 644

10.1.3 A Generic Formula for the Outage Probability 644

10.1.3.1 Nakagami/Nakagami Scenario 645

10.1.3.2 Rice/Rice Scenario 646

10.1.3.3 Rice/Nakagami Scenario 647

10.1.3.4 Nakagami/Rice Scenario 647

10.2 Outage Probability with a Minimum Desired Signal Power Constraint 648

10.2.1 Models and Problem Formulation 648

10.2.1.1 Fading and System Models 648

10.2.1.2 Outage Probability Definition 648

10.2.2 Rice/I.I.D. Nakagami Scenario 649

10.2.2.1 Rice/I.I.D. Rayleigh Scenario 649

10.2.2.2 Extension to Rice/I.I.D. Nakagami Scenario 652

10.2.2.3 Numerical Examples 652

10.2.3 Nakagami/I.I.D. Rice Scenario 654

10.2.3.1 Rayleigh/I.I.D. Rice Scenario 654

10.2.3.2 Extension to Nakagami/I.I.D. Rice Scenario 656

10.2.3.3 Numerical Examples 657

10.3 Outage Probability with Dual-Branch SC and SSC Diversity 659

10.3.1 Fading and System Models 661

10.3.2 Outage Performance with Minimum Signal Power Constraint 661

10.3.2.1 Selection Combining 662

10.3.2.2 Switch-and-Stay Combining 663

10.3.2.3 Numerical Examples 664

10.4 Outage Rate and Average Outage Duration of Multiuser Communication Systems 667

References 671

Appendix 10A. A Probability Related to the CDF of the Difference of Two Chi-Square Variates with Different Degrees of Freedom 674

Appendix 10B. Outage Probability in the Nakagami/Nakagami Interference-Limited Scenario 678

Chapter 11 Optimum Combining—a Diversity Technique for Communication over Fading Channels in the Presence of Interference 681

11.1 Performance of Diversity Combining Receivers 682

11.1.1 Single Interferer; Independent, Identically Distributed Fading 682

11.1.1.1 Rayleigh Fading—Exact Evaluation of Average Bit Error Probability 686

11.1.1.2 Rayleigh Fading—Approximate Evaluation of Average Bit Error Probability 689

11.1.1.3 Extension to Other Modulations 692

11.1.1.4 Rician Fading—Evaluation of Average Bit Error Probability 693

11.1.1.5 Nakagami-m Fading—Evaluation of Average Bit Error Probability 695

11.1.2 Multiple Equal Power Interferers; Independent, Identically Distributed Fading 697

11.1.2.1 Number of Interferers Less than Number of Array Elements 700

11.1.2.2 Number of Interferers Equal to or Greater than Number of Array Elements 706

11.1.3 Comparison with Results for MRC in the Presence of Interference 710

11.1.4 Multiple Arbitrary Power Interferers; Independent, Identically Distributed Fading 715

11.1.4.1 Average SEP of M-PSK 715

11.1.4.2 Numerical Results 716

11.1.5 Multiple-Symbol Differential Detection in the Presence of Interference 718

11.1.5.1 Decision Metric 718

11.1.5.2 Average BEP 718

11.2 Optimum Combining with Multiple Transmit and Receive Antennas 721

11.2.1 System, Channel, and Signals Models 721

11.2.2 Optimum Weight Vectors and Output SIR 723

11.2.3 PDF of Output SIR and Outage Probability 723

11.2.3.1 PDF of Output SIR 724

11.2.3.2 Outage Probability 724

11.2.3.3 Special Case When L t = 1

725

11.2.4 Key Observations 726

11.2.4.1 Distribution of Antenna Elements 726

11.2.4.2 Effects of Correlation between Receiver Antenna Pairs 726

11.2.5 Numerical Examples 727

References 729

Appendix 11A. Distributions of the Largest Eigenvalue of Certain Quadratic Forms in Complex Gaussian Vectors 732

11A.1 General Result 732

11A.2 Special Case 733

Chapter 12 Direct-Sequence Code-Division Multiple Access (ds-cdma) 735

12.1 Single-Carrier DS-CDMA Systems 736

12.1.1 System and Channel Models 736

12.1.1.1 Transmitted Signal 736

12.1.1.2 Channel Model 737

12.1.1.3 Receiver 738

12.1.2 Performance Analysis 739

12.1.2.1 General Case 740

12.1.2.2 Application to Nakagami-m Fading Channels 740

12.2 Multicarrier DS-CDMA Systems 741

12.2.1 System and Channel Models 742

12.2.1.1 Transmitter 742

12.2.1.2 Channel 743

12.2.1.3 Receiver 743

12.2.1.4 Notations 744

12.2.2 Performance Analysis 745

12.2.2.1 Conditional SNR 745

12.2.2.2 Average BER 749

12.2.3 Numerical Examples 750

References 754

Part 5 Coded Communication Systems

Chapter 13 Coded Communication over Fading Channels 759

13.1 Coherent Detection 761

13.1.1 System Model 761

13.1.2 Evaluation of Pairwise Error Probability 763

13.1.2.1 Known Channel State Information 764

13.1.2.2 Unknown Channel State Information 768

13.1.3 Transfer Function Bound on Average Bit Error Probability 772

13.1.3.1 Known Channel State Information 774

13.1.3.2 Unknown Channel State Information 774

13.1.4 An Alternative Formulation of the Transfer Function Bound 774

13.1.5 An Example 775

13.2 Differentially Coherent Detection 781

13.2.1 System Model 781

13.2.2 Performance Evaluation 783

13.2.2.1 Unknown Channel State Information 783

13.2.2.2 Known Channel State Information 785

13.2.3 An Example 785

13.3 Numerical Results—Comparison between the True Upper Bounds and Union–Chernoff Bounds 787

References 792

Appendix 13A. Evaluation of a Moment Generating Function Associated with Differential Detection of
M-PSK Sequences 793

Chapter 14 Multichannel Transmission—Transmit Diversity and Space-Time Coding 797

14.1 A Historical Perspective 799

14.2 Transmit versus Receive Diversity—Basic Concepts 800

14.3 Alamouti’s Diversity Technique—a Simple Transmit Diversity Scheme Using Two Transmit Antennas 803

14.4 Generalization of Alamouti’s Diversity Technique to Orthogonal Space-Time Block Code Designs 809

14.5 Alamouti’s Diversity Technique Combined with Multidimensional Trellis-Coded Modulation 812

14.5.1 Evaluation of Pairwise Error Probability Performance on Fast Rician Fading Channels 814

14.5.2 Evaluation of Pairwise Error Probability Performance on Slow Rician Fading Channels 817

14.6 Space-Time Trellis-Coded Modulation 818

14.6.1 Evaluation of Pairwise Error Probability Performance on Fast Rician Fading Channels 820

14.6.2 Evaluation of Pairwise Error Probability Performance on Slow Rician Fading Channels 821

14.6.3 An Example 824

14.6.4 Approximate Evaluation of Average Bit Error Probability 827

14.6.4.1 Fast-Fading Channel Model 827

14.6.4.2 Slow-Fading Channel Model 829

14.6.5 Evaluation of the Transfer Function Upper Bound on Average Bit Error Probability 831

14.6.5.1 Fast-Fading Channel Model 831

14.6.5.2 Slow-Fading Channel Model 833

14.7 Other Combinations of Space-Time Block Codes and Space-Time Trellis Codes 833

14.7.1 Super-Orthogonal Space-Time Trellis Codes 834

14.7.1.1 The Parameterized Class of Space-Time Block Codes and System Model 834

14.7.1.2 Evaluation of the Pairwise Error Probability 836

14.7.1.3 Extension of the Results to Super-Orthogonal Codes with More than Two Transmit Antennas 844

14.7.1.4 Approximate Evaluation of Average Bit Error Probability 845

14.7.1.5 Evaluation of the Transfer Function Upper Bound on the Average Bit Error Probability 846

14.7.1.6 Numerical Results 848

14.7.2 Super-Quasi-Orthogonal Space-Time Trellis Codes 850

14.7.2.1 Signal Model 850

14.7.2.2 Evaluation of Pairwise Error Probability 852

14.7.2.3 Examples 853

14.7.2.4 Numerical Results 857

14.8 Disclaimer 858

References 859

Chapter 15 Capacity of Fading Channels 863

15.1 Channel and System Model 863

15.2 Optimum Simultaneous Power and Rate Adaptation 865

15.2.1 No Diversity 865

15.2.2 Maximal-Ratio Combining 866

15.3 Optimum Rate Adaptation with Constant Transmit Power 867

15.3.1 No Diversity 868

15.3.2 Maximal-Ratio Combining 869

15.4 Channel Inversion with Fixed Rate 869

15.4.1 No Diversity 870

15.4.2 Maximal-Ratio Combining 870

15.5 Numerical Examples 871

15.6 Capacity of MIMO Fading Channels 876

References 877

Appendix 15A. Evaluation of J n (µ) 878

Appendix 15B. Evaluation of I n (µ) 880

Index 883