Digital Communication over Fading Channels

Team DDU......Page 1
Table Of Content......Page 10
Preface......Page 28
Nomenclature......Page 34
CHAPTER 1 Introduction......Page 40
1.1.1 Average Signal-to-Noise Ratio (SNR)......Page 41
1.1.2 Outage Probability......Page 42
1.1.3 Average Bit Error Probability (BEP)......Page 43
1.1.4 Amount of Fading......Page 49
1.1.5 Average Outage Duration......Page 50
References......Page 51
2.1.1 Envelope and Phase Fluctuations......Page 54
2.1.3 Frequency-Flat and Frequency-Selective Fading......Page 55
2.2 Modeling of Flat-Fading Channels......Page 56
2.2.1.1 Rayleigh......Page 57
2.2.1.2 Nakagami-q (Hoyt)......Page 59
2.2.1.3 Nakagami-n (Rice)......Page 60
2.2.1.4 Nakagami-m......Page 61
2.2.1.5 Weibull......Page 62
2.2.1.6 Beckmann......Page 65
2.2.1.7 Spherically-Invariant Random Process Model......Page 67
2.2.2 Log-Normal Shadowing......Page 69
2.2.3.1 Composite Gamma/Log-Normal Distribution......Page 70
2.2.3.3 K Distribution......Page 71
2.2.3.4 Rician Shadowed Distributions......Page 73
2.3 Modeling of Frequency-Selective Fading Channels......Page 74
References......Page 76
3.1 Ideal Coherent Detection......Page 82
3.1.1 Multiple Amplitude-Shift-Keying (M-ASK) or Multiple Amplitude Modulation (M-AM)......Page 84
3.1.2 Quadrature Amplitude-Shift-Keying (QASK) or Quadrature Amplitude Modulation (QAM)......Page 85
3.1.3 M-ary Phase-Shift-Keying (M-PSK)......Page 87
3.1.4 Differentially Encoded M-ary Phase-Shift-Keying (M-PSK)......Page 90
3.1.4.1 π/4-QPSK......Page 91
3.1.5 Offset QPSK (OQPSK) or Staggered QPSK (SQPSK)......Page 92
3.1.6 M-ary Frequency-Shift-Keying (M-FSK)......Page 93
3.1.7 Minimum-Shift-Keying (MSK)......Page 95
3.2 Nonideal Coherent Detection......Page 99
3.3 Noncoherent Detection......Page 103
3.4.1.1 One-Symbol Observation......Page 105
3.4.1.2 Multiple-Symbol Observation......Page 106
3.4.2.1 M-ary Differential Phase-Shift-Keying (M-DPSK)......Page 108
3.4.2.2 Conventional Detection (Two-Symbol Observation)......Page 110
3.4.2.3 Multiple-Symbol Detection......Page 113
References......Page 115
CHAPTER 4 Alternative Representations of Classical Functions......Page 120
4.1.1 One-Dimensional Case......Page 121
4.1.2 Two-Dimensional Case......Page 123
4.1.3 Other Forms for One- and Two-Dimensional Cases......Page 125
4.1.4 Alternative Representations of Higher Powers of the Gaussian Q-Function......Page 127
4.2.1 First-Order Marcum Q-Function......Page 130
4.2.1.1 Upper and Lower Bounds......Page 134
4.2.2 Generalized (mth-Order) Marcum Q-Function......Page 137
4.2.2.1 Upper and Lower Bounds......Page 142
4.3 The Nuttall Q-Function......Page 150
4.4 Other Functions......Page 154
References......Page 156
Appendix 4A. Derivation of Eq. (4.2)......Page 157
5.1 Integrals Involving the Gaussian Q-Function......Page 160
5.1.2 Nakagami-q (Hoyt) Fading Channel......Page 162
5.1.4 Nakagami-m Fading Channel......Page 163
5.1.6 Composite Log-Normal Shadowing/Nakagami-m Fading Channel......Page 165
5.2 Integrals Involving the Marcum Q-Function......Page 168
5.2.1 Rayleigh Fading Channel......Page 169
5.2.5 Log-Normal Shadowing Channel......Page 170
5.2.6 Composite Log-Normal Shadowing/Nakagami-m Fading Channel......Page 171
5.2.7 Some Alternative Closed-Form Expressions......Page 172
5.3 Integrals Involving the Incomplete Gamma Function......Page 174
5.3.1 Rayleigh Fading Channel......Page 175
5.3.3 Nakagami-n (Rice) Fading Channel......Page 176
5.3.6 Composite Log-Normal Shadowing/Nakagami-m Fading Channel......Page 177
5.4.1 The M-PSK Error Probability Integral......Page 178
5.4.2 Arbitrary Two-Dimensional Signal Constellation Error Probability Integral......Page 179
5.4.3.1 Rayleigh Fading Channel......Page 181
5.4.4 Integer Powers of M-PSK Error Probability Integrals......Page 182
5.4.4.1 Rayleigh Fading Channel......Page 183
References......Page 185
5A.1 Exact Closed-Form Results......Page 186
5A.2 Upper and Lower Bounds......Page 202
CHAPTER 6 New Representations of Some Probability Density and Cumulative Distribution Functions for Correlative Fading Applications......Page 206
6.1 Bivariate Rayleigh PDF and CDF......Page 207
6.2 PDF and CDF for Maximum of Two Rayleigh Random Variables......Page 212
6.3 PDF and CDF for Maximum of Two Nakagami-m Random Variables......Page 214
6.4.1 The Maximum of Two Log-Normal Random Variables......Page 217
6.4.2 The Minimum of Two Log-Normal Random Variables......Page 220
References......Page 222
CHAPTER 7 Optimum Receivers for Fading Channels......Page 226
7.1 The Case of Known Amplitudes, Phases, and Delays-Coherent Detection......Page 228
7.2.1 Rayleigh Fading......Page 232
7.2.2 Nakagami-m Fading......Page 233
7.3 The Case of Known Amplitudes and Delays but Unknown Phases......Page 235
7.4.1 One-Symbol Observation-Noncoherent Detection......Page 236
7.4.1.1 Rayleigh Fading......Page 238
7.4.1.2 Nakagami-m Fading......Page 243
7.4.2 Two-Symbol Observation-Conventional Differentially Coherent Detection......Page 248
7.4.2.1 Rayleigh Fading......Page 251
7.4.3 Ns-Symbol Observation-Multiple Differentially Coherent Detection......Page 254
7.4.3.2 Nakagami-m Fading......Page 255
7.5.1 One-Symbol Observation-Noncoherent Detection......Page 256
7.5.1.1 Rayleigh Fading......Page 257
7.5.2 Two-Symbol Observation-Conventional Differentially Coherent Detection......Page 258
References......Page 259
8.1 Performance Over the AWGN Channel......Page 260
8.1.1.1 Multiple Amplitude-Shift-Keying (M-ASK) or Multiple Amplitude Modulation (M-AM)......Page 261
8.1.1.2 Quadrature Amplitude-Shift-Keying (QASK) or Quadrature Amplitude Modulation (QAM)......Page 262
8.1.1.3 M-ary Phase-Shift-Keying (M-PSK)......Page 265
8.1.1.4 Differentially Encoded M-ary Phase-Shift-Keying (M-PSK) and π/4-QPSK......Page 271
8.1.1.5 Offset QPSK (OQPSK) or Staggered QPSK (SQPSK)......Page 272
8.1.1.6 M-ary Frequency-Shift-Keying (M-FSK)......Page 273
8.1.2 Nonideal Coherent Detection......Page 274
8.1.4.1 Conventional Detection (One-Symbol Observation)......Page 279
8.1.4.2 Multiple-Symbol Detection......Page 281
8.1.5.1 M-ary Differential Phase-Shift-Keying (M-DPSK)......Page 282
8.1.5.2 M-DPSK with Multiple-Symbol Detection......Page 286
8.1.5.3 π/4-Differential QPSK (π/4-DQPSK)......Page 287
8.1.6 Generic Results for Binary Signaling......Page 288
8.2.1 Ideal Coherent Detection......Page 289
8.2.1.1 Multiple Amplitude-Shift-Keying (M-ASK) or Multiple Amplitude Modulation (M-AM)......Page 290
8.2.1.2 Quadrature Amplitude-Shift-Keying (QASK) or Quadrature Amplitude Modulation (QAM)......Page 291
8.2.1.3 M-ary Phase-Shift-Keying (M-PSK)......Page 293
8.2.1.4 Differentially Encoded M-ary Phase-Shift-Keying (M-PSK) and π/4-QPSK......Page 295
8.2.1.6 M-ary Frequency-Shift-Keying (M-FSK)......Page 299
8.2.2 Nonideal Coherent Detection......Page 304
8.2.2.1 Simplified Noisy Reference Loss Evaluation......Page 310
8.2.3 Noncoherent Detection......Page 318
8.2.4 Partially Coherent Detection......Page 319
8.2.5 Differentially Coherent Detection......Page 321
8.2.5.1 M-ary Differential Phase-Shift-Keying (M-DPSK)-Slow Fading......Page 322
8.2.5.2 M-ary Differential Phase-Shift-Keying (M-DPSK)-Fast Fading......Page 327
8.2.6 Performance in the Presence of Imperfect Channel Estimation......Page 331
8.2.6.1 Signal Model and Symbol Error Probability Evaluation for Rayleigh Fading......Page 332
8.2.6.2 Special Cases......Page 334
References......Page 338
Appendix 8A. Stein's Unified Analysis of the Error Probability Performance of Certain Communication Systems......Page 341
CHAPTER 9 Performance of Multichannel Receivers......Page 348
9.1.2 Mathematical Modeling......Page 349
9.1.3.1 Pure Combining Techniques......Page 350
9.1.3.2 Hybrid Combining Techniques......Page 352
9.2 Maximal-Ratio Combining (MRC)......Page 353
9.2.1 Receiver Structure......Page 354
9.2.2 PDF-Based Approach......Page 356
9.2.3.1 Average Bit Error Rate of Binary Signals......Page 357
9.2.3.2 Average Symbol Error Rate of M-PSK Signals......Page 359
9.2.3.3 Average Symbol Error Rate of M-AM Signals......Page 360
9.2.3.4 Average Symbol Error Rate of Square M-QAM Signals......Page 361
9.2.4 Bounds and Asymptotic SER Expressions......Page 363
9.3.1 Receiver Structure......Page 368
9.3.2 Average Output SNR......Page 369
9.3.3.1 Binary Signals......Page 370
9.3.3.2 Extension to M-PSK Signals......Page 376
9.3.4 Approximate Error Rate Analysis......Page 377
9.4 Noncoherent and Differentially Coherent Equal Gain Combining......Page 379
9.4.1.1 Receiver Structures......Page 380
9.4.1.2 Exact Analysis of Average Bit Error Probability......Page 383
9.4.1.3 Bounds on Average Bit Error Probability......Page 389
9.4.2 M-ary Orthogonal FSK......Page 390
9.4.2.1 Exact Analysis of Average Bit Error Probability......Page 393
9.4.2.2 Numerical Examples......Page 401
9.4.3.1 Decision Metrics......Page 404
9.4.3.2 Average Bit Error Rate Performance......Page 405
9.4.3.3 Asymptotic (Large Ns ) Behavior......Page 408
9.4.3.4 Numerical Results......Page 409
9.5 Optimum Diversity Combining of Noncoherent FSK......Page 412
9.5.1 Comparison with the Noncoherent Equal Gain Combining Receiver......Page 414
9.5.2 Extension to the M-ary Orthogonal FSK Case......Page 415
9.6.1 MRC and Noncoherent EGC......Page 416
9.6.2 Coherent EGC......Page 417
9.6.3 Numerical Examples......Page 418
9.7 Impact of Fading Correlation......Page 426
9.7.1.1 PDF......Page 427
9.7.2 Model B: D Identically Distributed Branches with Constant Correlation......Page 429
9.7.2.2 MGF......Page 430
9.7.3.2 MGF......Page 431
9.7.4.1 MGF......Page 432
9.7.4.2 Special Cases of Interest......Page 433
9.7.4.3 Proof that Correlation Degrades Performance......Page 434
9.7.5 Numerical Examples......Page 436
9.8 Selection Combining......Page 441
9.8.1 MGF of Output SNR......Page 442
9.8.2 Average Output SNR......Page 443
9.8.3.1 Analysis......Page 446
9.8.3.2 Numerical Example......Page 447
9.8.4.1 BDPSK and Noncoherent BFSK......Page 448
9.8.4.2 Coherent BPSK and BFSK......Page 450
9.8.4.3 Numerical Example......Page 452
9.9 Switched Diversity......Page 454
9.9.1.1 Performance of SSC over Independent Identically Distributed Branches......Page 456
9.9.1.2 Effect of Branch Unbalance......Page 470
9.9.1.3 Effect of Branch Correlation......Page 473
9.9.2 Multibranch Switch-and-Examine Combining......Page 476
9.9.2.1 Classical Multibranch SEC......Page 477
9.9.2.2 Multibranch SEC with Post-selection......Page 480
9.9.2.3 Scan-and-Wait Combining......Page 483
9.10 Performance in the Presence of Outdated or Imperfect Channel Estimates......Page 493
9.10.1 Maximal-Ratio Combining......Page 494
9.10.2 Noncoherent EGC over Rician Fast Fading......Page 495
9.10.3 Selection Combining......Page 498
9.10.4.1 SSC Output Statistics......Page 499
9.10.4.3 Average Probability of Error......Page 500
9.10.5 Numerical Results......Page 501
9.11.1 Two-Dimensional Diversity Schemes......Page 503
9.11.1.1 Performance Analysis......Page 505
9.11.2 Generalized Selection Combining......Page 506
9.11.2.1 I.I.D. Rayleigh Case......Page 509
9.11.2.2 Non-I.I.D. Rayleigh Case......Page 529
9.11.2.3 I.I.D. Nakagami-m Case......Page 534
9.11.2.4 Partial-MGF Approach......Page 539
9.11.2.5 I.I.D. Weibull Case......Page 547
9.11.3 Generalized Selection Combining with Threshold Test per Branch (T-GSC)......Page 549
9.11.3.1 Average Error Probability Performance......Page 552
9.11.3.2 Outage Probability Performance......Page 557
9.11.3.3 Performance Comparisons......Page 561
9.11.4.1 GSSC Output Statistics......Page 568
9.11.5 Generalized Selection Combining Based on the Log-Likelihood Ratio......Page 569
9.11.5.1 Optimum (LLR-Based) GSC for Equiprobable BPSK......Page 570
9.11.5.3 Optimum GSC for Noncoherently Detected Equiprobable Orthogonal BFSK......Page 573
9.12.1.2 Channel Model......Page 574
9.12.2.1 Switching Strategy and Mechanism......Page 576
9.12.3 Average BER Analysis......Page 577
9.12.3.2 Nonidentically Distributed Branches......Page 579
9.12.4 Rayleigh Fading......Page 580
9.12.4.1 Identically Distributed Branches......Page 581
9.12.4.2 Nonidentically Distributed Branches......Page 584
9.12.5 Impact of the Severity of Fading......Page 585
9.12.5.1 Average BER......Page 587
9.12.6.1 System Model and Switching Operation......Page 589
9.12.6.2 Average Probability of Error......Page 592
9.12.6.3 Numerical Examples......Page 599
9.13.1 System and Channel Models......Page 603
9.13.2.1 Moments of the Output SNR......Page 605
9.13.2.2 Outage Probability......Page 607
9.13.3 Selection Combining......Page 608
9.13.3.1 Moments of the Output SNR......Page 609
9.13.4 Switched Combining......Page 612
9.13.4.1 Moments of the Output SNR......Page 613
9.13.4.2 Outage Probability......Page 618
9.14 Average Outage Duration......Page 621
9.14.1.2 GSC Mode of Operation......Page 622
9.14.2.2 General Formula for the Average LCR of GSC......Page 623
9.14.3.1 Generic Expressions for GSC......Page 626
9.14.3.2 Special Cases: SC and MRC......Page 627
9.14.4 Numerical Examples......Page 628
9.15.1 System, Channel, and Signal Models......Page 631
9.15.2 Optimum Weight Vectors and Output SNR......Page 632
9.15.3.1 CDF of S......Page 633
9.15.3.2 PDF of S......Page 635
9.15.3.3 PDF of Output SNR and Outage Probability......Page 636
9.15.3.4 Special Cases......Page 637
9.15.3.5 Numerical Results and Discussion......Page 638
References......Page 641
Appendix 9A. Alternative Forms of the Bit Error Probability for a Decision Statistic that Is a Quadratic Form of Complex Gaussian Random Variables......Page 656
9B.1 Euler Summation-Based Technique......Page 662
9B.2 Gauss–Chebyshev Quadrature-Based Technique......Page 663
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......Page 664
Appendix 9D. Proof of Theorem 9.1......Page 668
Appendix 9E. Direct Proof of Eq. (9.438)......Page 669
Appendix 9F. Special Definite Integrals......Page 671
CHAPTER 10 Outage Performance of Multiuser Communication Systems......Page 676
10.1.1 A Probability Related to the CDF of the Difference of Two Chi-Square Variates with Different Degrees of Freedom......Page 677
10.1.2.1 Channel Fading Models......Page 680
10.1.3 A Generic Formula for the Outage Probability......Page 681
10.1.3.1 Nakagami/Nakagami Scenario......Page 682
10.1.3.2 Rice/Rice Scenario......Page 683
10.1.3.4 Nakagami/Rice Scenario......Page 684
10.2.1.2 Outage Probability Definition......Page 685
10.2.2.1 Rice/I.I.D. Rayleigh Scenario......Page 686
10.2.2.3 Numerical Examples......Page 689
10.2.3.1 Rayleigh/I.I.D. Rice Scenario......Page 691
10.2.3.2 Extension to Nakagami/I.I.D. Rice Scenario......Page 693
10.2.3.3 Numerical Examples......Page 694
10.3 Outage Probability with Dual-Branch SC and SSC Diversity......Page 696
10.3.2 Outage Performance with Minimum Signal Power Constraint......Page 698
10.3.2.1 Selection Combining......Page 699
10.3.2.2 Switch-and-Stay Combining......Page 700
10.3.2.3 Numerical Examples......Page 701
10.4 Outage Rate and Average Outage Duration of Multiuser Communication Systems......Page 704
References......Page 708
Appendix 10A. A Probability Related to the CDF of the Difference of Two Chi-Square Variates with Different Degrees of Freedom......Page 711
Appendix 10B. Outage Probability in the Nakagami/Nakagami Interference-Limited Scenario......Page 715
CHAPTER 11 Optimum Combining-a Diversity Technique for Communication over Fading Channels in the Presence of Interference......Page 718
11.1.1 Single Interferer; Independent, Identically Distributed Fading......Page 719
11.1.1.1 Rayleigh Fading-Exact Evaluation of Average Bit Error Probability......Page 723
11.1.1.2 Rayleigh Fading-Approximate Evaluation of Average Bit Error Probability......Page 726
11.1.1.3 Extension to Other Modulations......Page 729
11.1.1.4 Rician Fading-Evaluation of Average Bit Error Probability......Page 730
11.1.1.5 Nakagami-m Fading-Evaluation of Average Bit Error Probability......Page 732
11.1.2 Multiple Equal Power Interferers; Independent, Identically Distributed Fading......Page 734
11.1.2.1 Number of Interferers Less than Number of Array Elements......Page 737
11.1.2.2 Number of Interferers Equal to or Greater than Number of Array Elements......Page 743
11.1.3 Comparison with Results for MRC in the Presence of Interference......Page 747
11.1.4.1 Average SEP of M-PSK......Page 752
11.1.4.2 Numerical Results......Page 753
11.1.5.2 Average BEP......Page 755
11.2.1 System, Channel, and Signals Models......Page 758
11.2.3 PDF of Output SIR and Outage Probability......Page 760
11.2.3.2 Outage Probability......Page 761
11.2.3.3 Special Case When Lt = 1......Page 762
11.2.4.2 Effects of Correlation between Receiver Antenna Pairs......Page 763
11.2.5 Numerical Examples......Page 764
References......Page 766
11A.1 General Result......Page 769
11A.2 Special Case......Page 770
CHAPTER 12 Direct-Sequence Code-Division Multiple Access (DS-CDMA)......Page 772
12.1.1.1 Transmitted Signal......Page 773
12.1.1.2 Channel Model......Page 774
12.1.1.3 Receiver......Page 775
12.1.2 Performance Analysis......Page 776
12.1.2.2 Application to Nakagami-m Fading Channels......Page 777
12.2 Multicarrier DS-CDMA Systems......Page 778
12.2.1.1 Transmitter......Page 779
12.2.1.3 Receiver......Page 780
12.2.1.4 Notations......Page 781
12.2.2.1 Conditional SNR......Page 782
12.2.2.2 Average BER......Page 786
12.2.3 Numerical Examples......Page 787
References......Page 791
CHAPTER 13 Coded Communication over Fading Channels......Page 796
13.1.1 System Model......Page 798
13.1.2 Evaluation of Pairwise Error Probability......Page 800
13.1.2.1 Known Channel State Information......Page 801
13.1.2.2 Unknown Channel State Information......Page 805
13.1.3 Transfer Function Bound on Average Bit Error Probability......Page 809
13.1.4 An Alternative Formulation of the Transfer Function Bound......Page 811
13.1.5 An Example......Page 812
13.2.1 System Model......Page 818
13.2.2.1 Unknown Channel State Information......Page 820
13.2.3 An Example......Page 822
13.3 Numerical Results-Comparison between the True Upper Bounds and Union–Chernoff Bounds......Page 824
References......Page 829
Appendix 13A. Evaluation of a Moment Generating Function Associated with Differential Detection of M-PSK Sequences......Page 830
CHAPTER 14 Multichannel Transmission-Transmit Diversity and Space-Time Coding......Page 834
14.1 A Historical Perspective......Page 836
14.2 Transmit versus Receive Diversity-Basic Concepts......Page 837
14.3 Alamouti's Diversity Technique-a Simple Transmit Diversity Scheme Using Two Transmit Antennas......Page 840
14.4 Generalization of Alamouti's Diversity Technique to Orthogonal Space-Time Block Code Designs......Page 846
14.5 Alamouti's Diversity Technique Combined with Multidimensional Trellis-Coded Modulation......Page 849
14.5.1 Evaluation of Pairwise Error Probability Performance on Fast Rician Fading Channels......Page 851
14.5.2 Evaluation of Pairwise Error Probability Performance on Slow Rician Fading Channels......Page 854
14.6 Space-Time Trellis-Coded Modulation......Page 855
14.6.1 Evaluation of Pairwise Error Probability Performance on Fast Rician Fading Channels......Page 857
14.6.2 Evaluation of Pairwise Error Probability Performance on Slow Rician Fading Channels......Page 858
14.6.3 An Example......Page 861
14.6.4.1 Fast-Fading Channel Model......Page 864
14.6.4.2 Slow-Fading Channel Model......Page 866
14.6.5.1 Fast-Fading Channel Model......Page 868
14.7 Other Combinations of Space-Time Block Codes and Space-Time Trellis Codes......Page 870
14.7.1.1 The Parameterized Class of Space-Time Block Codes and System Model......Page 871
14.7.1.2 Evaluation of the Pairwise Error Probability......Page 873
14.7.1.3 Extension of the Results to Super-Orthogonal Codes with More than Two Transmit Antennas......Page 881
14.7.1.4 Approximate Evaluation of Average Bit Error Probability......Page 882
14.7.1.5 Evaluation of the Transfer Function Upper Bound on the Average Bit Error Probability......Page 883
14.7.1.6 Numerical Results......Page 885
14.7.2.1 Signal Model......Page 887
14.7.2.2 Evaluation of Pairwise Error Probability......Page 889
14.7.2.3 Examples......Page 890
14.7.2.4 Numerical Results......Page 894
14.8 Disclaimer......Page 895
References......Page 896
15.1 Channel and System Model......Page 900
15.2.1 No Diversity......Page 902
15.2.2 Maximal-Ratio Combining......Page 903
15.3 Optimum Rate Adaptation with Constant Transmit Power......Page 904
15.3.1 No Diversity......Page 905
15.4 Channel Inversion with Fixed Rate......Page 906
15.4.2 Maximal-Ratio Combining......Page 907
15.5 Numerical Examples......Page 908
15.6 Capacity of MIMO Fading Channels......Page 913
References......Page 914
Appendix 15A. Evaluation of Jn(µ)......Page 915
Appendix 15B. Evaluation of In(µ)......Page 917
Index......Page 920