Mobile Radio Channels

MOBILE RADIO
CHANNELS......Page 3
Contents......Page 7
Preface to the Second Edition......Page 13
List of Acronyms......Page 17
List of Symbols......Page 21
1.1 The Evolution of Mobile Radio Systems......Page 35
1.2 Basic Knowledge of Mobile Radio Channels......Page 42
1.3 Structure of this Book......Page 46
2.1.1 Basic Definitions of Probability Theory......Page 51
2.1.2 Important Probability Density Functions......Page 58
2.1.3 Functions of Random Variables......Page 69
2.2 Stochastic Processes......Page 71
2.2.1 Stationary Processes......Page 74
2.2.2 Ergodic Processes......Page 76
2.2.3 Level-Crossing Rate and Average Duration of Fades......Page 77
2.2.4 Linear Systems with Stochastic Inputs......Page 79
2.3.1 Deterministic Continuous-Time Signals......Page 82
2.3.2 Deterministic Discrete-Time Signals......Page 84
Appendix 2.A Derivation of Rice’s General Formula for the Level-Crossing Rate......Page 86
3 Rayleigh and Rice Channels......Page 89
3.1 System Theoretical Description of Multipath Channels......Page 90
3.2 Formal Description of Rayleigh and Rice Channels......Page 95
3.3.1 Autocorrelation Function and Spectrum of the Complex Envelope......Page 96
3.3.2 Autocorrelation Function and Spectrum of the Envelope......Page 99
3.3.3 Autocorrelation Function and Spectrum of the Squared Envelope......Page 101
3.4 Statistical Properties of Rayleigh and Rice Channels......Page 103
3.4.1 Probability Density Function of the Envelope and the Phase......Page 104
3.4.2 Probability Density Function of the Squared Envelope......Page 106
3.4.3 Level-Crossing Rate and Average Duration of Fades......Page 107
3.4.4 The Statistics of the Fading Intervals of Rayleigh Channels......Page 111
Appendix 3.A Derivation of the Jakes Power Spectral Density and the Corresponding Autocorrelation Function......Page 118
Appendix 3.B Derivation of the Autocorrelation Function of the Envelope......Page 122
Appendix 3.C Derivation of the Autocovariance Spectrum of the Envelope Under Isotropic Scattering Conditions......Page 124
Appendix 3.D Derivation of the Level-Crossing Rate of Rice Processes with Different Spectral Shapes of the Underlying Gaussian Random Processes......Page 125
4 Introduction to Sum-of-Sinusoids Channel Models......Page 129
4.1 Principle of Deterministic Channel Modelling......Page 130
4.2 Elementary Properties of Deterministic Sum-of-Sinusoids Processes......Page 136
4.3 Statistical Properties of Deterministic Sum-of-Sinusoids Processes......Page 141
4.3.1 Probability Density Function of the Envelope and the Phase......Page 142
4.3.2 Level-Crossing Rate and Average Duration of Fades......Page 149
4.3.3 Statistics of the Fading Intervals at Low Signal Levels......Page 154
4.3.4 Stationarity and Ergodicity of Sum-of-Sinusoids Processes......Page 156
4.4 Classes of Sum-of-Sinusoids Processes......Page 157
4.5 Basics of Sum-of-Cisoids Channel Models......Page 160
4.5.1 Elementary Properties of Stochastic Sum-of-Cisoids Processes......Page 161
4.5.2 Probability Density Function of the Envelope and Phase......Page 163
4.7 Further Reading......Page 169
Appendix 4.A Derivation of the Autocorrelation Function of the Squared Envelope of Complex Deterministic Gaussian Processes......Page 170
Appendix 4.B Derivation of the Exact Solution of the Level-Crossing Rate and the Average Duration of Fades of Deterministic Rice Processes......Page 171
5 Parametrization of Sum-of-Sinusoids Channel Models......Page 183
5.1.1 Method of Equal Distances (MED)......Page 185
5.1.2 Mean-Square-Error Method (MSEM)......Page 191
5.1.3 Method of Equal Areas (MEA)......Page 196
5.1.4 Monte Carlo Method (MCM)......Page 204
5.1.5 Jakes Method (JM)......Page 212
5.1.6 Lp-Norm Method (LPNM)......Page 223
5.1.7 Method of Exact Doppler Spread (MEDS)......Page 235
5.1.8 Randomized Method of Exact Doppler Spread (RMEDS)......Page 239
5.1.9 Method of Exact Doppler Spread with Set Partitioning (MEDS-SP)......Page 241
5.2 Methods for Computing the Phases......Page 246
5.3 Fading Intervals of Deterministic Rayleigh Processes......Page 248
5.4.2 Extended Method of Exact Doppler Spread (EMEDS)......Page 256
5.4.3 Lp-Norm Method (LPNM)......Page 258
5.4.4 Generalized Method of Equal Areas (GMEA)......Page 259
5.4.5 Performance Analysis......Page 262
5.5 Concluding Remarks and Further Reading......Page 268
Appendix 5.A Analysis of the Relative Model Error by Using the Monte Carlo Method......Page 270
Appendix 5.B Proof of the Convergence of the Sample Mean Autocorrelation Function by Using the MEDS-SP......Page 272
Appendix 5.C Proof of the Condition for Uncorrelated Inphase and Quadrature Components of SOC Processes......Page 273
6 Frequency-Nonselective Channel Models......Page 275
6.1.1 Modelling and Analysis of Short-Term Fading......Page 277
6.1.2 Modelling and Analysis of Long-Term Fading......Page 288
6.1.3 The Stochastic Extended Suzuki Process of Type I......Page 291
6.1.4 The Deterministic Extended Suzuki Process of Type I......Page 296
6.1.5 Applications and Simulation Results......Page 299
6.2 The Extended Suzuki Process of Type II......Page 302
6.2.1 Modelling and Analysis of Short-Term Fading......Page 303
6.2.2 The Stochastic Extended Suzuki Process of Type II......Page 313
6.2.3 The Deterministic Extended Suzuki Process of Type II......Page 317
6.2.4 Applications and Simulation Results......Page 321
6.3 The Generalized Rice Process......Page 324
6.3.1 The Stochastic Generalized Rice Process......Page 325
6.3.2 The Deterministic Generalized Rice Process......Page 329
6.3.3 Applications and Simulation Results......Page 332
6.4.1 The Stochastic Modified Loo Model......Page 334
6.4.2 The Deterministic Modified Loo Model......Page 345
6.4.3 Applications and Simulation Results......Page 351
6.5 Modelling of Nonstationary Land Mobile Satellite Channels......Page 353
6.5.1 Lutz’s Two-State Channel Model......Page 354
6.5.2 M-State Channel Models......Page 356
6.5.3 Modelling of Nonstationary Real-World LMS Channels......Page 357
7 Frequency-Selective Channel Models......Page 369
7.1 The Ellipse Model of Parsons and Bajwa......Page 370
7.2 System Theoretical Description of Frequency-Selective Channels......Page 372
7.3.1 Correlation Functions......Page 376
7.3.2 The WSSUS Model According to Bello......Page 378
7.3.3 The COST 207 Channel Models......Page 386
7.3.4 The HIPERLAN/2 Channel Models......Page 390
7.4 Frequency-Selective Sum-of-Sinusoids Channel Models......Page 391
7.4.1 System Functions of Sum-of-Sinusoids Uncorrelated Scattering (SOSUS) Models......Page 392
7.4.2 Correlation Functions and Power Spectral Densities of SOSUS Models......Page 398
7.4.3 Delay Power Spectral Density, Doppler Power Spectral Density, and Characteristic Quantities of SOSUS Models......Page 402
7.4.4 Determination of the Model Parameters of SOSUS Models......Page 406
7.4.5 Simulation Models for the COST 207 Channel Models......Page 410
7.5 Methods for Modelling of Given Power Delay Profiles......Page 412
7.5.1 Problem Description......Page 413
7.5.2 Methods for the Computation of the Discrete Propagation Delays and the Path Gains......Page 415
7.5.3 Comparison of the Parameter Computation Methods......Page 425
7.5.4 Applications to Measured Power Delay Profiles......Page 427
7.6.1 The Sum-of-Cisoids Uncorrelated Scattering (SOCUS) Model......Page 430
7.6.2 The Principle of Perfect Channel Modelling......Page 437
7.6.3 Application to a Measured Wideband Indoor Channel......Page 438
7.7 Further Reading......Page 440
Appendix 7.A Specification of the L-Path COST 207 Channel Models......Page 443
Appendix 7.B Specification of the L-Path HIPERLAN/2 Channel Models......Page 447
8 MIMO Channel Models......Page 451
8.1 The Generalized Principle of Deterministic Channel Modelling......Page 452
8.2 The One-Ring MIMO Channel Model......Page 455
8.2.1 The Geometrical One-Ring Scattering Model......Page 456
8.2.2 The Reference Model for the One-Ring MIMO Channel Model......Page 457
8.2.3 Simulation Models for the One-Ring MIMO Channel Model......Page 463
8.2.4 Parameter Computation Methods......Page 467
8.2.5 Performance Evaluation......Page 468
8.2.6 Simulation Results......Page 470
8.3 The Two-Ring MIMO Channel Model......Page 472
8.3.1 The Geometrical Two-Ring Scattering Model......Page 473
8.3.2 The Reference Model for the Two-Ring MIMO Channel Model......Page 474
8.3.3 Simulation Models for the Two-Ring MIMO Channel Model......Page 479
8.3.4 Isotropic and Non-Isotropic Scattering Scenarios......Page 483
8.3.5 Parameter Computation Methods......Page 485
8.4 The Elliptical MIMO Channel Model......Page 491
8.4.1 The Geometrical Elliptical Scattering Model......Page 492
8.4.2 The Reference Model for the Elliptical MIMO Channel Model......Page 493
8.4.3 Simulation Models for the Elliptical MIMO Channel Model......Page 497
8.4.4 Model Extensions......Page 500
8.5 Further Reading......Page 503
Appendix 8.A Proof of Ergodicity......Page 506
9 High-Speed Channel Simulators......Page 509
9.1 Discrete-Time Deterministic Processes......Page 510
9.2.1 Look-Up Table System......Page 512
9.2.2 Matrix System......Page 515
9.2.3 Shift Register System......Page 517
9.3.1 Elementary Properties of Discrete-Time Deterministic Processes......Page 518
9.3.2 Statistical Properties of Discrete-Time Deterministic Processes......Page 525
9.4 Realization Complexity and Simulation Speed......Page 534
9.5 Comparison of the Sum-of-Sinusoids Method with the Filter Method......Page 536
9.6 Further Reading......Page 539
10.1 Design of Multiple Uncorrelated Rayleigh Fading Waveforms......Page 541
10.1.1 Problem Description......Page 542
10.1.2 Generalized Method of Exact Doppler Spread (GMEDSq)......Page 545
10.1.3 Related Parameter Computation Methods......Page 550
10.1.4 The Effect of Finite Simulation Time on the Cross-Correlation Properties......Page 552
10.1.5 Further Reading......Page 554
10.2 Spatial Channel Models for Shadow Fading......Page 555
10.2.1 The Reference Model for Shadow Fading......Page 556
10.2.2 The Simulation Model for Shadow Fading......Page 557
10.2.3 Correlation Models for Shadow Fading......Page 561
10.2.4 Further Reading......Page 569
10.3.1 The Reference Model for Frequency Hopping Channels......Page 570
10.3.2 The Simulation Model for Frequency Hopping Channels......Page 572
10.3.3 Performance Analysis......Page 574
10.3.5 Further Reading......Page 578
Appendix 10.A Derivation of the Spatial Autocorrelation Function of Lognormal Processes......Page 579
Appendix 10.C Derivation of the Level-Crossing Rate of Sum-of-Sinusoids Shadowing Simulators......Page 580
Appendix 10.D Application of the Method of Equal Areas (MEA) on the Gudmundson Correlation Model......Page 582
Appendix 10.E Derivation of the Time-Frequency Cross-Correlation Function of Frequency Hopping Channels......Page 583
Appendix 10.F Parametrization of Frequency Hopping Channel Simulators......Page 585
References......Page 587
Index......Page 605