Mobile Radio Channels

Matthias Pätzold was born in Engelsbach, Germany, in 1958. He received the Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering from Ruhr-University Bochum, Bochum, Germany, in 1985 and 1989, respectively, and the habil. degree in communications engineering from the Technical University of Hamburg-Harburg, Hamburg, Germany, in 1998. From 1990 to 1992, he was with ANT Nachrichtentechnik GmbH, Backnang, Germany, where he was engaged in digital satellite communications. From 1992 to 2001, he was with the Department of Digital Networks at the Technical University Hamburg-Harburg. Since 2001, he has been a full professor of mobile communications with the University of Agder, Grimstad, Norway. He is author of the books “Mobile Radio Channels - Modelling, Analysis, and Simulation” (in German) (Wiesbaden, Germany: Vieweg, 1999) and “Mobile Fading Channels” (John Wiley & Sons, 2002) and “Mobile Radio Channels, 2nd Edition” (John Wiley & Sons, 2011). His current research interests include mobile radio communications, especially multipath fading channel modelling, multiple-input multiple-output (MIMO) systems, channel parameter estimation, and coded-modulation techniques for fading channels.

• Preface to the Second Edition xi List of Acronyms xvList of Symbols xix1 Introduction 11.1 The Evolution of Mobile Radio Systems 11.2 Basic Knowledge of Mobile Radio Channels 81.3 Structure of this Book 122 Random Variables, Stochastic Processes, and Deterministic Signals 172.1 Random Variables 172.1.1 Basic Definitions of Probability Theory 172.1.2 Important Probability Density Functions 242.1.3 Functions of Random Variables 352.2 Stochastic Processes 372.2.1 Stationary Processes 402.2.2 Ergodic Processes 422.2.3 Level-Crossing Rate and Average Duration of Fades 432.2.4 Linear Systems with Stochastic Inputs 452.3 Deterministic Signals 482.3.1 Deterministic Continuous-Time Signals 482.3.2 Deterministic Discrete-Time Signals 502.4 Further Reading 52Appendix 2.A Derivation of Rice’s General Formula for the Level-Crossing Rate 523 Rayleigh and Rice Channels 553.1 System Theoretical Description of Multipath Channels 563.2 Formal Description of Rayleigh and Rice Channels 613.3 Elementary Properties of Rayleigh and Rice Channels 623.3.1 Autocorrelation Function and Spectrum of the Complex Envelope 623.3.2 Autocorrelation Function and Spectrum of the Envelope 653.3.3 Autocorrelation Function and Spectrum of the Squared Envelope 673.4 Statistical Properties of Rayleigh and Rice Channels 693.4.1 Probability Density Function of the Envelope and the Phase 703.4.2 Probability Density Function of the Squared Envelope 723.4.3 Level-Crossing Rate and Average Duration of Fades 733.4.4 The Statistics of the Fading Intervals of Rayleigh Channels 773.5 Further Reading 84Appendix 3.A Derivation of the Jakes Power Spectral Density and theCorresponding Autocorrelation Function 84Appendix 3.B Derivation of the Autocorrelation Function of the Envelope 88Appendix 3.C Derivation of the Autocovariance Spectrum of the Envelope UnderIsotropic Scattering Conditions 90Appendix 3.D Derivation of the Level-Crossing Rate of Rice Processes withDifferent Spectral Shapes of the Underlying Gaussian RandomProcesses 914 Introduction to Sum-of-Sinusoids Channel Models 954.1 Principle of Deterministic Channel Modelling 964.2 Elementary Properties of Deterministic Sum-of-Sinusoids Processes 1024.3 Statistical Properties of Deterministic Sum-of-Sinusoids Processes 1074.3.1 Probability Density Function of the Envelope and the Phase 1084.3.2 Level-Crossing Rate and Average Duration of Fades 1154.3.3 Statistics of the Fading Intervals at Low Signal Levels 1204.3.4 Stationarity and Ergodicity of Sum-of-Sinusoids Processes 1224.4 Classes of Sum-of-Sinusoids Processes 1234.5 Basics of Sum-of-Cisoids Channel Models 1264.5.1 Elementary Properties of Stochastic Sum-of-Cisoids Processes 1274.5.2 Probability Density Function of the Envelope and Phase 1294.6 Criteria for the Performance Evaluation 1354.7 Further Reading 135Appendix 4.A Derivation of the Autocorrelation Function of the Squared Envelopeof Complex Deterministic Gaussian Processes 136Appendix 4.B Derivation of the Exact Solution of the Level-Crossing Rate and theAverage Duration of Fades of Deterministic Rice Processes 1375 Parametrization of Sum-of-Sinusoids Channel Models 1495.1 Methods for Computing the Doppler Frequencies and Gains 1515.1.1 Method of Equal Distances (MED) 1515.1.2 Mean-Square-Error Method (MSEM) 1575.1.3 Method of Equal Areas (MEA) 1625.1.4 Monte Carlo Method (MCM) 1705.1.5 Jakes Method (JM) 1785.1.6 Lp-Norm Method (LPNM) 1895.1.7 Method of Exact Doppler Spread (MEDS) 2015.1.8 Randomized Method of Exact Doppler Spread (RMEDS) 2055.1.9 Method of Exact Doppler Spread with Set Partitioning (MEDS-SP) 2075.2 Methods for Computing the Phases 2125.3 Fading Intervals of Deterministic Rayleigh Processes 2145.4 Parametrization of Sum-of-Cisoids Channel Models 2225.4.1 Problem Description 2225.4.2 Extended Method of Exact Doppler Spread (EMEDS) 2225.4.3 Lp-Norm Method (LPNM) 2245.4.4 Generalized Method of Equal Areas (GMEA) 2255.4.5 Performance Analysis 2285.5 Concluding Remarks and Further Reading 234Appendix 5.A Analysis of the Relative Model Error by Using the Monte CarloMethod 236Appendix 5.B Proof of the Convergence of the Sample Mean AutocorrelationFunction by Using the MEDS-SP 238Appendix 5.C Proof of the Condition for Uncorrelated Inphase and QuadratureComponents of SOC Processes 2396 Frequency-Nonselective Channel Models 2416.1 The Extended Suzuki Process of Type I 2436.1.1 Modelling and Analysis of Short-Term Fading 2436.1.2 Modelling and Analysis of Long-Term Fading 2546.1.3 The Stochastic Extended Suzuki Process of Type I 2576.1.4 The Deterministic Extended Suzuki Process of Type I 2626.1.5 Applications and Simulation Results 2656.2 The Extended Suzuki Process of Type II 2686.2.1 Modelling and Analysis of Short-Term Fading 2696.2.2 The Stochastic Extended Suzuki Process of Type II 2796.2.3 The Deterministic Extended Suzuki Process of Type II 2836.2.4 Applications and Simulation Results 2876.3 The Generalized Rice Process 2906.3.1 The Stochastic Generalized Rice Process 2916.3.2 The Deterministic Generalized Rice Process 2956.3.3 Applications and Simulation Results 2986.4 The Modified Loo Model 3006.4.1 The Stochastic Modified Loo Model 3006.4.2 The Deterministic Modified Loo Model 3116.4.3 Applications and Simulation Results 3176.5 Modelling of Nonstationary Land Mobile Satellite Channels 3196.5.1 Lutz’s Two-State Channel Model 3206.5.2 M-State Channel Models 3226.5.3 Modelling of Nonstationary Real-World LMS Channels 3237 Frequency-Selective Channel Models 3357.1 The Ellipse Model of Parsons and Bajwa 3367.2 System Theoretical Description of Frequency-Selective Channels 3387.3 Frequency-Selective Stochastic Channel Models 3427.3.1 Correlation Functions 3427.3.2 The WSSUS Model According to Bello 3447.3.3 The COST 207 Channel Models 3527.3.4 The HIPERLAN/2 Channel Models 3587.4 Frequency-Selective Sum-of-Sinusoids Channel Models 3587.4.1 System Functions of Sum-of-Sinusoids Uncorrelated Scattering(SOSUS) Models 3587.4.2 Correlation Functions and Power Spectral Densities ofSOSUS Models 3647.4.3 Delay Power Spectral Density, Doppler Power Spectral Density,and Characteristic Quantities of SOSUS Models 3687.4.4 Determination of the Model Parameters of SOSUS Models 3727.4.5 Simulation Models for the COST 207 Channel Models 3767.5 Methods for Modelling of Given Power Delay Profiles 3787.5.1 Problem Description 3797.5.2 Methods for the Computation of the Discrete Propagation Delays andthe Path Gains 3817.5.3 Comparison of the Parameter Computation Methods 3917.5.4 Applications to Measured Power Delay Profiles 3937.6 Perfect Modelling and Simulation of Measured Wideband Mobile RadioChannels 3967.6.1 The Sum-of-Cisoids Uncorrelated Scattering (SOCUS) Model 3967.6.2 The Principle of Perfect Channel Modelling 4037.6.3 Application to a Measured Wideband Indoor Channel 4047.7 Further Reading 406Appendix 7.A Specification of the L-Path COST 207 Channel Models 409Appendix 7.B Specification of the L-Path HIPERLAN/2 Channel Models 4138 MIMO Channel Models 4178.1 The Generalized Principle of Deterministic Channel Modelling 4188.2 The One-Ring MIMO Channel Model 4218.2.1 The Geometrical One-Ring Scattering Model 4228.2.2 The Reference Model for the One-Ring MIMO Channel Model 4238.2.3 Simulation Models for the One-Ring MIMO Channel Model 4298.2.4 Parameter Computation Methods 4338.2.5 Performance Evaluation 4348.2.6 Simulation Results 4368.3 The Two-Ring MIMO Channel Model 4388.3.1 The Geometrical Two-Ring Scattering Model 4398.3.2 The Reference Model for the Two-Ring MIMO Channel Model 4408.3.3 Simulation Models for the Two-Ring MIMO Channel Model 4458.3.4 Isotropic and Non-Isotropic Scattering Scenarios 4498.3.5 Parameter Computation Methods 4518.4 The Elliptical MIMO Channel Model 4578.4.1 The Geometrical Elliptical Scattering Model 4588.4.2 The Reference Model for the Elliptical MIMO Channel Model 4598.4.3 Simulation Models for the Elliptical MIMO Channel Model 4638.4.4 Model Extensions 4668.5 Further Reading 469Appendix 8.A Proof of Ergodicity 4729 High-Speed Channel Simulators 4759.1 Discrete-Time Deterministic Processes 4769.2 Realization of Discrete-Time Deterministic Processes 4789.2.1 Look-Up Table System 4789.2.2 Matrix System 4819.2.3 Shift Register System 4839.3 Properties of Discrete-Time Deterministic Processes 4849.3.1 Elementary Properties of Discrete-Time Deterministic Processes 4849.3.2 Statistical Properties of Discrete-Time Deterministic Processes 4919.4 Realization Complexity and Simulation Speed 5009.5 Comparison of the Sum-of-Sinusoids Method with the Filter Method 5029.6 Further Reading 50510 Selected Topics in Mobile Radio Channel Modelling 50710.1 Design of Multiple Uncorrelated Rayleigh Fading Waveforms 50710.1.1 Problem Description 50810.1.2 Generalized Method of Exact Doppler Spread (GMEDSq) 51110.1.3 Related Parameter Computation Methods 51610.1.4 The Effect of Finite Simulation Time on the Cross-CorrelationProperties 51810.1.5 Further Reading 52010.2 Spatial Channel Models for Shadow Fading 52110.2.1 The Reference Model for Shadow Fading 52210.2.2 The Simulation Model for Shadow Fading 52310.2.3 Correlation Models for Shadow Fading 52710.2.4 Further Reading 53510.3 Frequency Hopping Mobile Radio Channels 53610.3.1 The Reference Model for Frequency Hopping Channels 53610.3.2 The Simulation Model for Frequency Hopping Channels 53810.3.3 Performance Analysis 54010.3.4 Simulation Results 54410.3.5 Further Reading 544Appendix 10.A Derivation of the Spatial Autocorrelation Function of LognormalProcesses 545Appendix 10.B Derivation of the Level-Crossing Rate of Spatial LognormalProcesses 546Appendix 10.C Derivation of the Level-Crossing Rate of Sum-of-SinusoidsShadowing Simulators 546Appendix 10.D Application of the Method of Equal Areas (MEA) on theGudmundson Correlation Model 548Appendix 10.E Derivation of the Time-Frequency Cross-Correlation Function ofFrequency Hopping Channels 549Appendix 10.F Parametrization of Frequency Hopping Channel Simulators 551References 553Index 571