P. Mohana Shankar. Fading and Shadowing. in Wireless Systems. ^ Springer

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1 P. Mohana Shankar Fading and Shadowing in Wireless Systems ^ Springer

2 Contents 1 Overview Outline 1 References 5 2 Concepts of Probability and Statistics Introduction Random Variables, Probability Density Functions, and Cumulative Distribution Functions Characteristic Functions, Moment Generating Functions and Laplace Transforms Some Commonly Used Probability Density Functions Beta Distribution Binomial Distribution Cauchy Distribution Chi-Squared Distribution Erlang Distribution Exponential Distribution F (Fisher-Snedecor) Distribution Gamma Distribution Generalized Gamma Distribution Inverse Gaussian (Wald) Distribution Laplace Distribution Lognormal Distribution Nakagami Distribution Non-Central Chi-Squared Distribution Normal (Gaussian) Distribution Poisson Distribution Rayleigh Distribution Rectangular or Uniform Distribution 38 ix

3 x Contents Student's t Distribution Weibull Distribution Joint, Marginal and Conditional Densities Expectation, Covariance, Correlation, Independence, and Orthogonality Central Limit Theorem Transformation of Random Variables Derivation of the pdf and CDF of Y=g(X) Probability Density Function of Z=X+Y Joint pdf of Functions of Two or More Random Variables Use of CHF to Obtain pdf of Sum of Random Variables Some Transformations of Interest in Wireless Communications Some Bivariate Correlated Distributions of Interest in Wireless Communications Bivariate Normal pdf Bivariate Nakagami pdf Bivariate Gamma pdf Bivariate Generalized Gamma pdf Bivariate Weibull pdf Bivariate Rician Distribution Order Statistics A Few Special Cases of Order Statistics in Wireless Communications Decision Theory and Error Rates Gaussian Case Non-Gaussian Case Upper Bounds on the Tail Probability Chebyshev Inequality Chernoff Bound Stochastic Processes Summary 102 References Modems for Wireless Communications Introduction Optimum Receiver, Pulse Shaping, and Nyquist's Criteria Efficiency of Digital Modulation Techniques Geometric Representation of Signals and Orthonormal Functions Modulation Techniques Amplitude Shift Keying Phase Shift Keying 122

4 Contents M Frequency Shift Keying Amplitude and Phase Shift Keying Limitations of BPSK and Justification for MPSK General Nonlinear Modulation Schemes Frequency Shift Keying Digital Frequency Modulation (DFM) and Minimum Shift Keying (MSK) Gaussian Minimum Shift Keying Orthogonal M-ary FSK Error Rates for MSK, OQPSK, n/4 QPSK, and GMSK Error Rates for Differentially Encoded Signals Orthogonal Frequency Division Multiplexing Summary 163 Appendix 163 References Modeling of Fading and Shadowing Introduction Background Models for Short-Term Fading Rayleigh Fading Rician Fading Nakagami Fading Gamma, Generalized Gamma, and Weibull Fading Models for Shadowing Models for Shadowed Fading Channels Nakagami-Lognormal Models Nakagami-Gamma or Generalized K Models Nakagami-Inverse-Gaussian Model Generalized Gamma Model Amount of Fading in Shadowed Fading Channels Composite Model for Fading, Shadowing, and Shadowed Fading General Cascaded Models Statistical Background of Cascaded Fading Channels Cascaded Approach to Shadowed Fading Channels N*Weibull Channels Double Rician Channels Comparison of Different Models Average Probability of Error Outage Probability Other General Fading Models A few Additional Quantitative Measures of Fading and Shadowing 283

5 xjj Contents Ergodic Channel Capacity Second Order Statistics of Fading, Shadowing, and Shadowed Fading Channels Summary 298 Appendix 299 References Diversity Techniques Introduction Concept of Diversity Space Diversity Frequency Diversity Polarization Diversity Time Diversity Multipath Diversity Diversity Combining Algorithms Selection Combining Maximal Ratio Combining Equal Gain Combining Preliminary Comparison of the Three Combining Algorithms Selection Combining and Switched and Stay Combining Effects of Branch Correlation on Combining Algorithms Shadowing Mitigation and Macrodiversity Macro- and Microdiversity Systems (Hybrid Diversity) Generalized Selection Combining Quantitative Comparison of Diversity Combining Algorithms Amount of Fading Average Probability of Error Outage Probability Diversity in Generalized Gamma and Weibull Channels Diversity in Cascaded Nakagami Channels Generalized Selection Combining Summary 410 References Interference in Wireless Channels Introduction Outage Probabilities Rayleigh Channels Nakagami Channels Shadowed Fading Channels Average Probability of Error 433

6 Contents wii Probability Density Function (Rayleigh Channels) Probability Density Function (Nakagami Channels) Probability Density Function (Shadowed Fading Channels) Error Rates (Rayleigh Channels) Error Rates (Nakagami Channels) Error Rates (Shadowed Fading Channels) Error Rates Following Diversity Summary 451 References 451 Index 455

Index. offset-qpsk scheme, 237, 238 phase constellation, 235

Index. offset-qpsk scheme, 237, 238 phase constellation, 235 Index A American Digital Cellular and Japanese Digital Cellular systems, 243 Amount of fading (AF) cascaded fading channels, 340, 342 Gaussian pdf, 575 lognormal shadowing channel, 574, 576 MRC diversity,