Wireless Multi-Antenna Channels

Professor Serguei L. Primak, The University of Western Ontario, CanadaProfessor Primak is an Associate Professor at the University of the Western Ontario, Canada. His main areas of interest include modelling and performance evaluation of MIMO systems, Markov processes, non-Gaussian random processes and communications aspects of robotic assisted telesurgery. He has co-authored a book "Stochastic Methods and their Applications to Communications: Stochastic Differential Equations Approach", Wiley, 2004.Professor Valeri Kontorovich, CINVESTAV-IPN, MexicoProfessor Kontorovich is a Professor at the CINVESTAV-IPN, Mexico. His main areas of interest include modelling and performance evaluation of MIMO systems, Markov processes, non-Gaussian random processes, fractal, electromagnetic compatibility and other related topics. Professor Kontorovich has co-authored a book "Stochastic Methods and their Applications to Communications: Stochastic Differential Equations Approach", Wiley, 2004, and has co-authored 4 other books (In Russian) and a large number of publications in the field of communications.

• About the Series Editors xi1 Introduction 11.1 General remarks 11.2 Signals, interference, and types of parallel channels 32 Four-parametric model of a SISO channel 72.1 Multipath propagation 72.2 Random walk approach to modeling of scattering field 132.2.1 Random walk in two dimensions as a model for scattering field 132.2.2 Phase distribution and scattering strength 142.2.3 Distribution of intensity 142.2.4 Distribution of the random phase 172.3 Gaussian case 182.3.1 Four-parametric distribution family 182.3.2 Distribution of the magnitude 202.3.3 Distribution of the phase 272.3.4 Moment generating function, moments and cumulants of four-parametric distribution 292.3.5 Some aspects of multiple scattering propagation 293 Models of MIMO channels 333.1 General classification of MIMO channel models 333.2 Physical models 333.2.1 Deterministic models 343.2.2 Geometry-based stochastic models 353.3 Analytical models 363.3.1 Channel matrix model 373.4 Geometrical phenomenological models 473.4.1 Scattering from rough surfaces 483.5 On the role of trigonometric polynomials in analysis and simulation of MIMO channels 493.5.1 Measures of dependency 503.5.2 Non-negative trigonometric polynomials and their use in estimation of AoD and AoA distribution 513.5.3 Approximation of marginal PDF using non-negative polynomials 513.6 Canonical expansions of bivariate distributions and the structure MIMO channel covariance matrix 523.6.1 Canonical variables and expansion 523.6.2 General structure of the full covariance matrix 543.6.3 Relationship to other models 543.7 Bivariate von Mises distribution with correlated transmit and receive sides 563.7.1 Single cluster scenario 563.7.2 Multiple clusters scenario 583.8 Bivariate uniform distributions 583.8.1 Harmonic coupling 583.8.2 Markov-type bivariate density 613.9 Analytical expression for the diversity measure of an antenna array 623.9.1 Relation of the shape of the spatial covariance function to trigonometric moments 623.9.2 Approximation of the diversity measure for a large number of antennas 643.9.3 Examples 663.9.4 Leading term analysis of degrees of freedom 703.10 Effect of AoA/AoD dependency on the SDoF 723.11 Space-time covariance function 723.11.1 Basic equation 723.11.2 Approximations 733.12 Examples: synthetic data and uniform linear array 753.13 Approximation of a matrix by a Toeplitz matrix 773.14 Asymptotic expansions of diversity measure 783.15 Distributed scattering model 794 Modeling of wideband multiple channels 814.1 Standard models of channels 824.1.1 Cost 259/273 824.1.2 3gpp Scm 834.1.3 WINNER channel models 844.2 MDPSS based wideband channel simulator 844.2.1 Geometry of the problem 844.2.2 Statistical description 854.2.3 Multi-cluster environment 874.2.4 Simulation of dynamically changing environment 884.3 Measurement based simulator 894.4 Examples 914.4.1 Two cluster model 924.4.2 Environment specified by joint AoA/AoD/ToA distribution 934.4.3 Measurement based simulator 954.5 Appendix A: simulation parameters 965 Capacity of communication channels 995.1 Introduction 995.2 Ergodic capacity of MIMO channel 1005.2.1 Capacity of a constant (static) MIMO channel 1005.2.2 Alternative normalization 1025.2.3 Capacity of a static MIMO channel under different operation modes 1035.2.4 Ergodic capacity of a random channel 1045.2.5 Ergodic capacity of MIMO channels 1065.2.6 Asymptotic analysis of capacity and outage capacity 1065.3 Effects of MIMO models and their parameters on the predicted capacity of MIMO channels 1095.3.1 Channel estimation and effective SNR 1105.3.2 Achievable rates in Rayleigh channels with partial CSI 1135.3.3 Examples 1165.4 Time evolution of capacity 1195.4.1 Time evolution of capacity in SISO channels 1195.4.2 SISO channel capacity evolution 1205.5 Sparse MIMO channel model 1225.6 Statistical properties of capacity 1245.6.1 Some mathematical expressions 1245.7 Time-varying statistics 1255.7.1 Unordered eigenvalues 1255.7.2 Single cluster capacity LCR and AFD 1265.7.3 Approximation of multi-cluster capacity LCR and AFD 1265.7.4 Statistical simulation results 1296 Estimation and prediction of communication channels 1316.1 General remarks on estimation of time-varying channels 1316.2 Velocity estimation 1316.2.1 Velocity estimation based on the covariance function approximation 1316.2.2 Estimation based on reflection coefficients 1326.3 K-factor estimation 1336.3.1 Moment matching estimation 1336.3.2 I/Q based methods 1346.4 Estimation of four-parametric distributions 1356.5 Estimation of narrowband MIMO channels 1386.5.1 Superimposed pilot estimation scheme 1386.5.2 LS estimation 1406.5.3 Scaled least-square (SLS) estimation 1426.5.4 Minimum MSE 1446.5.5 Relaxed MMSE estimators 1466.6 Using frames for channel state estimation 1486.6.1 Properties of the spectrum of a mobile channel 1496.6.2 Frames based on DPSS 1506.6.3 Discrete prolate spheroidal sequences 1506.6.4 Numerical simulation 1547 Effects of prediction and estimation errors on performance of communication systems 1577.1 Kolmogorov–Szegö-Krein formula 1607.2 Prediction error for different antennas and scattering characteristics 1627.2.1 SISO channel 1627.2.2 SIMO channel 1657.2.3 MISO channel 1677.2.4 MIMO channel 1707.3 Summary of infinite horizon prediction results 1747.4 Eigenstructure of two cluster correlation matrix 1757.5 Preliminary comments on finite horizon prediction 1767.6 SISO channel prediction 1787.6.1 Wiener filter 1787.6.2 Single pilot prediction in a two cluster environment 1797.6.3 Single cluster prediction with multiple past samples 1817.6.4 Two cluster prediction with multiple past samples 1827.6.5 Role of oversampling 1877.7 What is the narrowband signal for a rectangular array? 1887.8 Prediction using the UIU model 1907.8.1 Separable covariance matrix 1917.8.2 1 × 2 unseparable example 1927.8.3 Large number of antennas: no noise 1937.8.4 Large number of antennas: estimation in noise 1947.8.5 Effects of the number of antennas, scattering geometry, and observation time on the quality of prediction 1957.9 Numerical simulations 1987.9.1 SISO channel single cluster 1987.9.2 Two cluster prediction 1987.10 Wiener estimator 1997.11 Approximation of the Wiener filter 2017.11.1 Zero order approximation 2027.11.2 Perturbation solution 2027.12 Element-wise prediction of separable process 2037.13 Effect of prediction and estimation errors on capacity calculations 2047.14 Channel estimation and effective SNR 2057.14.1 System model 2057.14.2 Estimation error 2057.14.3 Effective SNR 2077.15 Achievable rates in Rayleigh channels with partial CSI 2087.15.1 No CSI at the transmitter 2087.15.2 Partial CSI at the transmitter 2097.15.3 Optimization of the frame length 2117.16 Examples 2117.16.1 P(0, 0) Estimation 2117.16.2 Effect of non-uniform scattering 2137.17 Conclusions 2147.18 Appendix A: Szegö summation formula 2157.19 Appendix B: matrix inversion lemma 2168 Coding, modulation, and signaling over multiple channels 2198.1 Signal constellations and their characteristics 2198.2 Performance of OSTBC in generalized Gaussian channels and hardening effect 2248.2.1 Introduction 2248.2.2 Channel representation 2258.2.3 Probability of error 2278.2.4 Hardening effect 2298.3 Differential time-space modulation (DTSM) and an effective solution for the non-coherent MIMO channel 2338.3.1 Introduction to DTSM 2338.3.2 Performance of autocorrelation receiver of DSTM in generalized Gaussian channels 2348.3.3 Comments on MIMO channel model 2358.3.4 Differential space-time modulation 2358.3.5 Performance of DTSM 2378.3.6 Numerical results and discussions 2438.3.7 Some comments 243Bibliography 245Index 257