Wireless Multi-Antenna Channels -- Contents -- About the Series Editors -- 1 Introduction -- 1.1 General remarks -- 1.2 Signals, interference, and types of parallel channels -- 2 Four-parametric model of a SISO channel -- 2.1 Multipath propagation -- 2.2 Random walk approach to modeling of scattering field -- 2.2.1 Random walk in two dimensions as a model for scattering field -- 2.2.2 Phase distribution and scattering strength -- 2.2.3 Distribution of intensity -- 2.2.4 Distribution of the random phase -- 2.3 Gaussian case -- 2.3.1 Four-parametric distribution family -- 2.3.2 Distribution of the magnitude -- 2.3.3 Distribution of the phase -- 2.3.4 Moment generating function, moments and cumulants of four-parametric distribution -- 2.3.5 Some aspects of multiple scattering propagation -- 3 Models of MIMO channels -- 3.1 General classification of MIMO channel models -- 3.2 Physical models -- 3.2.1 Deterministic models -- 3.2.2 Geometry-based stochastic models -- 3.3 Analytical models -- 3.3.1 Channel matrix model -- 3.4 Geometrical phenomenological models -- 3.4.1 Scattering from rough surfaces -- 3.5 On the role of trigonometric polynomials in analysis and simulation of MIMO channels -- 3.5.1 Measures of dependency -- 3.5.2 Non-negative trigonometric polynomials and their use in estimation of AoD and AoA distribution -- 3.5.3 Approximation of marginal PDF using non-negative polynomials -- 3.6 Canonical expansions of bivariate distributions and the structure MIMO channel covariance matrix -- 3.6.1 Canonical variables and expansion -- 3.6.2 General structure of the full covariance matrix -- 3.6.3 Relationship to other models -- 3.7 Bivariate von Mises distribution with correlated transmit and receive sides -- 3.7.1 Single cluster scenario -- 3.7.2 Multiple clusters scenario -- 3.8 Bivariate uniform distributions -- 3.8.1 Harmonic coupling.

3.8.2 Markov-type bivariate density -- 3.9 Analytical expression for the diversity measure of an antenna array -- 3.9.1 Relation of the shape of the spatial covariance function to trigonometric moments -- 3.9.2 Approximation of the diversity measure for a large number of antennas -- 3.9.3 Examples -- 3.9.4 Leading term analysis of degrees of freedom -- 3.10 Effect of AoA/AoD dependency on the SDoF -- 3.11 Space-time covariance function -- 3.11.1 Basic equation -- 3.11.2 Approximations -- 3.12 Examples: synthetic data and uniform linear array -- 3.13 Approximation of a matrix by a Toeplitz matrix -- 3.14 Asymptotic expansions of diversity measure -- 3.15 Distributed scattering model -- 4 Modeling of wideband multiple channels -- 4.1 Standard models of channels -- 4.1.1 COST 259/273 -- 4.1.2 3GPP SCM -- 4.1.3 WINNER channel models -- 4.2 MDPSS based wideband channel simulator -- 4.2.1 Geometry of the problem -- 4.2.2 Statistical description -- 4.2.3 Multi-cluster environment -- 4.2.4 Simulation of dynamically changing environment -- 4.3 Measurement based simulator -- 4.4 Examples -- 4.4.1 Two cluster model -- 4.4.2 Environment specified by joint AoA/AoD/ToA distribution -- 4.4.3 Measurement based simulator -- 4.5 Appendix A: simulation parameters -- 5 Capacity of communication channels -- 5.1 Introduction -- 5.2 Ergodic capacity of MIMO channel -- 5.2.1 Capacity of a constant (static) MIMO channel -- 5.2.2 Alternative normalization -- 5.2.3 Capacity of a static MIMO channel under different operation modes -- 5.2.4 Ergodic capacity of a random channel -- 5.2.5 Ergodic capacity of MIMO channels -- 5.2.6 Asymptotic analysis of capacity and outage capacity -- 5.3 Effects of MIMO models and their parameters on the predicted capacity of MIMO channels -- 5.3.1 Channel estimation and effective SNR -- 5.3.2 Achievable rates in Rayleigh channels with partial CSI.

5.3.3 Examples -- 5.4 Time evolution of capacity -- 5.4.1 Time evolution of capacity in SISO channels -- 5.4.2 SISO channel capacity evolution -- 5.5 Sparse MIMO channel model -- 5.6 Statistical properties of capacity -- 5.6.1 Some mathematical expressions -- 5.7 Time-varying statistics -- 5.7.1 Unordered eigenvalues -- 5.7.2 Single cluster capacity LCR and AFD -- 5.7.3 Approximation of multi-cluster capacity LCR and AFD -- 5.7.4 Statistical simulation results -- 6 Estimation and prediction of communication channels -- 6.1 General remarks on estimation of time-varying channels -- 6.2 Velocity estimation -- 6.2.1 Velocity estimation based on the covariance function approximation -- 6.2.2 Estimation based on reflection coefficients -- 6.3 K-factor estimation -- 6.3.1 Moment matching estimation -- 6.3.2 I/Q based methods -- 6.4 Estimation of four-parametric distributions -- 6.5 Estimation of narrowband MIMO channels -- 6.5.1 Superimposed pilot estimation scheme -- 6.5.2 LS estimation -- 6.5.3 Scaled least-square (SLS) estimation -- 6.5.4 Minimum MSE -- 6.5.5 Relaxed MMSE estimators -- 6.6 Using frames for channel state estimation -- 6.6.1 Properties of the spectrum of a mobile channel -- 6.6.2 Frames based on DPSS -- 6.6.3 Discrete prolate spheroidal sequences -- 6.6.4 Numerical simulation -- 7 Effects of prediction and estimation errors on performance of communication systems -- 7.1 Kolmogorov-Szegö-Krein formula -- 7.2 Prediction error for different antennas and scattering characteristics -- 7.2.1 SISO channel -- 7.2.2 SIMO channel -- 7.2.3 MISO channel -- 7.2.4 MIMO channel -- 7.3 Summary of infinite horizon prediction results -- 7.4 Eigenstructure of two cluster correlation matrix -- 7.5 Preliminary comments on finite horizon prediction -- 7.6 SISO channel prediction -- 7.6.1 Wiener filter.

7.6.2 Single pilot prediction in a two cluster environment -- 7.6.3 Single cluster prediction with multiple past samples -- 7.6.4 Two cluster prediction with multiple past samples -- 7.6.5 Role of oversampling -- 7.7 What is the narrowband signal for a rectangular array? -- 7.8 Prediction using the UIU model -- 7.8.1 Separable covariance matrix -- 7.8.2 1 x 2 unseparable example -- 7.8.3 Large number of antennas: no noise -- 7.8.4 Large number of antennas: estimation in noise -- 7.8.5 Effects of the number of antennas, scattering geometry, and observation time on the quality of prediction -- 7.9 Numerical simulations -- 7.9.1 SISO channel single cluster -- 7.9.2 Two cluster prediction -- 7.10 Wiener estimator -- 7.11 Approximation of the Wiener filter -- 7.11.1 Zero order approximation -- 7.11.2 Perturbation solution -- 7.12 Element-wise prediction of separable process -- 7.13 Effect of prediction and estimation errors on capacity calculations -- 7.14 Channel estimation and effective SNR -- 7.14.1 System model -- 7.14.2 Estimation error -- 7.14.3 Effective SNR -- 7.15 Achievable rates in Rayleigh channels with partial CSI -- 7.15.1 No CSI at the transmitter -- 7.15.2 Partial CSI at the transmitter -- 7.15.3 Optimization of the frame length -- 7.16 Examples -- 7.16.1 P(0, 0) Estimation -- 7.16.2 Effect of non-uniform scattering -- 7.17 Conclusions -- 7.18 Appendix A: Szegö summation formula -- 7.19 Appendix B: matrix inversion lemma -- 8 Coding, modulation, and signaling over multiple channels -- 8.1 Signal constellations and their characteristics -- 8.2 Performance of OSTBC in generalized Gaussian channels and hardening effect -- 8.2.1 Introduction -- 8.2.2 Channel representation -- 8.2.3 Probability of error -- 8.2.4 Hardening effect -- Index -- 8.3 Differential time-space modulation (DTSM) and an effective solution for the non-coherent MIMO channel.

8.3.1 Introduction to DTSM -- 8.3.2 Performance of autocorrelation receiver of DSTM in generalized Gaussian channels -- 8.3.3 Comments on MIMO channel model -- 8.3.4 Differential space-time modulation -- 8.3.5 Performance of DTSM -- 8.3.6 Numerical results and discussions -- 8.3.7 Some comments -- Bibliography.