Adaptive Wireless. Communications. gl CAMBRIDGE UNIVERSITY PRESS. MIMO Channels and Networks SIDDHARTAN GOVJNDASAMY DANIEL W.

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1 Adaptive Wireless Communications MIMO Channels and Networks DANIEL W. BLISS Arizona State University SIDDHARTAN GOVJNDASAMY Franklin W. Olin College of Engineering, Massachusetts gl CAMBRIDGE UNIVERSITY PRESS ^0

2 Contents Preface Acknowledgments page xvii xviii 1 History Development of electromagnetics Early wireless communications Developing communication theory Television broadcast Modern communications advances Early packet-radio networks Wireless local-area networks 10 2 Notational and mathematical preliminaries Notation Table of symbols Scalars Vectors and matrices Vector products Matrix products Norms, traces, and determinants Norm Trace Determinants Matrix decompositions Eigen analysis Eigenvalues of 2 x 2 Hermitian matrix Singular-value decomposition QR decomposition Matrix subspaces Special matrix forms Element shifted symmetries Eigenvalues of low-rank matrices Matrix inversion Inversion of matrix sum 28

3 viii Contents 2.6 Useful matrix approximations Log determinant of identity plus small-valued matrix Hermitian matrix raised to large power Real derivatives of multivariate expressions Derivative with respect to real vectors Complex derivatives Cauchy-Riemann equations Wirtinger calculus for complex variables Multivariate Wirtinger calculus Complex gradient Integration over complex variables Path and contour integrals Volume integrals Fourier transform Useful Fourier relationships Discrete Fourier transform Laplace transform Constrained optimization Equality constraints Inequality constraints Calculus of variations Order of growth notation Special functions Gamma function Hypergeometric series Beta function Lambert W function Bessel functions Error function Gaussian Q-function Marcum Q-function 63 Problems 63 3 Probability and statistics Probability Bayes' theorem Change of variables Central moments of a distribution Noncentral moments of a distribution Characteristic function Cumulants of distributions Multivariate probability distributions Gaussian distribution Rayleigh distribution Exponential distribution 73

4 Contents ix Central x2 distribution Noncentral x2 distribution F distribution Rician distribution Nakagami distribution Poisson distribution Beta distribution Logarithmically normal distribution Sum of random variables Product of Gaussians Convergence of random variables Convergence modes of random variables Relationship between modes of convergence Random processes Wide-sense stationary random processes Action of linear-time-invariant systems on wide-sense stationary random processes White-noise processes Poisson processes Eigenvalue distributions of finite Wishart matrices Asymptotic eigenvalue distributions of Wishart matrices Marcenko-Pastur theorem Estimation and detection in additive Gaussian noise Estimation in additive Gaussian noise Detection in additive Gaussian noise Receiver operating characteristics Cramer-Rao parameter estimation bound Real parameter formulation Real multivariate Cramer-Rao bound Cramer-Rao bound for complex parameters 105 Problems Wireless communications fundamentals Communication stack Reference digital radio link Wireless channel Thermal noise Cellular networks Frequency reuse Multiple access in cells Ad hoc wireless networks Achievable data rates in ad hoc wireless networks Sampled signals 137 Problems 138

5 x Contents 5 Simple channels Antennas Line-of-sight attenuation Gain versus effective area Beamwidth Channel capacity Geometric interpretation Mutual information Additive Gaussian noise channel Additive Gaussian noise channel with state Energy per bit 165 Problems Antenna arrays Wavefront Geometric interpretation Steering vector Array beam pattern Beam pattern in a plane Linear arrays Beam pattern symmetry for linear arrays Fourier transform interpretation Continuous Fourier transform approximation Sparse arrays Sparse arrays on a regular lattice Irregular random sparse arrays Polarization-diverse arrays Polarization formulation 196 Problems Angle-of-arrival estimation Maximum-likelihood angle estimation with known reference Maximum-likelihood angle estimation with unknown signal Beamscan Minimum-variance distortionless response MuSiC Example comparison of spatial energy estimators Local angle-estimation performance bounds Cramer-Rao bound of angle estimation Cramer-Rao bound: signal in the mean Cramer-Rao bound: random signal Threshold estimation Types of transmitted signals Known reference signal test statistic Independent Rician random variables 221

6 Contents xi Correlated Rician random variables Unknown complex Gaussian signal Vector sensor 235 Problems MIMO channel Flat-fading channel Interference Maximizing entropy Flat-fading MIMO capacity Channel-state information at the transmitter Informed-transmitter (IT) capacity Uninformed-transmitter (UT) capacity Capacity ratio, cjt/cut Frequency-selective channels x2 Line-of-sight channel Stochastic channel models Spatially uncorrelated Gaussian channel model Spatially correlated Gaussian channel model Large channel matrix capacity Large-dimension Gaussian probability density Uninformed transmitter spectral efficiency bound Informed transmitter capacity Outage capacity SNR distributions Total power Fractional loss Channel estimation Cramer-Rao bound Estimated versus average SNR Average SNR Estimated SNR MIMO capacity for estimated SNR in block fading Interpretation of various capacities Channel-state information at transmitter Reciprocity Channel estimation feedback 292 Problems Spatially adaptive receivers Adaptive spectral filtering Discrete Wiener filter Adaptive spatial processing Spatial matched filter Minimum-interference spatial beamforming 303

7 xii Contents MMSE spatial processing Maximum SINR SNR loss performance comparison Minimum-interference beamformer MMSE beamformer MIMO performance bounds of suboptimal adaptive receivers Receiver beamformer channel Iterative receivers Recursive least squares (RLS) Least mean squares (LMS) Multiple-antenna multiuser detector Maximum-likelihood demodulation Covariance matrix conditioning 337 Problems Dispersive and doubly dispersive channels Discretely sampled channel issues Noncommutative delay and Doppler operations Effect of frequency-selective fading Static frequency-selective channel model Frequency-selective channel compensation Eigenvalue distribution of space-time covariance matrix Space-time adaptive processing Orthogonal-frequency-division multiplexing Doubly dispersive channel model Doppler-domain representation Eigenvalue distribution of space-time-frequency covariance matrix Space-time-frequency adaptive processing Sparse space-time-frequency processing 362 Problems Space-time coding Rate diversity trade-off Probability of error formulation Outage probability formulation Block codes Alamouti's code Orthogonal space-time block codes Performance criteria for space-time codes Space-time trellis codes Trellis-coded modulation Space-time trellis coding Bit-interleaved coded modulation 381

8 Contents xiii Single-antenna bit-interleaved coded modulation Multiantenna bit-interleaved coded modulation Space-time turbo codes Direct modulation Universal codes Performance comparisons of space-time codes Computations versus performance 388 Problems x2 Network Introduction Achievable rates of the 2 x 2 MIMO network Single-antenna Gaussian interference channel Achievable rates of the MIMO interference channel Outer bounds of the capacity region of the Gaussian MIMO interference channel Outer bounds to the capacity region of the single-antenna Gaussian interference channel Outer bounds to the capacity region of the Gaussian interference channel with multiple antennas The 2x2 cognitive MIMO network Non-cooperative primary link Cooperative primary link 412 Problems Cellular networks Point-to-point links and networks Multiple access and broadcast channels Linear receivers in cellular networks with Rayleigh fading and constant transmit powers Link lengths in cellular networks General network model Antenna-selection receiver Matched filter Linear minimum-mean-square-error receiver Laplacian of the interference Linear receivers in cellular networks with power control System model Optimality of parallelized transmissions with link CSI Asymptotic spectral efficiency of parallelized system Application to power-controlled systems without out-ofcell interference Monte Carlo simulations Matched-filter receiver in power-controlled cellular networks 448

9 xiv Contents Application to power-controlled systems with out-of-cell interference Summary 467 Problems Ad hoc networks Introduction Capacity scaling laws of ad hoc wireless networks Multiantenna links in ad hoc wireless networks Asymptotic spectral efficiency of ad hoc wireless networks with limited transmit channel-state information and minimum-mean-square-error (MMSE) receivers Spatially distributed network model Asymptotic spectral efficiency without transmit channel-state information Maximum-signal-to-leakage-plus-noise ratio receiver Linear receiver structures in spatially distributed networks Linear MMSE receivers in Poisson networks Laplacian of the interference in Poisson networks and matched-filter and antenna-selection receivers Interference alignment 487 Problems Medium-access-control protocols The need for medium-access control The ALOHA protocol Carrier-sense multiple access (CSMA) CSMA with collision avoidance (CSMA/CA) Non-space-division multiple-access protocols Space-division multiple-access (SDMA) protocols Introduction A simple SDMA protocol SPACE-MAC The reciprocity assumption Ward protocol Summary of some existing SDMA protocols 513 Problems Cognitive radios Cognitive radio channel Cooperative cognitive links Cognitive spectral scavenging Orthogonal-frequency-division multiple access Game-theoretical analysis 523

10 Contents xv 16.3 Legacy signal detection Known training sequence Single-antenna signal energy detection Multiple-antenna legacy signal detection Optimizing spectral efficiency to minimize network interference Optimal SISO spectral efficiency Optimal MIMO spectral efficiency 542 Problems Multiple-antenna acquisition and synchronization Flat-fading MIMO model Flat-fading MIMO delay-estimation bound Synchronization as hypothesis testing Motivations for test statistic approaches Test statistics for fiat-fading channels Correlation MMSE beamformer Generalized-likelihood ratio test Spatial invariance Comparison of performance 557 Problems Practical issues Antennas Electrically small antennas Crossed polarimetric array Signal and noise model errors Noise figure Local oscillators Accuracy Phase noise Dynamic range Quantization Finite precision Analog nonlinearities Adaptive gain control Spurs Power consumption 568 References 569 Index 589

Adaptive Wireless Communications

Adaptive Wireless Communications Adopting a balanced mix of theory, algorithms, and practical design issues, this comprehensive volume explores cutting-edge applications in adaptive wireless communications,