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
Contents Preface Acknowledgments page xvii xviii 1 History 1 1.1 Development of electromagnetics 1 1.2 Early wireless communications 2 1.3 Developing communication theory 5 1.4 Television broadcast 6 1.5 Modern communications advances 7 1.5.1 Early packet-radio networks 9 1.5.2 Wireless local-area networks 10 2 Notational and mathematical preliminaries 12 2.1 Notation 12 2.1.1 Table of symbols 12 2.1.2 Scalars 12 2.1.3 Vectors and matrices 14 2.1.4 Vector products 16 2.1.5 Matrix products 17 2.2 Norms, traces, and determinants 19 2.2.1 Norm 19 2.2.2 Trace 19 2.2.3 Determinants 19 2.3 Matrix decompositions 21 2.3.1 Eigen analysis 21 2.3.2 Eigenvalues of 2 x 2 Hermitian matrix 22 2.3.3 Singular-value decomposition 22 2.3.4 QR decomposition 23 2.3.5 Matrix subspaces 24 2.4 Special matrix forms 26 2.4.1 Element shifted symmetries 26 2.4.2 Eigenvalues of low-rank matrices 26 2.5 Matrix inversion 27 2.5.1 Inversion of matrix sum 28
viii Contents 2.6 Useful matrix approximations 28 2.6.1 Log determinant of identity plus small-valued matrix 28 2.6.2 Hermitian matrix raised to large power 29 2.7 Real derivatives of multivariate expressions 29 2.7.1 Derivative with respect to real vectors 30 2.8 Complex derivatives 33 2.8.1 Cauchy-Riemann equations 34 2.8.2 Wirtinger calculus for complex variables 35 2.8.3 Multivariate Wirtinger calculus 38 2.8.4 Complex gradient 38 2.9 Integration over complex variables 39 2.9.1 Path and contour integrals 40 2.9.2 Volume integrals 42 2.10 Fourier transform 44 2.10.1 Useful Fourier relationships 45 2.10.2 Discrete Fourier transform 46 2.11 Laplace transform 48 2.12 Constrained optimization 48 2.12.1 Equality constraints 48 2.12.2 Inequality constraints 51 2.12.3 Calculus of variations 53 2.13 Order of growth notation 57 2.14 Special functions 58 2.14.1 Gamma function 58 2.14.2 Hypergeometric series 59 2.14.3 Beta function 61 2.14.4 Lambert W function 61 2.14.5 Bessel functions 62 2.14.6 Error function 63 2.14.7 Gaussian Q-function 63 2.14.8 Marcum Q-function 63 Problems 63 3 Probability and statistics 66 3.1 Probability 66 3.1.1 Bayes' theorem 66 3.1.2 Change of variables 67 3.1.3 Central moments of a distribution 68 3.1.4 Noncentral moments of a distribution 69 3.1.5 Characteristic function 70 3.1.6 Cumulants of distributions 70 3.1.7 Multivariate probability distributions 70 3.1.8 Gaussian distribution 71 3.1.9 Rayleigh distribution 72 3.1.10 Exponential distribution 73
Contents ix 3.1.11 Central x2 distribution 73 3.1.12 Noncentral x2 distribution 75 3.1.13 F distribution 76 3.1.14 Rician distribution 77 3.1.15 Nakagami distribution 78 3.1.16 Poisson distribution 78 3.1.17 Beta distribution 79 3.1.18 Logarithmically normal distribution 79 3.1.19 Sum of random variables 80 3.1.20 Product of Gaussians 81 3.2 Convergence of random variables 81 3.2.1 Convergence modes of random variables 82 3.2.2 Relationship between modes of convergence 83 3.3 Random processes 86 3.3.1 Wide-sense stationary random processes 88 3.3.2 Action of linear-time-invariant systems on wide-sense stationary random processes 88 3.3.3 White-noise processes 89 3.4 Poisson processes 91 3.5 Eigenvalue distributions of finite Wishart matrices 92 3.6 Asymptotic eigenvalue distributions of Wishart matrices 92 3.6.1 Marcenko-Pastur theorem 94 3.7 Estimation and detection in additive Gaussian noise 95 3.7.1 Estimation in additive Gaussian noise 95 3.7.2 Detection in additive Gaussian noise 96 3.7.3 Receiver operating characteristics 98 3.8 Cramer-Rao parameter estimation bound 99 3.8.1 Real parameter formulation 99 3.8.2 Real multivariate Cramer-Rao bound 102 3.8.3 Cramer-Rao bound for complex parameters 105 Problems 116 4 Wireless communications fundamentals 118 4.1 Communication stack 118 4.2 Reference digital radio link 119 4.2.1 Wireless channel 122 4.2.2 Thermal noise 123 4.3 Cellular networks 125 4.3.1 Frequency reuse 127 4.3.2 Multiple access in cells 128 4.4 Ad hoc wireless networks 132 4.4.1 Achievable data rates in ad hoc wireless networks 134 4.5 Sampled signals 137 Problems 138
x Contents 5 Simple channels 141 5.1 Antennas 141 5.2 Line-of-sight attenuation 143 5.2.1 Gain versus effective area 144 5.2.2 Beamwidth 147 5.3 Channel capacity 149 5.3.1 Geometric interpretation 149 5.3.2 Mutual information 156 5.3.3 Additive Gaussian noise channel 159 5.3.4 Additive Gaussian noise channel with state 162 5.4 Energy per bit 165 Problems 168 6 Antenna arrays 170 6.1 Wavefront 170 6.1.1 Geometric interpretation 172 6.1.2 Steering vector 173 6.2 Array beam pattern 174 6.2.1 Beam pattern in a plane 176 6.3 Linear arrays 179 6.3.1 Beam pattern symmetry for linear arrays 182 6.3.2 Fourier transform interpretation 182 6.3.3 Continuous Fourier transform approximation 184 6.4 Sparse arrays 186 6.4.1 Sparse arrays on a regular lattice 186 6.4.2 Irregular random sparse arrays 188 6.5 Polarization-diverse arrays 196 6.5.1 Polarization formulation 196 Problems 198 7 Angle-of-arrival estimation 201 7.1 Maximum-likelihood angle estimation with known reference 203 7.2 Maximum-likelihood angle estimation with unknown signal 205 7.3 Beamscan 205 7.4 Minimum-variance distortionless response 207 7.5 MuSiC 208 7.6 Example comparison of spatial energy estimators 210 7.7 Local angle-estimation performance bounds 211 7.7.1 Cramer-Rao bound of angle estimation 211 7.7.2 Cramer-Rao bound: signal in the mean 212 7.7.3 Cramer-Rao bound: random signal 214 7.8 Threshold estimation 218 7.8.1 Types of transmitted signals 219 7.8.2 Known reference signal test statistic 219 7.8.3 Independent Rician random variables 221
Contents xi 7.8.4 Correlated Rician random variables 226 7.8.5 Unknown complex Gaussian signal 231 7.9 Vector sensor 235 Problems 237 8 MIMO channel 239 8.1 Flat-fading channel 239 8.2 Interference 241 8.2.1 Maximizing entropy 242 8.3 Flat-fading MIMO capacity 243 8.3.1 Channel-state information at the transmitter 245 8.3.2 Informed-transmitter (IT) capacity 247 8.3.3 Uninformed-transmitter (UT) capacity 252 8.3.4 Capacity ratio, cjt/cut 256 8.4 Frequency-selective channels 258 8.5 2x2 Line-of-sight channel 259 8.6 Stochastic channel models 264 8.6.1 Spatially uncorrelated Gaussian channel model 265 8.6.2 Spatially correlated Gaussian channel model 266 8.7 Large channel matrix capacity 270 8.7.1 Large-dimension Gaussian probability density 270 8.7.2 Uninformed transmitter spectral efficiency bound 271 8.7.3 Informed transmitter capacity 272 8.8 Outage capacity 275 8.9 SNR distributions 275 8.9.1 Total power 277 8.9.2 Fractional loss 279 8.10 Channel estimation 281 8.10.1 Cramer-Rao bound 283 8.11 Estimated versus average SNR 286 8.11.1 Average SNR 287 8.11.2 Estimated SNR 287 8.11.3 MIMO capacity for estimated SNR in block fading 289 8.11.4 Interpretation of various capacities 290 8.12 Channel-state information at transmitter 291 8.12.1 Reciprocity 291 8.12.2 Channel estimation feedback 292 Problems 293 9 Spatially adaptive receivers 295 9.1 Adaptive spectral filtering 298 9.1.1 Discrete Wiener filter 298 9.2 Adaptive spatial processing 300 9.2.1 Spatial matched filter 301 9.2.2 Minimum-interference spatial beamforming 303
xii Contents 9.2.3 MMSE spatial processing 311 9.2.4 Maximum SINR 313 9.3 SNR loss performance comparison 315 9.3.1 Minimum-interference beamformer 317 9.3.2 MMSE beamformer 318 9.4 MIMO performance bounds of suboptimal adaptive receivers 322 9.4.1 Receiver beamformer channel 323 9.5 Iterative receivers 328 9.5.1 Recursive least squares (RLS) 328 9.5.2 Least mean squares (LMS) 331 9.6 Multiple-antenna multiuser detector 333 9.6.1 Maximum-likelihood demodulation 333 9.7 Covariance matrix conditioning 337 Problems 339 10 Dispersive and doubly dispersive channels 341 10.1 Discretely sampled channel issues 342 10.2 Noncommutative delay and Doppler operations 344 10.3 Effect of frequency-selective fading 345 10.4 Static frequency-selective channel model 348 10.5 Frequency-selective channel compensation 348 10.5.1 Eigenvalue distribution of space-time covariance matrix 349 10.5.2 Space-time adaptive processing 353 10.5.3 Orthogonal-frequency-division multiplexing 354 10.6 Doubly dispersive channel model 356 10.6.1 Doppler-domain representation 357 10.6.2 Eigenvalue distribution of space-time-frequency covariance matrix 358 10.7 Space-time-frequency adaptive processing 361 10.7.1 Sparse space-time-frequency processing 362 Problems 362 11 Space-time coding 365 11.1 Rate diversity trade-off 365 11.1.1 Probability of error formulation 366 11.1.2 Outage probability formulation 367 11.2 Block codes 369 11.2.1 Alamouti's code 371 11.2.2 Orthogonal space-time block codes 373 11.3 Performance criteria for space-time codes 374 11.4 Space-time trellis codes 376 11.4.1 Trellis-coded modulation 376 11.4.2 Space-time trellis coding 376 11.5 Bit-interleaved coded modulation 381
Contents xiii 11.5.1 Single-antenna bit-interleaved coded modulation 381 11.5.2 Multiantenna bit-interleaved coded modulation 382 11.5.3 Space-time turbo codes 384 11.6 Direct modulation 385 11.7 Universal codes 386 11.8 Performance comparisons of space-time codes 388 11.9 Computations versus performance 388 Problems 390 12 2x2 Network 392 12.1 Introduction 392 12.2 Achievable rates of the 2 x 2 MIMO network 393 12.2.1 Single-antenna Gaussian interference channel 393 12.2.2 Achievable rates of the MIMO interference channel 397 12.3 Outer bounds of the capacity region of the Gaussian MIMO interference channel 399 12.3.1 Outer bounds to the capacity region of the single-antenna Gaussian interference channel 399 12.3.2 Outer bounds to the capacity region of the Gaussian interference channel with multiple antennas 405 12.4 The 2x2 cognitive MIMO network 408 12.4.1 Non-cooperative primary link 409 12.4.2 Cooperative primary link 412 Problems 412 13 Cellular networks 414 13.1 Point-to-point links and networks 414 13.2 Multiple access and broadcast channels 414 13.3 Linear receivers in cellular networks with Rayleigh fading and constant transmit powers 422 13.3.1 Link lengths in cellular networks 423 13.3.2 General network model 425 13.3.3 Antenna-selection receiver 425 13.3.4 Matched filter 427 13.3.5 Linear minimum-mean-square-error receiver 429 13.3.6 Laplacian of the interference 432 13.4 Linear receivers in cellular networks with power control 436 13.4.1 System model 437 13.4.2 Optimality of parallelized transmissions with link CSI 438 13.4.3 Asymptotic spectral efficiency of parallelized system 442 13.4.4 Application to power-controlled systems without out-ofcell interference 445 13.4.5 Monte Carlo simulations 446 13.5 Matched-filter receiver in power-controlled cellular networks 448
xiv Contents 13.5.1 Application to power-controlled systems with out-of-cell interference 449 13.6 Summary 467 Problems 467 14 Ad hoc networks 470 14.1 Introduction 470 14.1.1 Capacity scaling laws of ad hoc wireless networks 470 14.2 Multiantenna links in ad hoc wireless networks 475 14.2.1 Asymptotic spectral efficiency of ad hoc wireless networks with limited transmit channel-state information and minimum-mean-square-error (MMSE) receivers 476 14.2.2 Spatially distributed network model 478 14.2.3 Asymptotic spectral efficiency without transmit channel-state information 480 14.2.4 Maximum-signal-to-leakage-plus-noise ratio receiver 482 14.3 Linear receiver structures in spatially distributed networks 484 14.3.1 Linear MMSE receivers in Poisson networks 484 14.3.2 Laplacian of the interference in Poisson networks and matched-filter and antenna-selection receivers 485 14.4 Interference alignment 487 Problems 491 15 Medium-access-control protocols 495 15.1 The need for medium-access control 495 15.2 The ALOHA protocol 496 15.3 Carrier-sense multiple access (CSMA) 498 15.3.1 CSMA with collision avoidance (CSMA/CA) 499 15.4 Non-space-division multiple-access protocols 504 15.5 Space-division multiple-access (SDMA) protocols 504 15.5.1 Introduction 504 15.5.2 A simple SDMA protocol 506 15.5.3 SPACE-MAC 507 15.5.4 The reciprocity assumption 509 15.5.5 Ward protocol 509 15.5.6 Summary of some existing SDMA protocols 513 Problems 518 16 Cognitive radios 520 16.1 Cognitive radio channel 521 16.1.1 Cooperative cognitive links 522 16.2 Cognitive spectral scavenging 522 16.2.1 Orthogonal-frequency-division multiple access 523 16.2.2 Game-theoretical analysis 523
Contents xv 16.3 Legacy signal detection 524 16.3.1 Known training sequence 524 16.3.2 Single-antenna signal energy detection 524 16.3.3 Multiple-antenna legacy signal detection 534 16.4 Optimizing spectral efficiency to minimize network interference 538 16.4.1 Optimal SISO spectral efficiency 540 16.4.2 Optimal MIMO spectral efficiency 542 Problems 545 17 Multiple-antenna acquisition and synchronization 547 17.1 Flat-fading MIMO model 548 17.2 Flat-fading MIMO delay-estimation bound 548 17.3 Synchronization as hypothesis testing 550 17.3.1 Motivations for test statistic approaches 551 17.4 Test statistics for fiat-fading channels 552 17.4.1 Correlation 552 17.4.2 MMSE beamformer 553 17.4.3 Generalized-likelihood ratio test 554 17.4.4 Spatial invariance 556 17.4.5 Comparison of performance 557 Problems 557 18 Practical issues 559 18.1 Antennas 559 18.1.1 Electrically small antennas 560 18.1.2 Crossed polarimetric array 560 18.2 Signal and noise model errors 560 18.3 Noise figure 561 18.4 Local oscillators 561 18.4.1 Accuracy 562 18.4.2 Phase noise 562 18.5 Dynamic range 563 18.5.1 Quantization 564 18.5.2 Finite precision 565 18.5.3 Analog nonlinearities 567 18.5.4 Adaptive gain control 568 18.5.5 Spurs 568 18.6 Power consumption 568 References 569 Index 589