Cognitive Radio Communication and Networking

Robert C. Qiu, Department of Electrical and Computer Engineering, Tennessee Technological University, USA Professor Qiu is currently Director of the Wireless Networking System Laboratory at Tennessee Technological University, USA. He was Founder-CEO and President of Wiscom Technologies, Inc., manufacturing and marketing WCDMA chipsets. Wiscom was acquired by Intel in 2003. Prior to Wiscom, he worked for GTE Labs, Inc. (now Verizon), Waltham, MA, and Bell Labs, Lucent, Whippany, NJ. He holds 5 U.S. patents (another two pending) in WCDMA. He is co-editor of Ultra-Wideband Wireless Communications and Networks (Wiley), and? has authored over 80 technical (journal/conference) papers and contributed 6 book chapters. Professor Qiu has contributed to 3GPP and IEEE standards bodies, and delivered invited seminars to institutions including Princeton University and the U.S. Army Research Lab. Dr. Qiu serves as Associate Editor, IEEE Transaction on Vehicular Technology, International Journal of Sensor Networks and Wireless Communication and Mobile Computing.

Preface xv 1 Introduction 1 1.1 Vision: "Big Data" 1 1.2 Cognitive Radio: System Concepts 2 1.3 Spectrum Sensing Interface and Data Structures 2 1.4 Mathematical Machinery 4 1.4.1 Convex Optimization 4 1.4.2 Game Theory 6 1.4.3 "Big Data" Modeled as Large Random Matrices 6 1.5 Sample Covariance Matrix 10 1.6 Large Sample Covariance Matrices of Spiked Population Models 11 1.7 Random Matrices and Noncommutative Random Variables 12 1.8 Principal Component Analysis 13 1.9 Generalized Likelihood Ratio Test (GLRT) 13 1.10 Bregman Divergence for Matrix Nearness 13 2 Spectrum Sensing: Basic Techniques 15 2.1 Challenges 15 2.2 Energy Detection: No Prior Information about Deterministic or Stochastic Signal 15 2.2.1 Detection in White Noise: Lowpass Case 16 2.2.2 Time-Domain Representation of the Decision Statistic 19 2.2.3 Spectral Representation of the Decision Statistic 19 2.2.4 Detection and False Alarm Probabilities over AWGN Channels 20 2.2.5 Expansion of Random Process in Orthonormal Series with Uncorrelated Coefficients: The Karhunen-Loeve Expansion 21 2.3 Spectrum Sensing Exploiting Second-Order Statistics 23 2.3.1 Signal Detection Formulation 23 2.3.2 Wide-Sense Stationary Stochastic Process: Continuous-Time 24 2.3.3 Nonstationary Stochastic Process: Continuous-Time 25 2.3.4 Spectrum Correlation-Based Spectrum Sensing for WSS Stochastic Signal: Heuristic Approach 29 2.3.5 Likelihood Ratio Test of Discrete-Time WSS Stochastic Signal 32 2.3.6 Asymptotic Equivalence between Spectrum Correlation and Likelihood Ratio Test 35 2.3.7 Likelihood Ratio Test of Continuous-Time Stochastic Signals in Noise: Selin's Approach 36 2.4 Statistical Pattern Recognition: Exploiting Prior Information about Signal through Machine Learning 39 2.4.1 Karhunen-Loeve Decomposition for Continuous-Time Stochastic Signal 39 2.5 Feature Template Matching 42 2.6 Cyclostationary Detection 47 3 Classical Detection 51 3.1 Formalism of Quantum Information 51 3.2 Hypothesis Detection for Collaborative Sensing 51 3.3 Sample Covariance Matrix 55 3.3.1 The Data Matrix 56 3.4 Random Matrices with Independent Rows 63 3.5 The Multivariate Normal Distribution 67 3.6 Sample Covariance Matrix Estimation and Matrix Compressed Sensing 77 3.6.1 The Maximum Likelihood Estimation 81 3.6.2 Likelihood Ratio Test (Wilks Test) for Multisample Hypotheses 83 3.7 Likelihood Ratio Test 84 3.7.1 General Gaussian Detection and Estimator-Correlator Structure 84 3.7.2 Tests with Repeated Observations 90 3.7.3 Detection Using Sample Covariance Matrices 94 3.7.4 GLRT for Multiple Random Vectors 95 3.7.5 Linear Discrimination Functions 97 3.7.6 Detection of Correlated Structure for Complex Random Vectors 98 4 Hypothesis Detection of Noncommutative Random Matrices 101 4.1 Why Noncommutative Random Matrices? 101 4.2 Partial Orders of Covariance Matrices: A < B 102 4.3 Partial Ordering of Completely Positive Mappings: (A) < (B) 104 4.4 Partial Ordering of Matrices Using Majorization: A B 105 4.5 Partial Ordering of Unitarily Invariant Norms: |||A||| < |||B||| 109 4.6 Partial Ordering of Positive Definite Matrices of Many Copies: K k=1 Ak K k=1 Bk 109 4.7 Partial Ordering of Positive Operator Valued Random Variables: Prob(A X B) 110 4.8 Partial Ordering Using Stochastic Order: A st B 115 4.9 Quantum Hypothesis Detection 115 4.10 Quantum Hypothesis Testing for Many Copies 118 5 Large Random Matrices 119 5.1 Large Dimensional Random Matrices: Moment Approach, Stieltjes Transform and Free Probability 119 5.2 Spectrum Sensing Using Large Random Matrices 121 5.2.1 System Model 121 5.2.2 Marchenko-Pastur Law 124 5.3 Moment Approach 129 5.3.1 Limiting Spectral Distribution 130 5.3.2 Limits of Extreme Eigenvalues 133 5.3.3 Convergence Rates of Spectral Distributions 136 5.3.4 Standard Vector-In, Vector-Out Model 137 5.3.5 Ge