Cognitive Radio Communication and Networking

Michael C. Wicks, PhD, received undergraduate degrees from Mohawk Valley Community College and Rensselaer Polytechnic Institute, and graduate degrees from Syracuse University, all in electrical engineering. He is a Fellow of the IEEE and a member of the Association of Old Crows. Dr. Wicks is a Principal Research Engineer in the U.S. Air Force Research Laboratory in the Sensor Directorate, Radar Signal Processing Branch. He has authored over 125 papers, reports, and patents.

The author presents a unified treatment of this highly interdisciplinary topic to help define the notion of cognitive radio. The book begins with addressing issues such as the fundamental system concept and basic mathematical tools such as spectrum sensing and machine learning, before moving on to more advanced concepts and discussions about the future of cognitive radio. From the fundamentals in spectrum sensing to the applications of cognitive algorithms to radio communications, and discussion of radio platforms and testbeds to show the applicability of the theory to practice, the author aims to provide an introduction to a fast moving topic for students and researchers seeking to develop a thorough understanding of cognitive radio networks.
* Examines basic mathematical tools before moving on to more advanced concepts and discussions about the future of cognitive radio
* Describe the fundamentals of cognitive radio, providing a step by step treatment of the topics to enable progressive learning
* Includes questions, exercises and suggestions for extra reading at the end of each chapter
* Companion website hosting MATLAB codes, and supplementary material including exercises
 
Topics covered in the book include: Spectrum Sensing: Basic Techniques; Cooperative Spectrum Sensing Wideband Spectrum Sensing; Agile Transmission Techniques: Orthogonal Frequency Division Multiplexing Multiple Input Multiple Output for Cognitive Radio; Convex Optimization for Cognitive Radio; Cognitive Core (I): Algorithms for Reasoning and Learning; Cognitive Core (II): Game Theory; Cognitive Radio Network IEEE 802.22: The First Cognitive Radio Wireless Regional Area Network Standard, and Radio Platforms and Testbeds.

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

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