Cognitive Radio Communication and Networking
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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.
Content
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 Generalized Densities 138
5.4 Stieltjes Transform 139
5.4.1 Basic Theorems 143
5.4.2 Large Random Hankel, Markov and Toepltiz Matrices 149
5.4.3 Information Plus Noise Model of Random Matrices 152
5.4.4 Generalized Likelihood Ratio Test Using Large Random Matrices 157
5.4.5 Detection of High-Dimensional Signals in White Noise 164
5.4.6 Eigenvalues of (A + B)-1B and Applications 169
5.4.7 Canonical Correlation Analysis 171
5.4.8 Angles and Distances between Subspaces 173
5.4.9 Multivariate Linear Model 173
5.4.10 Equality of Covariance Matrices 174
5.4.11 Multiple Discriminant Analysis 174
5.5 Case Studies and Applications 175
5.5.1 Fundamental Example of Using Large Random Matrix 175
5.5.2 Stieltjes Transform 177
5.5.3 Free Deconvolution 178
5.5.4 Optimal Precoding of MIMO Systems 178
5.5.5 Marchenko and Pastur's Probability Distribution 179
5.5.6 Convergence and Fluctuations Extreme Eigenvalues 180
5.5.7 Information plus Noise Model and Spiked Models 180
5.5.8 Hypothesis Testing and Spectrum Sensing 183
5.5.9 Energy Estimation in a Wireless Network 185
5.5.10 Multisource Power Inference 187
5.5.11 Target Detection, Localization, and Reconstruction 187
5.5.12 State Estimation and Malignant Attacker in the Smart Grid 191
5.5.13 Covariance Matrix Estimation 193
5.5.14 Deterministic Equivalents 197
5.5.15 Local Failure Detection and Diagnosis 200
5.6 Regularized Estimation of Large Covariance Matrices 200
5.6.1 Regularized Covariance Estimates 201
5.6.2 Banding the Inverse 203
5.6.3 Covariance Regularization by Thresholding 204
5.6.4 Regularized Sample Covariance Matrices 206
5.6.5 Optimal Rates of Convergence for Covariance Matrix Estimation 208
5.6.6 Banding Sample Autocovariance Matrices of Stationary Processes 211
5.7 Free Probability 213
5.7.1 Large Random Matrices and Free Convolution 218
5.7.2 Vandermonde Matrices 221
5.7.3 Convolution and Deconvolution with Vandermonde Matrices 229
5.7.4 Finite Dimensional Statistical Inference 232
6 Convex Optimization 235
6.1 Linear Programming 237
6.2 Quadratic Programming 238
6.3 Semidefinite Programming 239
6.4 Geometric Programming 239
6.5 Lagrange Duality 241
6.6 Optimization Algorithm 242
6.6.1 Interior Point Methods 242
6.6.2 Stochastic Methods 243
6.7 Robust Optimization 244
6.8 Multiobjective Optimization 248
6.9 Optimization for Radio Resource Management 249
6.10 Examples and Applications 250
6.10.1 Spectral Efficiency for Multiple Input Multiple Output Ultra-Wideband Communication System 250
6.10.2 Wideband Waveform Design for Single Input Single Output Communication System with Noncoherent Receiver 256
6.10.3 Wideband Waveform Design for Multiple Input Single Output Cognitive Radio 262
6.10.4 Wideband Beamforming Design 268
6.10.5 Layering as Optimization Decomposition for Cognitive Radio Network 272
6.11 Summary 282
7 Machine Learning 283
7.1 Unsupervised Learning 288
7.1.1 Centroid-Based Clustering 288
7.1.2 k-Nearest Neighbors 289
7.1.3 Principal Component Analysis 289
7.1.4 Independent Component Analysis 290
7.1.5 Nonnegative Matrix Factorization 291
7.1.6 Self-Organizing Map 292
7.2 Supervised Learning 293
7.2.1 Linear Regression 293
7.2.2 Logistic Regression 294
7.2.3 Artificial Neural Network 294
7.2.4 Decision Tree Learning 294
7.2.5 Naive Bayes Classifier 295
7.2.6 Support Vector Machines 295
7.3 Semisupervised Learning 298
7.3.1 Constrained Clustering 298
7.3.2 Co-Training 298
7.3.3 Graph-Based Methods 299
7.4 Transductive Inference 299
7.5 Transfer Learning 299
7.6 Active Learning 299
7.7 Reinforcement Learning 300
7.7.1 Q-Learning 300
7.7.2 Markov Decision Process 301
7.7.3 Partially Observable MDPs 302
7.8 Kernel-Based Learning 303
7.9 Dimensionality Reduction 304
7.9.1 Kernel Principal Component Analysis 305
7.9.2 Multidimensional Scaling 307
7.9.3 Isomap 308
7.9.4 Locally-Linear Embedding 308
7.9.5 Laplacian Eigenmaps 309
7.9.6 Semidefinite Embedding 309
7.10 Ensemble Learning 311
7.11 Markov Chain Monte Carlo 312
7.12 Filtering Technique 313
7.12.1 Kalman Filtering 314
7.12.2 Particle Filtering 318
7.12.3 Collaborative Filtering 319
7.13 Bayesian Network 320
7.14 Summary 321
8 Agile Transmission Techniques (I): Multiple Input Multiple Output 323
8.1 Benefits of MIMO 323
8.1.1 Array Gain 323
8.1.2 Diversity Gain 323
8.1.3 Multiplexing Gain 324
8.2 Space Time Coding 324
8.2.1 Space Time Block Coding 325
8.2.2 Space Time Trellis Coding 326
8.2.3 Layered Space Time Coding 326
8.3 Multi-User MIMO 327
8.3.1 Space-Division Multiple Access 327
8.3.2 MIMO Broadcast Channel 328
8.3.3 MIMO Multiple Access Channel 330
8.3.4 MIMO Interference Channel 331
8.4 MIMO Network 334
8.5 MIMO Cognitive Radio Network 336
8.6 Summary 337
9 Agile Transmission Techniques (II): Orthogonal Frequency Division Multiplexing 339
9.1 OFDM Implementation 339
9.2 Synchronization 341
9.3 Channel Estimation 343
9.4 Peak Power Problem 345
9.5 Adaptive Transmission 345
9.6 Spectrum Shaping 347
9.7 Orthogonal Frequency Division Multiple Access 347
9.8 MIMO OFDM 349
9.9 OFDM Cognitive Radio Network 349
9.10 Summary 350
10 Game Theory 351
10.1 Basic Concepts of Games 351
10.1.1 Elements of Games 351
10.1.2 Nash Equilibrium: Definition and Existence 352
10.1.3 Nash Equilibrium: Computation 354
10.1.4 Nash Equilibrium: Zero-Sum Games 355
10.1.5 Nash Equilibrium: Bayesian Case 355
10.1.6 Nash Equilibrium: Stochastic Games 356
10.2 Primary User Emulation Attack Games 360
10.2.1 PUE Attack 360
10.2.2 Two-Player Case: A Strategic-Form Game 361
10.2.3 Game in Queuing Dynamics: A Stochastic Game 362
10.3 Games in Channel Synchronization 368
10.3.1 Background of the Game 368
10.3.2 System Model 368
10.3.3 Game Formulation 369
10.3.4 Bayesian Equilibrium 370
10.3.5 Numerical Results 371
10.4 Games in Collaborative Spectrum Sensing 372
10.4.1 False Report Attack 373
10.4.2 Game Formulation 373
10.4.3 Elements of Game 374
10.4.4 Bayesian Equilibrium 376
10.4.5 Numerical Results 379
11 Cognitive Radio Network 381
11.1 Basic Concepts of Networks 381
11.1.1 Network Architecture 381
11.1.2 Network Layers 382
11.1.3 Cross-Layer Design 384
11.1.4 Main Challenges in Cognitive Radio Networks 384
11.1.5 Complex Networks 385
11.2 Channel Allocation in MAC Layer 386
11.2.1 Problem Formulation 386
11.2.2 Scheduling Algorithm 387
11.2.3 Solution 389
11.2.4 Discussion 390
11.3 Scheduling in MAC Layer 391
11.3.1 Network Model 391
11.3.2 Goal of Scheduling 393
11.3.3 Scheduling Algorithm 393
11.3.4 Performance of the CNC Algorithm 395
11.3.5 Distributed Scheduling Algorithm 396
11.4 Routing in Network Layer 396
11.4.1 Challenges of Routing in Cognitive Radio 397
11.4.2 Stationary Routing 398
11.4.3 Dynamic Routing 402
11.5 Congestion Control in Transport Layer 404
11.5.1 Congestion Control in Internet 404
11.5.2 Challenges in Cognitive Radio 405
11.5.3 TP-CRAHN 406
11.5.4 Early Start Scheme 408
11.6 Complex Networks in Cognitive Radio 417
11.6.1 Brief Introduction to Complex Networks 418
11.6.2 Connectivity of Cognitive Radio Networks 421
11.6.3 Behavior Propagation in Cognitive Radio Networks 423
12 Cognitive Radio Network as Sensors 427
12.1 Intrusion Detection by Machine Learning 429
12.2 Joint Spectrum Sensing and Localization 429
12.3 Distributed Aspect Synthetic Aperture Radar 429
12.4 Wireless Tomography 433
12.5 Mobile Crowdsensing 434
12.6 Integration of 3S 435
12.7 The Cyber-Physical System 435
12.8 Computing 436
12.8.1 Graphics Processor Unit 437
12.8.2 Task Distribution and Load Balancing 437
12.9 Security and Privacy 438
12.10 Summary 438
Appendix A Matrix Analysis 441
A.1 Vector Spaces and Hilbert Space 441
A.2 Transformations 443
A.3 Trace 444
A.4 Basics of C *-Algebra 444
A.5 Noncommunicative Matrix-Valued Random Variables 445
A.6 Distances and Projections 447
A.6.1 Matrix Inequalities 450
A.6.2 Partial Ordering of Positive Semidefinite Matrices 451
A.6.3 Partial Ordering of Hermitian Matrices 451
References 453
Index 511
Preface
The idea of writing this book began at least five years ago when the first author taught a one first-year graduate course, on communications/wireless communications. After this course, some students pursued advanced topics such as convex optimization prior to their PhD research. MS students wanted to know more about the field before they began to design wireless systems. The first author taught such advanced courses regularly, and part of these materials provided the starting point for this book. After this book project began, additional authors were added so that we could meet with our deadlines and before the topics become outdated. Another title of this book could be Advanced Wireless Communications.
The most difficult part was to decide what to exclude. The wireless industry is still expanding rapidly after two decades of growth. The first author studied the second generation (2G) system—CDMA and GSM—during his university days. Now, 3G (WCDMA) and 4G (LTE) systems are available. Each system has its central concept and demands unique analytical skills. Generally professors find that their most significant responsibilities are to teach students the most difficult mathematical tools required to analyze and design fundamental system concepts. For example, in a GSM (TDMA) system, the equalizers are central to the system. For a CDMA system, a RAKE receiver is central (as is power control). For an LTE system, a multiple-input, multiple-output (MIMO) system combined with an orthogonal frequency division multiplexing (OFDM) is central.
This approach is adopted in our book. We cover the system concepts that are central to the next generation cognitive radio network (CRN). We claim that the following three analytical tools are central to the CRN: (1) large random matrices; (2) convex optimization; (3) game theory. The unified view is the so-called “Big Data”—high-dimensional data processing. Due to the unique nature of cognitive radio, we have an unparalleled challenge—having too much data at our disposal. In today's digital age, making sense of the data in real-time is central not only to major players like Facebook, Google and Amazon, but also to our telecommunication vendors. To successfully solve the Big Data problem however, there are still many hurdles. For one thing, the current tools are inadequate. Scientist and engineers with the skills to analyze the data are scarce. Future ECE students must learn the analytical skills obtained from studying Big Data. In addition to traditional fields, this book contains results from multi disciplinary fields: machine learning, financial engineering, statistics, quantum computing, etc. Social networking and the Smart Grid command more resources. Researchers must become more cost-conscious. Investments in other fields mentioned above can reduce the costs of solving these problems. Abstract mathematical connections are the best starting point toward this goal. This justifies our belief in teaching students the most difficult analytical skills that are not readily obtained after leaving schools. By studying this book, practical engineers will understand system concepts, and may make connections with other fields. Peer researchers can use this book as a reference.
Compared with previous systems, the CRN contains radios that are highly programmable; their modulation waveforms are changing rapidly and their frequencies are agile; their radio frequency (RF) front-ends are wideband (up to several GHz). In addition to the highly programmable nature of their physical layer functions, a CRN radio senses the spectrum at an unprecedentedly low signal-to-noise-ratio (SNR) (e.g., −21 dB required by the FCC). To support this fundamental spectrum sensing function, the system allocates computing resources with the ultimate goal of real-time operations. From another viewpoint, this radio is a powerful sensor with almost unlimited computing and networking capabilities. Through the combination of these two views, communications and sensing are merged into one function that transmits, receives, and processes programmable modulated waveforms. Real-time distributed computing is embedded in these two functions.
It is believed that we lack a coherent network theory that is valid for numerous applications. Rather, the state-of-the-art network is designed for special needs; when a new need arises, the network must be redesigned. Costs are wasteful due to the lack of a network theory. The cognitive radio poses unique challenges in networking.
Wireless technology is proliferating rapidly; the vision of pervasive wireless computing, communication, sensing and control offers the promise of many societal and individual benefits. Cognitive radios, through dynamic spectrum access, offer the promise of being a disruptive technology. Cognitive radios are fully programmable wireless devices that can (1) sense their environment and (2) dynamically adapt their transmission waveform, channel access method, spectrum use and networking protocols. It is anticipated that cognitive radio technology will become a general-purpose programmable radio that will serve as a universal platform for wireless system development, as microprocessors have served a similar role for computation. There is, however, a big gap between having a flexible cognitive radio, effectively a building block, and the large-scale deployment of cognitive radio networks that dynamically optimize spectrum use. Testbeds are critical but totally ignored since the materials become outdated when the book is published. We want to focus on the materials that can last.
One goal is aimed toward a large-scale cognitive radio network; in particular, we need to study novel cognitive algorithms using quantum information and machine learning techniques, to integrate FPGA, CPU and graphics processing unit (GPU) technology into state-of-the-art radio platforms, and to deploy these networks as testbeds in the real-world university environment. Our applications range from communications to radar/sensing and Smart Grid technologies. Cognitive radio networking/sensing for unmanned aerial vehicles (UAVs) is also very interesting and challenging due to its high mobility. Synchronization is critical. UAVs can be replaced with robots.
One task will pursue a new initiative of CRN as sensors and explore the vision of a dual-use sensing/communication system based on CRN. The motivation is to push the convergence of sensing and communication systems into a unified cognitive networking system. CRN is a cyber-physical system with the integrated capabilities of control, communications, and computing.
Due to the embedded function of cooperative spectrum sensing in CRN, rich information about the radio environment may be obtained. This information unique to CRN can be exploited to detect, indicate, recognize, or track the target or intruder in the covered area of a CRN. The data for this kind of information system are intrinsically high-dimensional and random. Hence, we can employ quantum detection, quantum state estimation, and quantum information theory in our new initiative using CRN as sensors. In this way, the sensing capability of CRN can be explored together with great improvement in performance.
Very often one views a cognitive radio as two fundamental functions: (1) spectrum sensing; (2) spectrum-aware resources allocation. In this second function, convex optimization plays a central role. Optimization stems from human instinct. We always like to do something in the best way. Optimization theory gives us a way to realize this kind of human instinct. With the enhancement of computing capability, optimization theory, especially convex optimization, is a powerful signal processing tool to handle Big Data. If the data mining problem can be formulated as a convex optimization problem, the global optimum can be achieved. There is no doubt about the results or performances. However, there is still a challenge to make optimization algorithms scalable on the data sets of millions or trillions of elements. Thus, more effort is needed to explore optimization theory before we gain the benefit of it.
A collection of nodes are studied. These nodes, in analogy with human beings, can both collaborate and compete. Game theory captures the fundamental role of competition for resources. Of course, many algorithms in game theory can be formulated as convex optimization problems. For the games in CRN, we have provided plenty of working knowledge of generic games such that the readers can begin the research without reading specific books on game theory. Several typical examples in CRN are given to illustrate how to use game theory to analyze cognitive radio. Moreover, many unique concerns of games in cognitive radio are explained in order to motivate new research directions.
We will explain the networking issues in CRN in a layer by layer manner. Only challenges specific to CRN are explained in order to distinguish from traditional communication networks. We hope that the corresponding chapter not only explains the state-of-the-art of CRN, but also motivates new ideas in the design of CRN.
The overall picture of this book is presented in Figure P.1. Novel applications of the CRN include:
1. The Smart Grid; Security is a challenge. 2. Wireless networking for for unmanned aerial vehicles. Synchronization is a challenge. 3. Cloud computing is integrated with the CRN. 4. The CRN is used as distributed sensing.Figure P.1 Connections of different chapters in this book.
Chapter 1 overviews the book. Twelve chapters are...
