Signal Processing for Cognitive Radios

This book examines signal processing techniques for cognitive radios. The book is divided into three parts:

Part I, is an introduction to cognitive radios and presents a history of the cognitive radio (CR), and introduce their architecture, functionalities, ideal aspects, hardware platforms, and state-of-the-art developments. Dr. Jayaweera also introduces the specific type of CR that has gained the most research attention in recent years: the CR for Dynamic Spectrum Access (DSA).

Part II of the book, Theoretical Foundations, guides the reader from classical to modern theories on statistical signal processing and inference. The author addresses detection and estimation theory, power spectrum estimation, classification, adaptive algorithms (machine learning), and inference and decision processes. Applications to the signal processing, inference and learning problems encountered in cognitive radios are interspersed throughout with concrete and accessible examples.

Part III of the book, Signal Processing in Radios, identifies the key signal processing, inference, and learning tasks to be performed by wideband autonomous cognitive radios. The author provides signal processing solutions to each task by relating the tasks to materials covered in Part II. Specialized chapters then discuss specific signal processing algorithms required for DSA and DSS cognitive radios.

Preface xv

Part I Introduction to Cognitive Radios 1

1 Introduction 3

1.1 Introduction 3

1.2 Signal Processing and Cognitive Radios 4

1.3 Software-Defined Radios 6

1.3.1 Software-Defined Radio Platforms 14

1.3.2 Software-Defined Radio Systems 15

1.4 From Software-Defined Radios to Cognitive Radios 19

1.4.1 The Spectrum Scarcity Problem 19

1.4.2 Emergence of CRs 21

1.5 What this Book is About 22

1.6 Summary 26

2 The Cognitive Radio 27

2.1 Introduction 27

2.2 A Functional Model of a Cognitive Radio 30

2.2.1 Spectrum Knowledge Acquisition (Spectrum Awareness) 30

2.2.2 Communications Decision-Making 33

2.2.3 Learning in Cognitive Radios 33

2.3 The Cognitive Radio Architecture 35

2.3.1 Spectrum Sensing Region of a Cognitive Engine 36

2.3.2 Radio Reconfiguration Region of a Cognitive Engine 36

2.3.3 Learning Region of a Cognitive Engine 37

2.3.4 Memory Region of a Cognitive Engine 37

2.4 The Ideal Cognitive Radio 38

2.5 Signal Processing Challenges in Cognitive Radios 39

2.6 Summary 40

3 Cognitive Radios and Dynamic Spectrum Sharing 42

3.1 Introduction 42

3.2 Interference and Spectrum Opportunities 46

3.3 Dynamic Spectrum Access 50

3.4 Dynamic Spectrum Leasing 54

3.5 Challenges in DSS Cognitive Radios 55

3.6 Cognitive Radios and Future of Wireless Communications 60

3.7 Summary 61

Part II theoretical foundations 65

4 Introduction to Detection Theory 67

4.1 Introduction 67

4.2 Optimality Criteria: Bayesian versus Non-Bayesian 71

4.2.1 The Bayesian Approach 72

4.2.2 A Non-Bayesian Approach: Neyman–Pearson Optimality Criterion 73

4.3 Parametric Signal Detection Theory 75

4.3.1 Bayesian Optimal Detection 76

4.3.2 Neyman–Pearson Optimal Detection 82

4.3.3 Another Non-Bayesian Alternative: The Generalized Likelihood Ratio Test 99

4.3.4 Parametric Signal Detection in Additive Noise 103

4.4 Nonparametric Signal Detection Theory 122

4.4.1 Signal Detection in Additive Zero-Median Noise: The Sign Test 124

4.4.2 Signal Detection in Additive Symmetric Noise: The Rank Test 125

4.4.3 Signal Detection in Additive Zero Median, Zero Mean, Finite-Variance Noise: The t-Test 126

4.5 Summary 127

5 Introduction to Estimation Theory 132

5.1 Introduction 132

5.2 Random Parameter Estimation: Bayesian Estimation 134

5.2.1 Minimum Mean-Squared Error Estimation 134

5.2.2 MMSE Estimation of Vector Parameters 135

5.2.3 Linear Minimum Mean-Squared Error Estimation 138

5.2.4 Maximum A Posteriori Probability Estimation 139

5.3 Nonrandom Parameter Estimation 140

5.3.1 Theory of Minimum Variance Unbiased Estimation 142

5.3.2 Best Linear Unbiased Estimator 147

5.3.3 Maximum Likelihood Estimation 152

5.3.4 Performance Bounds: Cramer-Rao Lower Bound 154

5.4 Summary 158

6 Power Spectrum Estimation 164

6.1 Introduction 164

6.2 PSD Estimation of a Stationary Discrete-Time Signal 168

6.2.1 Correlogram Method 168

6.2.2 Periodogram Method 170

6.2.3 Performance of the Periodogram PSD Estimate 172

6.3 Blackman–Tukey Estimator of the Power Spectrum 177

6.4 Other PSD Estimators Based on Modified Periodograms 181

6.4.1 Bartlett PSD Estimator 181

6.4.2 Welch PSD Estimator 183

6.5 PSD Estimation of Nonstationary Discrete-Time Signals 186

6.5.1 Temporally Windowed Observations 188

6.5.2 Temporal and Spectral Smoothing of PSD Estimates of Nonstationary Discrete-Time Signals 189

6.5.3 DFT-Based PSD Computation 191

6.6 Spectral Correlation of Cyclostationary Signals 192

6.6.1 Spectral Correlation and Spectral Autocoherence 196

6.6.2 Time-Averaged Spectral Correlation 197

6.6.3 Estimation of Spectral Correlation 198

6.7 Summary 200

7 Markov Decision Processes 207

7.1 Introduction 207

7.2 Markov Decission Processes 209

7.3 Finite-Horizon MDPs 212

7.3.1 Definitions 212

7.3.2 Optimal Policies for MDPs 216

7.4 Infinite-Horizon MDPs 222

7.4.1 Stationary Optimal Policies for Infinite-Horizon MDPs 224

7.4.2 Bellman-Optimality Equations 227

7.5 Partially Observable Markov Decision Processes 232

7.5.1 Definitions 233

7.5.2 Policy Evaluation for a Finite-Horizon POMDP 238

7.5.3 Optimality Equations for a Finite-Horizon POMDP 241

7.5.4 Optimal Policy Computation for a Finite-Horizon POMDP 242

7.5.5 Infinite-Horizon POMDPs 257

7.6 Summary 259

8 Bayesian Nonparametric Classification 269

8.1 Introduction 269

8.2 K-Means Classification Algorithm 274

8.3 X-Means Classification Algorithm 276

8.4 Dirichlet Process Mixture Model 278

8.4.1 Dirichlet Process 278

8.4.2 Construction of the Dirichlet Process 279

8.4.3 DPMM 282

8.5 Bayesian Nonparametric Classification Based on the DPMM and the Gibbs Sampling 283

8.5.1 DPMM-Based Classification of Scalar Observations 287

8.5.2 DPMM-Based Classification of Multidimensional Gaussian Observations 298

8.5.3 DPMM-Based Classification of Possibly Non-Gaussian Multidimensional Observations 308

8.6 Summary 315

Part III signal processing in cognitive radios 321

9 Wideband Spectrum Sensing 323

9.1 Introduction 323

9.2 Wideband Spectrum Sensing Problem 325

9.3 Wideband Spectrum Scanning Problem 326

9.4 Spectrum Segmentation and Subbanding 328

9.5 Wideband Spectrum Sensing Receiver 330

9.5.1 Homodyne Receiver Configuration 332

9.5.2 Super Heterodyne Digital Receiver Configuration 334

9.5.3 A/D Conversion and the Discrete-Time Received Signal Model 335

9.6 Subband Selection Problem in Wideband Spectrum Sensing 336

9.6.1 Subband Dynamics 338

9.6.2 A POMDP Model for Subband Selection 340

9.6.3 An Optimal Subband Selection Policy for Spectrum Sensing 347

9.6.4 A Reduced-Complexity Optimal Sensing Decision-Making Algorithm with Independent Channels 350

9.6.5 A Reduced Complexity Optimal Sensing Decision-Making Algorithm with Independent Subbands 354

9.6.6 Optimal Myopic Sensing Decision Policies 354

9.7 A Reduced Complexity Optimal Subband Selection Framework with an Alternative Reward Function 355

9.7.1 A New Model for Subband Dynamics 357

9.7.2 A Simplified Reward Function and a Reduced-Complexity Optimal Policy 359

9.7.3 A Reduced Complexity Optimal Policy for Independent Subbands 362

9.7.4 Optimal Myopic Policies with Reduced Dimensional Subband State Vectors 363

9.8 Machine-Learning Aided Subband Selection Policies 364

9.8.1 Q-Learning 365

9.8.2 Q-Learning in a POMDP: A Q-Learning Algorithm for Subband Selection 368

9.9 Summary 372

10 Spectral Activity Detection in Wideband Cognitive Radios 377

10.1 Introduction 377

10.2 Optimal Wideband Spectral Activity Detection 379

10.3 Wideband Spectral Activity Detection 386

10.4 Wavelet Transform-Based Wideband Spectral Activity Detection 392

10.4.1 Wavelet Transform 394

10.4.2 Edge Detection with Wavelet Transform 395

10.4.3 Spectral Activity Detection Based on Edge Detection 397

10.5 Wideband Spectral Activity Detection in Non-Gaussian Noise 398

10.5.1 Arbitrary but Known Noise Distribution 399

10.5.2 Robust Spectral Activity Detection 406

10.6 Wideband Spectral Activity Detection with Compressive Sampling 413

10.6.1 Compressive Sampling 415

10.6.2 Compressive Sensing of Wideband Spectrum 419

10.7 Summary 421

11 Signal Classification in Wideband Cognitive Radios 429

11.1 Introduction 429

11.2 Signal Classification Problem in a Wideband Cognitive Radio 431

11.3 Feature Extraction for Signal Classification 435

11.3.1 Carrier/Center Frequency 435

11.3.2 Cyclostationary Features 436

11.3.3 Modulation Type and Order Features 441

11.4 A Signal Classification Architecture for a Wideband Cognitive Radio 445

11.5 Bayesian Nonparametric Signal Classification 447

11.6 Sequential Bayesian Nonparametric Signal Classification 462

11.7 Summary 469

12 Primary Signal Detection in DSA Cognitive Networks 472

12.1 Introduction 472

12.2 Spectrum Sensing Problem in Dynamic Spectrum Sharing CR Networks 475

12.3 Autonomous Spectrum Sensing for Dynamic Spectrum Sharing 479

12.3.1 Secondary User Sensing Observations 480

12.3.2 Channel-State (Idle/Busy) Decisions 481

12.4 Limitations of Autonomous Spectrum Sensing 489

12.5 Cooperative Spectrum Sensing for Dynamic Spectrum Sharing 492

12.6 Cooperative Channel-State Detection 495

12.6.1 Local Processing and Sensing Reports from Secondary Users 498

12.6.2 Final Channel-State Decisions at the SSDC: Decision Fusion 502

12.7 Summary 516

13 Spectrum Decision-Making in DSA Cognitive Networks 519

13.1 Introduction 519

13.2 Primary Channel Dynamic Model 520

13.3 Sensing Decisions in DSS Networks with Autonomous Cognitive Radios 522

13.3.1 Optimal Sensing Policy Determination 525

13.3.2 Optimal Myopic Sensing Policy Determination 530

13.4 Sensing Decisions in Cooperative DSS Networks 533

13.4.1 Optimal SSDC Decisions for Independent Channel Dynamics 537

13.4.2 Optimal Myopic Sensing Decisions at the SSDC with Independent Channel Dynamics 541

13.5 Summary 550

14 Dynamic Spectrum Leasing in Cognitive Radio Networks 553

14.1 Introduction 553

14.2 DSL with Direct Rewards to Primary Users 555

14.2.1 Interference at the Primary Receiver 560

14.2.2 A Game Model for Dynamic Spectrum Leasing 565

14.2.3 Nash Equilibria in Noncooperative Games 570

14.2.4 Existence of a Nash Equilibrium in the DSL Game 573

14.3 DSL Based on Asymmetric Cooperation with Primary Users 587

14.3.1 A Primary–Secondary Coexistence Model 588

14.3.2 Asymmetric Cooperative Communications-Based DSL between Primary Users and a Centralized Secondary Network 591

14.3.3 Asymmetric Cooperative Communications-Based DSL between Primary Users and Autonomous Cognitive Secondary Users 604

14.4 Summary 609

15 Cooperative Cognitive Communications 613

15.1 Introduction 613

15.2 Cooperative Spectrum Sensing 619

15.3 Cooperative Spectrum Sensing and Channel-Access Decisions 621

15.4 Cooperative Communications Strategies in Cognitive Radio Networks 624

15.5 Asymmetric Cooperative Relaying in DSA Cognitive Radios 627

15.5.1 Secondary User Optimal Power Allocation for Asymmetric Cooperative Relaying 629

15.5.2 Centralized Assignment of Cognitive Radios for Cooperation with Primary Users: An Ideal Approach 635

15.5.3 Centralized Assignment of Cognitive Radios for Cooperation with Primary Users: A Realistic Approach 640

15.6 Summary 644

16 Machine Learning in Cognitive Radios 647

16.1 Introduction 647

16.2 Artificial Neural Networks 650

16.2.1 Learning Algorithms for LTUs 651

16.2.2 Layered Neural Networks 655

16.2.3 Learning in Layered Feed-Forward Networks: Back-Propagation Algorithm 656

16.2.4 Neural Networks in Cognitive Radios 662

16.3 Support Vector Machines 664

16.3.1 Statistical Learning Theory 665

16.3.2 Structural Risk Minimization with Support Vector Machines 669

16.3.3 Linear Support Vector Machines 670

16.3.4 Nonlinear Support Vector Machines 674

16.3.5 Kernel Function Implementation of Support Vector Machines 677

16.3.6 SVMs in Cognitive Radios 679

16.4 Reinforcement Learning 681

16.4.1 Temporal Difference Learning 683

16.4.2 Q-Learning in a POMDP: Replicated Q-Learning 684

16.4.3 Reinforcement Learning in Cognitive Radios 686

16.5 Multiagent Learning 688

16.5.1 Game-Theoretic Multiagent Learning 691

16.5.2 Cooperative Multiagent Learning 694

16.5.3 Multiagent Learning in Cognitive Radio Networks 696

16.6 Summary 698

Appendix A Nyquist Sampling Theorem 704

Appendix B A Collection of Useful Probability Distributions 711

B.1 Univariate Distributions 711

B.2 Multivariate Distributions 713

Appendix C Conjugate Priors 716

References 721

Index 740

SUDHARMAN K. JAYAWEERA earned his BE in Electrical Engineering from the University of Melbourne, Australia. He earned his MA and PhD degrees in Electrical Engineering from Princeton University, USA. He is currently an Associate Professor in Electrical Engineering at the University of New Mexico, Albuquerque, NM, USA. His research expertise is in signal processing and wireless communications.

DR. JAYAWEERA is a senior member of the IEEE. Currently he serves as the Associate Editor of IEEE Transactions on Vehicular Technology.