Cognitive Radio Techniques : Spectrum Sensing, Interference Mitigation, and Localization [1 ed.] 9781608072040, 9781608072033

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INTE G R A TE D M I C R O S Y S TE M S S E R IE S mobile communications series

Kandeepan Sithamparanathan is with the School of Electrical and Computer Engineering at RMIT University, Melbourne, Australia. He holds an M.Eng. in telecommunications and a Ph.D. in communications engineering, both from the University of Technology, Sydney, Australia. Andrea Giorgetti is with the Department of Electronics, Computer Sciences and Systems at the University of Bologna, Italy. He received a Laurea degree in electronic engineering and a Ph.D. in electronic engineering and computer science, both from the University of Bologna.

BOSTON

Cognitive R a d i o Techniques Spectrum Sensing, Interference Mitigation, and Localization

Sithamparanathan

ISBN 13: 978-1-60807-203-3 ISBN 10: 1-60807-203-7

Giorgetti

Include bar code

Cognitive RADIO Techniques

For the first time in any book, professionals find an adequately detailed treatment of spectrum sensing that covers nearly every aspect of the subject. Moreover, this valuable resource provides thorough working knowledge of localization and interference mitigation as enablers of cognitive radio technology. The book includes all the necessary mathematics, statistical and probabilistic treatments, and performance analysis to give readers a comprehensive understanding of the material.

Spectrum Sensing, Interference Mitigation, and Localization

Providing an in-depth treatment of the core enablers of cognitive radio technology, this unique book places emphasis on critical areas that have not been sufficiently covered in existing literature. Practitioners find expert guidance in the key enablers with respect to communications and signal processing. The book presents fundamentals, basic solutions, detailed discussions of important enabler issues, and advanced algorithms that save engineers time with their projects in the field.

mobile communications series

LONDON

www.artechhouse.com

Kandeepan Sithamparanathan • Andrea Giorgetti

Cognitive Radio Techniques Spectrum Sensing, Interference Mitigation, and Localization

For a listing of recent titles in the Artech House Mobile Communications Library, turn to the back of this book.

Cognitive Radio Techniques Spectrum Sensing, Interference Mitigation, and Localization Kandeepan Sithamparanathan Andrea Giorgetti

artechhouse.com

Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the U.S. Library of Congress.

British Library Cataloguing in Publication Data A catalog record for this book is available from the British Library.   ISBN 13: 978-1-60807-203-3 Cover design by Vicki Kane

© 2012 ARTECH HOUSE 685 Canton Street Norwood, MA 02062 All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, includ­ing photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this informa­tion. Use of a term in this book should not be regarded as affecting the validity of any trade­mark or service mark. 10 9 8 7 6 5 4 3 2 1

To my dear wife, Anjana Kandeepan, son, Arjunaa Kandeepan, parents, Mr. and Mrs. Sithamparanathan, and brother, Janarthana Sithamparanathan. – Kandeepan Sithamaparanathan To the memory of Ezio and Olga, to my wife, Alice, and dear daughter, Martina. – Andrea Giorgetti

Contents

Preface

xxi

1

Introduction to Cognitive Radios

1

1.1

Introduction

1

1.2

Definition of Cognitive Radios

3

1.3

Software-Defined Radios

4

1.4

The Cognitive Cycle

5

1.5 1.5.1 1.5.2 1.5.3

The Radio Scene Analysis Spectrum Occupancy Classification Hidden Terminals Locating Primary Users

7 9 9 10

1.6 1.6.1

Dynamic Spectrum Access and Management Spectrum Underlay and Overlay

10 11

1.7

Regulatory Aspects

13

vii

viii

Cognitive Radio Techniques

1.7.1 1.7.2 1.7.3

The IEEE DySPAN Standards Committee The IEEE 802.22 WRAN Standards The ETSI-RRS Technical Committee

14 15 16

1.8 1.8.1 1.8.2 1.8.3 1.8.4 1.8.5 1.8.6 1.8.7

Application Clusters Cellular Mobile Networks Energy Efficiency is Wireless Networks Public Safety Communications Coexistence of UWB Radio Technology Wireless Networks for Smart Grids Vehicular Networks Defense Application Systems

17 17 18 18 18 19 19 19

References

20

Part I

Spectrum Sensing in Cognitive Radios

23

2

Fundamentals of Spectrum Sensing and Detection

25

2.1

Introduction

25

2.2 2.2.1 2.2.2 2.2.3 2.2.4

Statistical Detection Techniques Maximum A Posteriori Detection Maximum Likelihood Detection The Neyman-Pearson Detector The Bayesian Risk-Based Detector

28 28 29 29 30

2.3

Continuous and Discrete Signal Detection

30

2.4 2.4.1 2.4.2 2.4.3 2.4.4

Detection Performance Detection Performance Versus the SNR Detection Performance Versus the Signal Observation Length The ROC Curves Area Under the ROC Curves

31 33 33 34 34



Contents

ix

2.5 2.5.1 2.5.2 2.5.3

Wireless Channel Models Mean Pathloss Shadowing Small Scale Fading

35 35 35 36

2.6 2.6.1 2.6.2 2.6.3

Basic Models for Spectrum Occupancy The Poisson-Exponential Model The Markov Modulated Poisson Process The Poisson-Pareto Burst Process

37 38 38 40

2.7

Stochastic Analysis of Radio Signals

40

2.8

Blind, Partial, and Complete Context Aware Signal Detection

42

2.8.1

Blind Signal Detection

42

2.8.2

Partial-Context Aware Signal Detection

42

2.8.3

Fully Context Aware Detection

42

2.9

Summary

43

References

43

3

Introduction to Spectrum Sensing Techniques

45

3.1

Introduction

45

3.2 3.2.1 3.2.2 3.2.3 3.2.4

Spectrum Sensing with Energy Detection Energy Detector Energy Detector in Gaussian Channel Energy Detector in Fading Channels Energy Detector in Fading Channels with Shadowing

46 46 47 49 51



Cognitive Radio Techniques

3.3 3.3.1 3.3.2 3.3.3

Energy detection and noise power uncertainty ED Threshold Mismatch SNR Wall Existence of the SNR Wall

52 53 53 55

3.4 3.4.1 3.4.2

Spectrum Sensing with Cyclostationary Feature Detection Cyclostationarity Analysis Cyclostationary Feature-Based Detector

56 57 59

3.5

Spectrum Sensing with Matched Filter Detection

60

3.6 3.6.1 3.6.2 3.6.3 3.6.4

Other Spectrum Sensing Techniques Covariance-Based Method Eigenvalue-Based Method Wavelet-Based Edge Detection Spectral Estimation Methods

61 62 63 63 64

3.7

Summary

65

References

65

4

Temporal Spectrum Sensing and Performance Analysis

69

4.1

Introduction

69

4.2

Temporal Periodic-Spectrum Sensing

71

4.3 4.3.1 4.3.2

Primary User Spectral Occupancy Model with Poisson Arrival Exponential Random Spectral Occupancy Time Pareto Random Spectral Occupancy Time

72 73 73



Contents

xi

4.3.3

Classifying Primary User Spectrum Occupancy Levels

74

4.4 4.4.1 4.4.2 4.4.3

Detection Performance of Periodic-Sensing with Poisson Arrival and Deterministic Occupancy Time Spectral Occupancy Probability Probability of Detection False Alarm Probability

75 75 76 78

4.5

Primary User Misdetection Risk Regions

80

4.6

Temporal Periodic-Sensing with Poisson-exponential Occupancy Model

82

4.7

Temporal Periodic-Sensing with Poisson-Pareto Occupancy Model

84

4.8

Temporal Periodic-Sensing Performance Comparison with Deterministic and Random Occupancies

85

4.9

Temporal Periodic-Sensing in Noise

86

4.10

Temporal Periodic-Sensing in Noise with Signal Fading/Shadowing 91

4.11

Optimum Sensing Period

92

4.12

Reality of Spectrum Occupancy Models

93

4.13

Summary

93

References

94

xii

Cognitive Radio Techniques

5

Cooperative Spectrum Sensing

97

5.1

Introduction

97

5.2 5.2.1 5.2.2

Spatio-Temporal Fusion Strategy Synchronized Reporting Nonsynchronized Reporting

99 100 100

5.3 5.3.1 5.3.2

Hard Decision Fusion Chair-Varshney Fusion Strategy The M-out-of-N Fusion Strategy

101 102 103

5.4 5.4.1 5.4.2 5.4.3

Soft Decision Fusion Optimal Soft Decision Fusion Equal Gain Soft Decision Fusion Maximal Ratio Soft Decision Fusion

106 107 108 109

5.5 5.5.1 5.5.2 5.5.3

Cluster-Based Cooperative Spectrum Sensing Space-Divisional Cluster Frequency-Divisional Cluster Time-Divisional Cluster

109 110 111 111

5.6

Noisy Reporting Channels

113

5.7 5.7.1 5.7.2 5.7.3 5.7.4 5.7.5

Other Issues in Cooperative Sensing Cooperation Overhead and the Reporting Channel Unreliable Reporter and Accreditation Security Issues Knowledge Distribution Spatial Limitation

115 116 116 116 117 117

5.8

Summary

117

References

118

Contents

xiii

6

Distributed Spectrum Sensing

121

6.1

Introduction

121

6.2

Parallel Topology-Based Distributed Sensing

123

6.3 6.3.1

Sequential Topology-Based Distributed Sensing Detection Performance

125 127

6.4

Tree Topology-Based Distributed Sensing

127

6.5 6.5.1 6.5.2 6.5.3

Ring-Around Distributed Sensing Message Passing in Ring-Around Sensing Hard Decision Fusion with the OR Rule Equal Ratio Combining Soft Decision-Based Fusion

128 130 130 131

6.6

Summary

132

References

132

7

Advanced Spectrum Sensing Topics

135

7.1

Introduction

135

7.2

Spectrum Sensing in UWB Radios with Frequency Sweeping

136

7.3 7.3.1 7.3.2

Spectrum Sensing in OFDM Systems The Likelihood Ratio Test Frequency Domain Detection

139 140 141

7.4 7.4.1

Combined Localization and Detection of Primary Users Detection Using the Likelihood Function fr|Hi(r|Hi)



142 143

xiv

Cognitive Radio Techniques

7.4.2

Detection Using the Output of 

144

7.5 7.5.1

Sequential Spectrum Sensing The Sequential Probability Ratio Test

145 145

7.6

Spectrum Sensing with Ordered Statistics

146

7.7 7.7.1 7.7.2

Spectrum Sensing with Reconfigurable Antennas Frequency Reconfigurability Radiation Pattern Reconfigurability

147 148 150

7.8

Spectrum Sensing in 3D-Space

150

7.9

Summary

153

References

154

Part II Coexistence and Interference Mitigation Techniques 8

Fundamentals of Coexistence and Interference Mitigation Techniques

8.1 8.1.1 8.1.2 8.1.3

Interference in Cognitive Radio and its Characterization Intentional Interference: From Jamming to Emulation Unintentional Interference Metrics to Quantify Interference and its Effects

8.2 8.2.1 8.2.2 8.2.3

Coexistence Scenarios Spatial Configuration of the Systems From Narrowband to Ultrawideband The Coexistence Region

157 159 160 160 163 163 167 169 170 172



Contents

xv

8.3 8.3.1 8.3.2 8.3.3 8.3.4 8.3.5

Interference Mitigation Techniques Interference Mitigation in Spread Spectrum CRs Power Control Band Relocation Spectrum Shaping Adaptive Antenna Techniques

173

8.4

Summary and Further Readings

176

References

176

9

Coexistence Analysis

181

9.1

Coexistence Between Heterogeneous Wireless Systems

182

9.2 9.2.1

Channel Model Block Fading Channel

183 185

9.3 9.3.1 9.3.2 9.3.3 9.3.4 9.3.5 9.3.6

Interference Modeling Gaussian Approximation Tone Approximation Multitone Approximation Band-Limited Gaussian Process Approximation Pulse Train Model Modeling the Interfering Power

185 186 186 187

9.4 9.4.1 9.4.2

The Effect of Narrowband Interference on a Wideband Communication Single-Carrier WB Communication in the Presence of NB Interference Multicarrier WB Communication in the Presence of NB Interference

174 175 175 175 176

188 188 188 189 190 203

xvi

Cognitive Radio Techniques

9.5 9.5.1 9.5.2

The Effect of Wideband Interference on a Narrowband Communication Single-Carrier NB Communication in the Presence of WB Interference Multicarrier NB Communication in the Presence of WB Interference

9.6

Summary and Further Readings

217

References

218

Coexistence in Network Scenarios

223

10

10.1 Coexistence Between Heterogeneous Networks 10.1.1 Network Scenario Definition

208 209 217

223 224

10.2 10.2.1 10.2.2

Statistical Characterization of Network Interference Interference Generated Outside the Guard Zone Interference From the Whole Plane

10.3 10.3.1 10.3.2 10.3.3

The Effect of Interference on Performance of Coexisting Networks Transmission Characteristics of the Nodes Narrowband Communication in the Presence of Wideband Network Interference Wideband Communication in the Presence of Narrowband Network Interference

10.4

Performance Examples of Heterogeneous Coexisting Networks

243

10.5

Summary and Further Readings

245

References

246

226 229 231

236 236 237 240



Contents

xvii

11

Interference Mitigation Techniques Enabling Coexistence

11.1 11.1.1 11.1.2 11.1.3

Cognitive Radio Transmission Techniques Enabling Coexistence Spectrum Interweave: Interference Avoiding Behavior Spectrum Underlay: Interference Controlling Behavior Spectrum Overlay: Interference Mitigating Behavior

11.2 11.2.1 11.2.2

The Secondary User Perspective: Performance of CR Transmission Strategies System Model Comparison of the SU Achievable Rates

11.3 11.3.1 11.3.2 11.3.3 11.3.4 11.3.5

The Primary User Perspective: Impact of CR Transmission Strategies The Scenario Cognitive Network Interference as a Misdetection Problem PU Outage due to Misdetection by a Single SU PU Outage due to Misdetections in a Cognitive Network A Case Study

261 262

11.4

Summary and Further Readings

265

References

266

12

Advanced Interference Mitigation Techniques

269

12.1

Interference Mitigation Techniques in UWB Radios

270

249 250 250 251 252

253 254 255

256 257 259 260

xviii

Cognitive Radio Techniques

12.1.1 12.1.2

Interference Mitigation in UWB Impulse Radio Interference Mitigation in MB-OFDM UWB Radio

271 279

12.2 Interference Mitigation in Spatial Domain 12.2.1 Example: MIMO Beamforming

283 284

12.3

Summary and Further Readings

287

References

287

Part III Localization and Radio Environment Mapping

291

13

Fundamentals of Ranging and Localization for Cognitive Radio

293

13.1 13.1.1 13.1.2 13.1.3 13.1.4

Ranging Techniques and Enabling Technologies Time-Based Ranging RSS-Based Ranging Other Ranging Techniques Error Sources in Time-Based Ranging

294 294 296 297 298

13.2 13.2.1 13.2.2

Performance Limits of Time-based Ranging: From Theory to Practice Theoretical Performance Limits Practical Schemes

302 303 304

13.3

Cognitive Ranging

306

13.4 Localization Techniques 13.4.1 Single-Hop Localization 13.4.2 Multihop Localization

308 309 311



Contents

xix

13.4.3 Anchor-Free Localization 13.4.4 Location Tracking 13.4.5 Case Study

312 313 314

13.5

Summary and Further Readings

316

References

316

14

Localization of Primary Users

321

14.1 14.1.1 14.1.2 14.1.3 14.1.4 14.1.5 14.1.6

Localization of Noncollaborative Emitters Range-Free Localization of PUs Semirange-Based Localization of PUs RSSI-Based Localization of PUs Other Range-Based Algorithms Tracking of PUs Case Study

322 323 324 325 329 330 331

14.2 Radio Environment Mapping 14.2.1 Radio Cartography 14.2.2 Database for SU Access Control

334 336 338

14.3

Summary and Further Readings

339

References

339

Conclusions and Future Work

343

Glossary

349

About the Authors

355

Index

357

15

Preface The topic on cognitive radios has stormed the communications engineering field over the past decade. At this stage, a good understanding of the cognitive radio technology exists in terms of the advantages, challenges, and critical problems associated with it. The key application related to cognitive radios is dynamic spectrum access, a field that is sufficiently investigated and closer to a half a dozen of books exist currently treating this topic extensively. Moreover, the concept, underlying principles, systems theory, and requirements of cognitive radios are also well-treated in different perspectives in many books. The main objective of this book is to treat some of the core functionalities related cognitive radios and provide an in-depth and a wide range of knowledge for enabling the technology. This book mainly focusses on radio scene analysis and interference mitigation topics, which are not treated well enough in any of the currently existing books on cognitive radios. This book provides an extensive treatment on cognitive radio techniques for radio scene analysis with spectrum sensing techniques, localization techniques, and interference mitigation techniques. This book is considered to be a good reference for engineers (that are practicing cognitive radio related developments), researchers, and higher degree students that are working on radio scene analysis and interference mitigation for cognitive radios and networks. The corresponding performance analysis provided in the book further enables one to understand the capabilities of the various techniques presented and provides sufficient knowledge to perform additional research work. xxi

xxii

Cognitive Radio Techniques

The authors believe that this is a much-needed book in the field of cognitive radios, addressing some of the core enabling functionalities of cognitive radio technology in great depth. In this regard, the entire book is grouped into three major parts covering: Part I – Spectrum Sensing in Cognitive Radios Part II – Coexistence and Interference Mitigation Techniques Part III – Localization and Radio Environment Mapping In addition, an introductory chapter (Chapter 1) is devoted to kick-start with the topic cognitive radio by explaining the cognitive cycle, cognitive engine, and the latest advancements around the world in terms of standardizations and applications. Moreover, we also emphasize on the fact that different interpretations exist for the term, cognitive radio, which was originally coined by Professor Joseph Mitola, and therefore we present various definitions for the same. In Part I of the book, six chapters are devoted to the topic on spectrum sensing, as briefly summarized subsequently. In Chapter 2, we provide the preliminaries for understanding the rest of the chapters in Part II on spectrum sensing; in Chapter 3, some of the basic spectrum sensing techniques are presented together with their statistical performance evaluations. Chapter 4 presents a good insight to how spectrum sensing techniques perform considering the temporal variations in radio environment, whereas Chapter 5 and Chapter 6 present collaborative spectrum sensing to enhance the performance in a cognitive radio network. Chapter 7 presents some advanced spectrum sensing topics that may be considered by researchers and students to pursue further research. In Part II of the book, the coexistence of the radios and interference mitigation are covered over five chapters. In Chapter 8, we provide the fundamentals of coexistence and interference mitigation, followed by coexistence analysis in Chapter 9 presenting various interference models. The coexistence in network scenarios is covered in Chapter 10, followed by interference mitigation techniques and advanced interference mitigation techniques in Chapter 11 and Chapter 12, respectively. In Part III of the book, localization and radio environment mapping are covered in two chapters. Chapter 13 presents some fundamentals of localization and tracking for cognitive radios considering various approaches, and Chapter 14 covers localization of primary users and the generation of radio environmental maps. It is rather important to note here that the cognitive radio-related issues covered in Part III have a lot of prospect for further research.



Preface

xxiii

Finally, we provide some concluding remarks and future research directions in Chapter 15. This book would have never been written without some wise people that encouraged the authors to pursue such a difficult task. Dr. Sithamparanathan would like to initially thank his wife, parents, brother, uncles, aunts, and cousins for the great support throughout his education and professional carrier. A great deal of appreciation goes towards his Ph.D. mentor Professor Sam Reisenfeld (Macquarie University, Sydney) for turning on the switch in his carrier to become a researcher and an academic subsequently. Professor Reisenfeld’s support, encouragement, assistance, supervision, and guidance were all well-received and perceived, and had made a great impact without doubt. Finally, Dr. Sithamparanathan would like to thank the School of Electrical and Computer Engineering at the RMIT University (Melbourne, Australia), the National ICT Australia, and the CREATE-NET Research Center (Trento, Italy) for their support in completing this project. Dr. Giorgetti would like to express his deepest gratitude to colleagues at the University of Bologna: Professor Marco Chiani, who has been, and maybe still is, a mentor for him; Professor Davide Dardari, who taught him all secrets about localization; Professor Oreste Andrisano, who supported him for many years starting from his Ph.D.; and Andrea Mariani, Ph.D. student at the University of Bologna, for many discussions about cognitive radio. Dr. Giorgetti would also like to thank Professor Moe Z. Win of the Massachusetts Institute of Technology (MIT) for sharing the authentic passion for research. Furthermore, this book was inspired by the research activities carried out by the authors within the European FP7 ICT integrated project, Co­Existing Short Range Radio by Advanced UltraWideBand Radio Technology, EUWB (FP7-ICT-215669). The authors would like to thank the European Commission for having supported their research activity where collaborations such as this can thrive. The authors would like to thank the anonymous reviewer for his useful comments. The authors would also like to thank their families for their endless patience and support.

. NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program.

1 Introduction to Cognitive Radios The electronic radio chips used in traditional communication devices are quite dumb in the sense that they only perform things according to what the hardware circuitries of the chip are designed for. The new paradigm shift in wireless communications, especially in the radio technology with the use of ­softwaredefined radios, enables intelligence to be embedded such that the radios can think and act accordingly. This gives rise to the new paradigm of radios known as cognitive radios. The cognitive radios are defined by specific functionalities in order to think and act, learning the radio environment and gathering intelligence with the corresponding decision-making processes are some of the main functionalities of a cognitive radio. The embedded intelligence in the radios is then used to perform efficient communications by optimizing the usage of the scarce radio resources, such as the radio spectrum. In this chapter, we provide a detailed introduction to the topic of cognitive radios.

1.1  Introduction Over the past several decades—ever since radio technology was born–the radio spectrum has become more and more crowded, especially as new wireless technologies and applications are continuously being born. As a result, the incumbent users, or the licensed users, of the spectrum (also known as the primary users of the spectrum) have continued to grow gradually. A need therefore to 



Cognitive Radio Techniques

address the efficiency of utilizing the scarce radio spectrum ­became eminent and was intensely discussed by the radio regulatory bodies around the world. Studies have shown that the radio spectrum bands that are already in use for communications are underutilized at different geographic locations at certain times. This then gives the space to utilize such unused spectrum by secondary users in the spatio-temporal domain whenever the primary users of the spectrum are not utilizing it. Correspondingly, the concept of dynamic spectrum access (DSA) was discussed; the radio spectrum can be accessed opportunistically on a need basis by a given radio whenever a particular portion of the radio spectrum becomes free, thus increasing the utilization of the spectrum. In order to dynamically and intelligently utilize such unused spectrum by the secondary users without interfering with the licensed users of the spectrum, the secondary radios need to be able to learn the occupancy of the spectrum in real-time. By learning the radio environment, the radios need to then make appropriate decisions to perform certain actions, such as whether to access the spectrum or not, and if accessed, what would be the corresponding transmission parameters (i.e., the transmit power). In order to execute all these functionalities at the radio level, the corresponding radio devices need to be able to think and adapt intelligently. Thus, we introduce the concept of cognitive radios. The term cognitive radio was originally coined by Mitola [1, 2] in his conceptual proposal of the ideal cognitive radios. In his proposal, Mitola identified the requirement to have a cognitive cycle implemented in the form of a cognitive engine into radios enabled by software-defined radio technology. The cognitive cycle is presented in detail later in this chapter. With the help of the cognitive engine, the cognitive radio terminal will then learn the radio environment in-real time and act correspondingly. Mitola’s proposal for ideal cognitive radios spans across all the layers of the communication protocol stack for optimizing the utilization of radio resources. This concept was then adopted by Haykin [3] by defining the respective physical layer communications and signal processing aspects associated with it. This then lead to an in-depth treatment of cognitive radio research around the world, giving an exploded number of research papers and articles produced on the very same topic within the past decade. This entire book is devoted to addressing signal processing and the corresponding physical layer communication issues of cognitive radios and networks. The original proposals on cognitive radio from Mitola, and hence the derived version from Haykin, were mainly concentrated around dynamic spectrum access. The term “cognitive radio” however is very broad and one could consider that dynamic spectrum access is one of the applications for



Introduction to Cognitive Radios



cognitive radios. In other words, once intelligence is brought into the radios, it then opens the space to perform ultimately anything that we want the radio to do dynamically and intelligently. In this sense, another classical application of cognitive radios seen in the current era is green communications [4]. In green communications, cognitive radios are deployed to optimize the usage of energy in wireless networks by intelligently and dynamically adapting to energy efficient links and channels. For both dynamic spectrum access and green communications, it is necessary for the cognitive radio nodes to learn the radio environment in order to maximize the efficiency on the utilization of the parameter of our interest. In this context, we cover three major learning and adapting functionalities of cognitive radios in this book: spectrum sensing, interference mitigation, and localization of radio nodes. In the rest of this chapter, we elaborate on the concept of cognitive radio by looking at the cognitive cycle and it functionalities, radio scene analysis, the concept of dynamic spectrum access, and some of the standardization activities in this space. We also touch upon some of the application clusters that consider adopting the cognitive radio technology for future i­mplementation.

1.2  Definition of Cognitive Radios There has been no globally adopted official/formal definition for cognitive radios as yet, however different definitions are presented in the literature as well as by the radio regulatory authorities around the world. As the name stands for cognitive radio—one could define it in many ways. All it means at the end is bringing intelligence to radios or embedding intelligence into radios that could then learn, adopt and react accordingly. Below we summarize some of the known definitions of cognitive r­adios; · Joe Mitola definition [5]:

“A really smart radio that would be self-, RF- and user-aware, and that would include language technology and machine vision along with a lot of high-fidelity knowledge of the radio environment.” · Simon Haykin definition [3]: “Cognitive radio is an intelligent wireless communication system that is aware of its surrounding environment (i.e., outside world), and uses the methodology of understanding by building to learn from the environment and adapt its internal states to statistical variations in the incoming RF stimuli by making corresponding changes in certain



Cognitive Radio Techniques

·

·

·

·

operating parameters (e.g., transmit-power, carrier frequency, and modulation strategy) in real-time, with two primary objectives in mind: - Highly reliable communications whenever and wherever needed; - Efficient utilization of the radio spectrum.” ITU-R definition [6]: “Cognitive radio system (CRS): A radio system employing technology that allows the system to obtain knowledge of its operational and geographical environment, established policies and its internal state; to dynamically and autonomously adjust its operational parameters and protocols according to its obtained knowledge in order to achieve predefined objectives; and to learn from the results obtained.” SDR Forum definition [7]: “Cognitive Radio (design paradigm-1): An approach to wireless engineering wherein the radio, radio network, or wireless system is endowed with awareness, reason, and agency to intelligently adapt operational aspects of the radio, radio network, or wireless system.” The IEEE (DYSPAN) definition [8]: “A type of radio in which communication systems are aware of their environment and internal state and can make decisions about their radio operating behavior based on that information and predefined objectives.” ETSI RRS definition [9]: “A radio system employing technology that allows the system to obtain knowledge of its operational and geographical environment, established policies and its internal state; to dynamically and autonomously adjust its operational parameters and protocols according to its obtained knowledge in order to achieve predefined objectives; and to learn from the results obtained.”

1.3  Software-Defined Radios The key enabling technology for cognitive radios is the software define radio technology (SDR). In order to implement the cognitive functionalities within the radio, it needs to be reconfigurable, and the reconfigurable feature is enabled by software. Due to the reconfigurable nature of the radio, the same is also known as reconfigurable radios (RR). One could raise the question as to how we define the term “software-defined radios,” does this mean that any radio that has a line of software code built-in is known as a software-



Introduction to Cognitive Radios



defined radio? The answer to this can be directly seen from the formally defined terms above. The SDR Forum [7] defines this as a “radio in which some or all of the physical layer functions are Software Defined,” where the term “software­defined” is defined as “the use of software processing within the radio system or device to implement operating (but not control) functions.” This definition clearly outlines the difference between having software controllable radio and software implemented radio. The same is also defined by the ITU-R as [6] “radio transmitter and/or receiver employing a technology that allows the RF operating parameters including, but not limited to, frequency range, modulation type, or output power to be set or altered by software, excluding changes to operating parameters which occur during the normal pre-installed and predetermined operation of a radio according to a system specification or standard.” The same dentition as the above (ITU-R definition) is also adopted by the ETSI-RRS working group [9]. Reference architectures have also been defined for software defined radios by the corresponding bodies, and can be found in [7, 10].

1.4  The Cognitive Cycle The cognitive cycle in the context of cognitive radios was originally scoped by Mitola, the same was then adopted by Haykin with a trimmed-down version describing the necessary communications, learning, and signal processing functionalities. In Mitola’s [1] proposal for the cognitive cycle, seven key capabilities or functionalities were defined, as depicted in Figure 1.1. The sensing function is performed in order to learn the environment; for example, learning the radio frequency channels in use in dynamic spectrum access networks or learning the wireless channel gain for green communications. The corresponding functionality is one of the key topics of this book and the whole of second is devoted to this. The second functionality is perception, which is related to determining the radio environment based on the sensed information. The perception of the radio environment can vary based on the available information; for example, the cognitive radio may only know the frequency channels being used in the environment at the current time, or it may know additional information, such as what radio technologies are being used or the geolocation of the radios. The inference can be performed by collating all the information in a parallel or hierarchical manner. The perception functionality is another main topic of this book and is treated in the final part in terms of localizing the primary users of the spectrum in



Cognitive Radio Techniques

n th cognitive cycle

Orient

Observe/Sense Initial cycle

External World

Establish priority normal

immediate urgent

Learn

Plan

(n-1) th cycle

Act/Stimulate

Decide

Figure 1.1  The cognitive cycle defined by Joseph Mitola [1].

the environment. It should be noted that this (localization) is not the only operation corresponding to the perception functionality. The third functionality is orienting; that is, to orient itself to decide on the necessary action to perform. The basis for orienting is to see if what was perceived is something the cognitive radio is familiar with to make a corresponding action or something alternative. The rest of the functionalities are planning to identify any alternative actions, making decisions to decide upon the best possible action, taking action to perform the corresponding action, and finally, learning autonomously to learn from the previous six capabilities by means of experience. Haykin’s model of the cognitive cycle [3] is oriented towards the communications, learning and signal processing aspects as described in Figure 1.1. As shown in the figure, three main tasks are considered in the cognitive cycle. The first one is radio scene analysis, which includes the e­stimation of the total interference in the environment by computing the inter­ference temperature and performing spectrum sensing in order to identify the spectrum availability known as spectrum holes. The second task is channel i­dentification that relates to estimating the channel-state information and pre. Interference temperature is a measure on the amount interference power in the radio environment, this topic is further treated in Chapter 8.





Introduction to Cognitive Radios

Radio spectrum user 1

Radio spectrum user 2

Radio spectrum user M

Radio Environment Radiate signal

Radio Stimuli Transmitter side

Receiver side Radio Environment Map

Transmitter with Power control, waveform shaping, adaptive coding and modulation, and direction transmission capabilities

Channel State Estimator

Spatial, temporal and frequency information of the radio environment Feedback channel

Coherent Receiver

Cognitive Transceiver Unit data source

data sink

Figure 1.2  The cognitive cycle similar to that defined by Haykin [3].

dicting the capacity of the channel to be used by the cognitive radio transmitter. Finally, the third task described is transmit power control and dynamic spectrum management.

1.5  The Radio Scene Analysis As mentioned, the entire book is devoted to radio scene analysis addressing different aspects of the topic and providing a range of techniques and solutions. The topic does not necessarily bind a set of tasks or corresponding techniques, since conceptually, what radio scene analysis means is that creating a complete of partial knowledge of the radio environment for a given cognitive radio node in the network. The radio scene may or may not change over time and space and depending on the amount of knowledge gathered and acquired it could provide sufficient or insufficient information for a cognitive radio node to perform its action. The creation of the radio scene that we consider here is using sensing and inferring rather than being informed by an agent or a central unit that has a global knowledge of the radio environment by maintaining a database. Figure 1.3 depicts an example of a radio scene mapping in a cognitive radio network. The corresponding is also know



Cognitive Radio Techniques

f

t

f

f f Secondary user Legacy user

t

t t

Spectral occupation

Figure 1.3  An example of a radio scene map in a cognitive radio network.

as the radio environment map (REM). Some of the key functionalities identified for creating the radio scene are: · Interference temperature estimation; · Spectral hole detection by means of spectrum sensing; · Space-time analysis and processing, for time varying radio scenes in

space; · Locating incumbent users of the spectrum in the environment. We briefly touch upon the interference temperature in this chapter and on space-time processing using time-frequency analysis in the next chapter. The topics on spectrum sensing with spectral hole detection and localization of incumbent users are treated in depth in Part I and Part III respectively, whereas the interference issues are addressed in Part II, in this book. Some of the other functionalities related to radio scene analysis that could be treated as secondary functionalities are: · Estimating radio transmission parameters of the incumbent, such as

transmit power, transmit modulation and coding methods; · Estimating the traffic pattern and the usage pattern of the incumbent users; · Identifying the radio technology or technologies used by the incumbent users. The secondary functionalities required for the creation of the radio scene may depend on the actual requirements of the user, for example if a



Introduction to Cognitive Radios



cognitive radio node is expecting to cooperate with an incumbent user for energy efficiency by means of data relaying, then the energy consumption and cost details are of interest to the cognitive radio node [4]. Note that in this case, the cognitive radio node does not necessarily need to be a secondary user of the spectrum. 1.5.1  Spectrum Occupancy Classification

The usage of a particular band of spectrum can be broadly classified into three categories. The purpose of the classification is mainly to identify the efficiency of spectral utilization and whether it could be improved or not. The three broad categories are [4]: · Black Spaces: spectrum occupied by high-power local interferers. · Gray Spaces: spectrum occupied partially by low-power interferers. · White Spaces: spectrum free of radio frequency interferers except for

ambient, natural, and man-made noise. The second category (grey space), to some extent, and the third category (white space), to a greater extent, are the ones that we are interested in for dynamic spectrum access with cognitive radios. Utilizing the grey space without a close-to-hundred percent radio scene knowledge may not be possible, as there is a higher chance of generating interference to the primary users of the spectrum and thus reducing the spectral efficiency. The white space, on the other hand, can be well-utilized by statistically characterizing the spectral usage, which is done using various sensing and learning techniques. Detecting white spaces is a spatio-temporal domain problem and becomes quite challenging, especially when the primary users of the spectrum are located further away from the cognitive radio nodes or if the primary users are shadowed by obstacles that could not be then sensed by the cognitive radio terminals. 1.5.2  Hidden Terminals

Due to shadowing and deep fading effects in wireless communications, or when the cognitive radio nodes are located further away from the primary user, the signal power received by the cognitive radio node from the primary user terminals can become very low such that the primary user is unable to be detected. The detection criteria in this case depends on the regulatory

10

Cognitive Radio Techniques

requirements as per with what probability can the cognitive radio detect the primary user, the detection probability in such cases is expected to be high (i.e., in the range of 0.9 or more) to ensure the primary users are not interfered due to cognitive radio transmissions. The phenomenon where the primary user is unable to be detected by the cognitive radio nodes is known as the hidden node problem or the hidden terminal problem in the cognitive radio literature. 1.5.3  Locating Primary Users

Detecting the spectral usage may not entirely mean that the secondary users cannot transmit in that particular spectral band. By further learning the position of the primary user, the secondary user can then isolate the region where the primary user is present and perform transmissions outside the region. Such directional transmission capabilities are made possible using intelligent power control mechanisms and directional antennas. By performing secondary transmissions in such a way, the cognitive radio nodes are able to use the spectrum in the spatial domain even though a primary user is detected in the environment. Localization techniques for cognitive radio networks are treated in the final part (Part III) of this book.

1.6  Dynamic Spectrum Access and Management Dynamic spectrum access, a topic well-addressed in literature [11–13], is the key application that gave rise to the concept of cognitive radios in wireless communications. In wireless systems, the scarce radio spectrum can be accessed in many ways, considering different strategies, methodologies, and/or policies. In this section, we provide the concepts on spectrum access models to understand how cognitive radios can be used for dynamic spectrum access. The models for spectrum access can be classified as the command and control model, exclusive-use model, commons model, and the shared model [11], which are explained below. In Figure 1.4, we present a taxonomy [14] of the spectrum access models. · The Command and Control Model: This is one of the oldest model

for spectrum access with a complete usage rights given to the user of the spectrum. Such a model had shown to be an inefficient way of utilizing the radio spectrum.



Introduction to Cognitive Radios

11

· The Exclusive-Use Model: In this model, the spectrum is licensed

to a user for exclusive usage with defined rules. In the case of when the licensed user is not fully utilizing the spectrum the unlicensed secondary user can be granted access to the spectrum by the licensed primary user. The exclusive-use model is further classified into a long term exclusive user model and a dynamic exclusive use model. · The Shared-Use Model: In this model the spectrum is shared and simultaneously accessed by the primary licensed user of the spectrum and the unlicensed secondary user of the spectrum. The secondary user of the spectrum will opportunistically access the spectrum without interfering with the primary user of the spectrum. The opportunistic access is done in two ways: spectrum overlay and spectrum underlay, which are described in Section 1.6.1. · The Commons Model: In this model all the users of the spectrum have equal rights to access the spectrum indicating that the spectrum is a common resource to every user. The commons model can be classified into Uncontrolled Commons model, Managed Commons model, and Private Commons model. The cognitive radio technology is expected to enable dynamic spectrum access considering the various spectrum access models given above to increase the spectral efficiency usage. As indicated in the cognitive cycle section previously, the corresponding functionalities of a cognitive radio allows it to intelligently learn, adapt, and orient itself in order dynamically access the spectrum under various rules and policies enforced by the regulator. 1.6.1  Spectrum Underlay and Overlay

In the shared spectrum access model, the concept of primary users and secondary users are clearly represented. The primary users are the licensed users of the spectrum, whereas the secondary users can opportunistically utilize the spectrum in the spatio-temporal domain. In other words, the secondary users are allowed to use the spectrum without interfering with the primary user operations. The cognitive radio technology clearly (in this case) is a strong candidate to act as a secondary radio node; using the intelligence, the cognitive radio-based secondary radio will adapt itself to utilize the spectrum. Two strategies are considered for sharing the spectrum as explained below. The first method is the spectrum underlay strategy, where the secondary users of the spectrum can use the spectrum by transmitting ­simultaneously

12

Cognitive Radio Techniques

Spectrum Access Models

Commandand control model

Commons model

Shared use of primary licensed spectrum model

Exclusive use model

Long-term exclusive use model

Spectrum underlay model

Uncontrolled commons model

Dynamic exclusive use model

Spectrum overlay model

Private commons model Cooperative and managed commons model

Figure 1.4  A broader classification of spectrum access models.

with the primary user. However, the transmit power of the secondary user transmissions needs to be such that it does not interfere with the primary user transmissions. The interference from the secondary users to the primary user should not exceed a specified limit characterized by the interference temperature limit. The underlay model of spectrum sharing is depicted in F­igure 1.5(b). Such a spectrum access model well suits ultrawideband (UWB) technology which transmits over large range of spectrum with a very low power spectral density [15]. The second method for sharing the spectrum is by using the overlay strategy, where the secondary users of the spectrum are allowed to access the spectrum in the spatio-temporal domain when the spectral portion is not used. The white spaces in the spectral band are identified and utilized by the secondary users. The secondary users are required to perform ­spectrum-sensing to identify the usage of the spectrum by the primary user prior to accessing it. Once the secondary users gain access to the spectrum, opportunistically, the spectrum sensing has to still be continued to identify whether any primary users have started to utilize the spectrum. In order to successfully perform transmissions, the secondary users need to perform



Introduction to Cognitive Radios

13

secondary users primary users

(a)

(b)

Frequency

Frequency

Figure 1.5  (a) Spectrum overlay strategy, and (b) spectrum underlay strategy.

radio scene analysis. The overlay spectrum access model is depicted in ­Figure 1.5(a).

1.7  Regulatory Aspects Many regulatory and standardization groups around the world have already started addressing cognitive radio related technology. Below, we summarize a few of them which have shown some promising progress at present. We cover the IEEE 802.22 WRAN standards that have already implemented its standard based on some basic functionalities of cognitive radios, the IEEE DySPAN Standards Committee (which is the key group that works on all the aspects of cognitive radio networks within the IEEE), and finally, the ETSI

14

Cognitive Radio Techniques

RRS technical committee that addresses reconfigurable radio systems-related recommendations. 1.7.1  The IEEE DySPAN Standards Committee

The IEEE Standards Committee on Dynamic Spectrum Access (DySPAN) was formulated in 2005 as the IEEE P1900 Standards Committee by the IEEE Communications Society and the IEEE Electromagnetic Compatibility Society. Since December 2010, it has been under the IEEE Communication Society as a Standards Committee. The main objectives of the Standards Committee [16] are to work on dynamic spectrum access-based systems and networks for improving the spectral efficiency of wireless communications, to address radio transmission interference, and to address information sharing amongst different wireless technologies. The Committee consists of several working groups as summarized below: · IEEE 1900.1: Standard Definitions and Concepts for Spectrum

Management and Advanced Radio System Technologies The IEEE 1900.1 Standards specify the terminologies and definitions used in the cognitive radio and dynamic spectrum access­related technologies. · IEEE 1900.2: Recommended Practice for Interference and Coexistence Analysis This Standards group address the coexistence- and interference­related issues with various wireless technologies within the same frequency bands as well as different frequency bands. · IEEE 1900.3: Recommended practice for conformance evaluation of software defined radio software modules This group has been dissolved; it was originally intended to provide compliances to the software modules related to the cognitive radio and software defined radio technologies. · IEEE 1900.4: Standard for Architectural building blocks enabling network-device distributed decision-making for optimized radio resource usage in heterogeneous wireless access networks. The IEEE 1900.4 has produced a standard defining the base blocks for (a) network resource managers, (b) device resource managers, and (c) the information to be exchanged between the building blocks. Moreover, the group is involved in defining the interfaces and protocols that are required to enable the above-mentioned groups.



Introduction to Cognitive Radios

15

· IEEE 1900.5: Standard on Policy Language and Policy Architec-

tures for Managing Cognitive Radio for Dynamic Spectrum Access A­pplications The IEEE 1900.5 group is involved in defining control architectures for policies and the corresponding requirements for policy language to support different vendors. · IEEE 1900.6: Standard on interfaces and data structures for exchanging spectrum-sensing information for dynamic spectrum access systems The IEEE 1900.6 group works on defining the interface and data structures for information exchange between cognitive radio nodes in regards to spectrum sensing. · IEEE 1900.7: Standard on radio interface for white space dynamic spectrum access radio systems supporting fixed and mobile operation The IEEE 1900.6 group works on standardizing the radio interface for medium access control (MAC) and physical (PHY) layers for radios deploying dynamic spectrum access in white spaces. 1.7.2  The IEEE 802.22 WRAN Standards

The IEEE 802.22 wireless regional area networks (WRAN) started as a working group in 2004 and became a full standard in 2009, the first standard to implement cognitive radio functionalities at the PHY and the MAC layers [17, 38]. The IEEE 802.22 standards provide secondary user operations with dynamic spectrum access in the television band white spaces between 54 MHz– 852 MHz. Similar to any access technologies, the IEEE 802.22 also has user radio terminals defined as the customer premise equipment (CPE); in this case, the cognitive radio nodes, and a base station (BS). Some of the incumbent users of this spectrum are television receivers and the wireless microphones that require interference protection from the secondary user transmissions in the network. The cognitive radios (based on the 802.22 standards) operate based on orthogonal frequency division multiplexing (OFDM) techniques with a total number of 2048 subcarriers. Furthermore the standards also provides power controlling at the cognitive radio terminals for reducing interference while achieving a certain level of throughput in the secondary communications. In the standards document [17] clause ten addresses the cognitive radio capabilities of the 802.22 system. We summarize a few of them below: · The spectrum management operation: The spectrum manager (SM)

coordinates important tasks related to the cognitive functionalities,

16

Cognitive Radio Techniques

such as maintaining the spectrum availability information, scheduling the spectrum-sensing operation, selecting channels and managing channels, access to the database, enforcing the standards related to IEEE 802.22 and policies, and enabling self-coexistence. · The spectrum-sensing automation: The spectrum-sensing automation (SSA) entity is an interface to the spectrum-sensing function that would execute relevant commands from the spectrum manager to enable spectrum sensing. · The spectrum-sensing process: The spectrum-sensing process in the standards defines a spectrum-sensing function (SSF) that is responsible for sensing the radio spectrum in the corresponding frequency bands. The observed results are reported to the spectrum manager at the bases station through the SSA. The spectrum-sensing function on the hand performs the actual sensing by observing the radio stimuli and generates a set of output parameters, such as the mean and the deviation of the received signal strength. · Geolocation: The standards defined two modes of geolocation, first using satellite-based geolocation technology (which is considred to be mandatary), and second using terrestrial based geolocation techniques by means of ranging, using the preambles in the superframe/frame, and by using the coexistence beacon protocol defined in the standards. 1.7.3  The ETSI-RRS Technical Committee

The European Telecommunication Standard Institute (ETSI) formed a Technical Committee on Reconfigurable Radio Systems (RRS) regulatory group to work on software defined radio technology framework and regulate cognitive radio technology. The ETSI-RRS committee consists of four working groups (WG) as summarized below; · WG-1 System Aspects: The working group on system aspects proposes

system level aspects of the reconfigurable radio systems and brings cohesiveness between the other three working groups within the committee. · WG-2 Reconfigurable Radio Equipment Architecture: This working group concentrates on radio equipment architecture and proposes common reference architectures for cognitive radio- and softwaredefined radio equipment-based devices.



Introduction to Cognitive Radios

17

· WG-3 Cognitive Management and Control: The working group on

cognitive management and control works on spectrum management and radio resource management for heterogeneous access technologies. The group has also presented a report on cognitive pilot channel (CPC) to support the management functionalities reconfigurable systems. · WG-4 RRS for Public Safety: This working group concentrates on the requirements relevant to public safety communications based on cognitive radio and software radio technologies, and provides system level definitions in public safety and defense working d­omains.

1.8  Application Clusters The intelligence embedded into the radios allow us to perform many adaptations based on our requirements; for example, one could use the intelligence to perform dynamic spectrum access, design energy-efficient ­communications and hence energy efficient networks, seamlessly adopt different radio technologies, improve the quality of service at the lower layers, and much more. In this section, we provide some application clusters where the concept of cognitive radios can be implemented and the corresponding rewards. 1.8.1  Cellular Mobile Networks

Cellular networks are the largest wireless networks that one could see in the current era where the number of users grows. The users in such systems are densely populated and unevenly spread in space at different times of the day and on different days of the week, thus giving rise to a similar usage pattern of the radio spectrum in space and time. The cognitive radio-based next generation solutions with intelligent PHY and MAC layers will enable to utilize the cellular spectrum more efficiently and also accommodate secondary users in the business model. Even though some interesting concepts are being considered [18, 19] it would be a great challenge to bring such cognitive radio technology into the cellular mobile networking domain due to many unanswered and open problems such as security, safety, accountability, and regulatory issues.

18

Cognitive Radio Techniques

1.8.2  Energy Efficiency is Wireless Networks

Harvesting energy in the wireless and mobile communication systems and networks is one of the key objectives of the telecommunications industry in large [20, 21]. Energy efficiency is strongly emphasized from base stations to radio user nodes at the PHY, MAC, and at the NET layers. Techniques are proposed to save energy in wireless networks by avoiding wastage one end and by implementing energy efficient methods, algorithms, and protocols on the other end [22]. In this sense, cognitive radios and cognitive networks with intelligence that have the capability to self-organize and self-configure is proposed as a strong candidate for green communications and green networking. The cognitive radios and networks can learn in real-time and adopt their transmission parameters and policies to improve energy efficiency [23, 24]. 1.8.3  Public Safety Communications

One of the domains where telecommunications require a rapid and vast improvement is the public safety domain. Currently, most of the communications technologies used in this sector date back many years and require some considerable upgrading. Very recently, the 3GPP-based technology Long Term Evolution (LTE) has been proposed for the use in public safety communications. Yet another issue related to public safety communications is the presence of different technologies used by different national agencies across a country. The cognitive radio technology in this context, with embedded intelligence, can address the needs and requirements to bring forward the telecommunications systems in the public safety domain [25–27]. 1.8.4  Coexistence of UWB Radio Technology

Due to the low-powered transmission over a very wide range of frequencies from 3.1 GHz to 10.6 GHz, the ultrawideband (UWB) radio technology is considered to as a potential candidate for the deployment cognitive radios. With the presence of various spectrum users within this frequency range, cognitive functionalities embedded into UWB radio devices will enable coexistence. Some of the wireless technologies present in this frequency range are WiMAX, C-band satellite, and DSRC. With the help of the cognitive functionalities, especially using the multiband OFDM (MB-OFDM) based standards, the UWB-based cognitive radios can adopt its transmission to accommodate legacy users of the spectrum [15, 28]. Some of the techniques



Introduction to Cognitive Radios

19

to enable coexistence with the help of cognitive radios are interference mitigation techniques, detect and avoid techniques, and spectrum sculpting techniques [15]. 1.8.5  Wireless Networks for Smart Grids

The recent developments in smart power grids show a potential application for the next generation wireless technology based on cognitive radio communications. A smart power grid requires an efficient wireless networking architecture addressing a large scale of metering data, covering different energy sources, such as power from solar or wind plants, variation in the amount of traffic, security issues and the required quality of service [29, 30]. Considering the number of users accessing the spectrum − and to have a spectrally efficient communications system meeting the above-mentioned requirements−cognitive radio technology is expected to play a key role in this domain. 1.8.6  Vehicular Networks

The vehicular communications network is a growing area in wireless commu­ nications. The development of the dedicated short-range communications (DSRC) technology for vehicular applications enables the implementation intelligent transport systems (ITS) to a greater extent. With the use of realtime information communicated via the vehicular network, the safety of passengers can be improved and, at the same time, the travel time can be improved. In this sense, cognitive radio technology can be introduced into such vehicular networks, the cognitive radio technology has the potential to address congestion avoidance in the spectrum, advanced power control, dynamic spectrum access and interoperability among various communication devices. The cognitive networks will enable the mobile vehicular network infrastructure to self-adopt and self-organize by means of embedded i­ntelligence. 1.8.7  Defense Application Systems

Defense communications is one of the most promising application areas for cognitive radio technology. Self-configurable and adaptable wireless nodes by knowing the environment is very much seen as a requirement these days

20

Cognitive Radio Techniques

in the areas of defense communication systems. The interference mitigation capability is one of the key advantages of cognitive radio systems, especially in battle fields or similar scenarios [40].

References   [1] Mitola, J., and G. Q. Maguire, Jr., “Cognitive radio: making software radios more personal,” IEEE Personal Communications, Vol. 6, 1999, pp. 13.   [2] Mitola, J., “Cognitive Radio,” Licentiate proposal, KTH, Ph.D. thesis, Stockholm, Sweden, 1998.   [3] Haykin, S., “Cognitive Radio: Brain-Empowered Wireless Communications,” IEEE Journal on Selected Areas of Communications, Vol. 23, No. 2, 2006, pp. 201-220.   [4] Rodriguez, J., P. Marques, A. Radwan, K. Moessner, R. Tafazolli, et al., “Cognitive R­adio and Cooperative Strategies for Power Saving in Multi-Standard Wireless Devices,” Future Network & Mobile Summit 2010, Florence, Italy, June 2010.   [5] Mannion, P., “Smart radios stretch spectrum,” Electronic Engineering Times (EETimes), Vol. 2006: A Global Sources and CMP joint venture, 2006.   [6] ITU-R Report SM.2152: Definitions of Software Defined Radio (SDR) and Cognitive Radio System (CRS), September 2009.   [7] SDR Forum: Cognitive Radio Definitions and Nomenclature, Approved Document SDRF-06-P0009-V1.0.0, 2008.   [8] IEEE Standard Definitions and Concepts for Dynamic Spectrum Access: Terminology Relating to Emerging Wireless Networks, System Functionality, and Spectrum Management, Approved June 2008, IEEE Communications Society, IEEE Standards Coordinating Committee 41 on Dynamic Spectrum Access Networks, IEEE-SA Standards Board, IEEE Std 1900.1-2008, Sep 2008.   [9] ETSI TR 102 802: Reconfigurable Radio Systems (RRS); Cognitive Radio System Concept, 2009. [10] Mueck, M., A. Piipponen, K. Kalliojarvi, G. Dimitrakopoulos, K. Tsagkaris, et al., “ETSI Reconfigurable Radio Systems Status and Future Directions on Software Defined Radio and Cognitive Radio Standards,” IEEE Communications Magazine, Vol. 48, No. 9, 2010. [11] Hossain, E., D. Niyato, and Z. Han, Dynamic Spectrum Access and Management in Cognitive Radio Networks, New York: Cambridge University Press, 2009. [12] Berlemann, L., and S. Mangold, Cognitive Radio and Dynamic Spectrum Access, Hoboken, NJ: John Wiley and Sons, 2009. [13] Chen, K.-C., and R. Prasad, Cognitive Radio Networks, Hoboken, NJ: John Wiley and Sons, 2009.



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[14] Buddhikot, M. M., “Understanding Dynamic Spectrum Access: Models, Taxonomy and Challenges,” Proceedings of IEEE DySPAN, Dublin, Ireland, April 2007. [15] Kandeepan, S., G. Baldini, and R. Piesiewicz, “UWB CognitiveRadios,” in Novel Applications of the UWB Technologies, B. Lembrikov (ed), online, InTech, 2011. [16] The IEEE Dynamic Spectrum Access Networks (DySPAN) Standards Committee: http://grouper.ieee.org/groups/dyspan/index.html, accessed August 3, 2012. [17] IEEE Std 802.22-2011-IEEE Standard for Information Technology-Telecommunications and information exchange between systems Wireless Regional Area Networks (WRAN)-Specific requirements, Part 22: Cognitive Wireless RAN Medium Access Control(MAC) and Physical Layer (PHY) Specifications: Policies and Procedures for Operation in the TV Bands, IEEE Computer Society, 2011. [18] Lee, W.-Y., and I. F. Akyildiz, “Spectrum-Aware Mobility Management in Cognitive Radio Cellular Networks,” IEEE Transactions of Mobile Computing, Vol. 11, No. 4, 2012, pp. 529–542. [19] ThexGTechnology Inc.: http://www.xgtechnology.com/, accessed August 3, 2012. [20] The GreenTouch Initiative: http://www.greentouch.org/, accessed August 3, 2012. [21] Green Radio: NECs Approach towards Energy-efficient Radio Access Networks, White P­aper, NEC Corporation, February 2010, NEC Corporation. [22] Wu, J., S. Rangan, and H. Zhang, Green Communications: Theoretical Fundamentals, Algorithms and Applications, Boca Raton, FL: CRC Press, 2012. [23] Zhang, H., “Cognitive Radio for Green Communications and Green Spectrum,” ­CHINACOM, Hangzhou, China, 2008. [24] Grace, D., J. Chen, T. Jiang, and P. D. Mitchell, “Using cognitive radio to deliver Green communications,” 4th International Conference on Cognitive Radio Oriented Wireless Networks and Communications (CROWNCOM), Hannover, June 2009. [25] FCC, Public Safety Technical Reference Center, http://www.fcc.gov/encyclopedia/ public-safety-technical-reference-center, accessed August 3, 2012. [26] Heskamp, M., R. Schiphorst, and K. Slump, “Public Safety and Cognitive Radio,” in Cognitive Radio Communications and Networks Principles and Practice, A. M. Wyglinski, M. Nekovee, and Y. Thomas (eds), San Diego, CA: Elsevier, 2012. [27] ETSI-RRS Working Group 4: Public Safety Communications: http://www.etsi.org/ website/technologies/RRS.aspx, accessed August 3, 2012. [28] EU-FP7 Project: EUWB-Coexisting Short Range Radio by Advanced Ultra-Wideband Radio Technology, work package 2: “UWB based Cognitive Radios,” 2008-2011: http://www.euwb.eu, accessed August 3, 2012. [29] Qiu, R. C., Z. Hu, Z. Chen, N. Guo, R. Ranganathan, et al., “Cognitive Radio Network for the Smart Grid: Experimental System Architecture, Control Algorithms, Security, and Microgrid Testbed,” IEEE Transactions on Smart Grid, Vol. 2, No. 4, 2011, pp. 724–740.

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[30] Yu, R.,Y. Zhang, S. Gjessing, C. Yuen, S. Xie, et al., “Cognitive Radio Based Hierarchical Communications Infrastructure for Smart Grid,” IEEE Network, 2011, September 2011, Vol. 25, No. 5Se, pp. 6–14. [31] Mitola, J., Cognitive Radio Architecture, Hoboken, NJ: John Wiley and Sons, 2006. [32] FCC (2002) Federal communications commission: Spectrum Policy Task Force Report, Federal Communications Commission ET Docket 02-135, November 2002. [33] FCC-Federal Communications Commission (2003), Facilitating Opportunities for Flexible, Efficient, and Reliable Spectrum Use Employing Cognitive RadioTechnologies, NPRM and Order, ET Docket No. 03-322, 2003. [34] ECC (CEPT) Report 159: Technical And Operational Requirements For The Possible Operation Of Cognitive Radio Systems In The White Spaces Of The Frequency Band 470– 790 MHz, Cardiff, 2011. [35] European Commission (Report): DG INFSO/B4/RSPG Secretariat, RSPG09-299, Radio Spectrum Policy Group Report On Cognitive Technologies, Final Draft Brussels, 2009. [36] Fette, B., (Ed.), Cognitive Radio Technology, Oxford: Elsevier Publishers, 2006. [37] Prasad, R. V., P. Pawelczak, J. A. Hoffmeyer, and H. S. Berger, “Cognitive Functionality in Next Generation Wireless Networks: Standardization Efforts,” IEEE Communications Magazine, April 2008, Vol. 46, No. 4, pp. 72–78. [38] Cordeiro, C., K. Challapali, D. Birru, and S. Shankar, “IEEE 802.22: The First Worldwide Wireless Standard based on Cognitive Radios,” Proceedings of First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN), New York City, NY, 2005. [39] Hossain, E., and V. Bhargava (eds), CognitiveWireless Communication Networks, New York: Springer, 2007. [40] Frenzel, L. E., “Cognitive Radios Connect Smart Battleplace, Defense Electronics,” 2011, http://rfdesign.com/military_defense_electronics/cognitive-radios-connect-smartbattleplace-0911/, accessed August 3, 2012.

Part I: Spectrum Sensing in Cognitive Radios

2 Fundamentals of Spectrum Sensing and Detection The cognitive radio node is required to learn the radio environment in order to perform its actions strategically. The learning part is enabled by means of spectrum sensing and detection, which is a unique and crucial feature specific to cognitive radio networks in general. The cognitive radio node continuously senses the spectrum and learns the environment by detecting the radio users in its vicinity. In this chapter, we present various statistical detection techniques which are well-developed and well-known in the literature of statistical signal processing. The cognitive radio devices use the statistical detection techniques in order to detect radio users in noisy environments with random transmission patterns. In this context–in addition to detection techniques–we present spectrum occupancy models, stochastic analysis of radio signals, and the concept of context aware signal detection.

2.1  Introduction Spectrum sensing is the process of sensing or sniffing the radio environment using an antenna [1, 2]. The sensed signal is used to derive a test statistic in order to make a decision on whether a radio user or multiple radio users are present in the environment depending on the problem and the defined 25

26

Cognitive Radio Techiniques

model. The decision-making process is known as detection, therefore the sensing/sniffing and decision-making processes together are known as spectrum sensing and detection. In most of the literature on spectrum sensing techniques for cognitive radio networks, authors commonly refer only to the term “spectrum sensing” in which case it is assumed that detection is also part of the process. In this chapter, we present how the spectrum sensing and detection process in cognitive radio networks can be formalized as a statistical detection problem and present various statistical detection methods that are commonly known in statistical signal processing theory [3, 4]. Consider the figure given in Figure 2.1(a), together with the corresponding communications system model given by the block diagram in

Radio-A

Cognitive radio node (a) A cognitive radio sensing a radio (incumbent) transmitter in the environment n(t)

Radio-A

Wireless channel

s(t)

+

r(t)

Cognitive radio node

(b) Corresponding system model in block diagram Figure 2.1  I llustrating the spectrum sensing and detection process in cognitive radio ­networks.



Fundamentals of Spectrum Sensing and Detection

27

­ igure 2.1(b). The cognitive radio node sniffs the spectrum in the time doF main using its antenna and processes the sniffed radio stimuli to make a decision on whether or not it has detected a radio user in the environment. The sniffed signal r(t) includes any radio signals in the environment plus the receiver noise component n(t) typically modeled as additive zero mean Gaussian noise with a variance of σ n2. In order to model the environment, we take a statistical approach and define two hypotheses H0 and H1, given by,

ì ν(t ); Hypothesis H 0 when no radio signal is present (2.1) r (t ) = í îs(t ) + ν(t ); Hypothesis H1 when radio signal is present

where, s(t) is the actual radio signal component sniffed by the antenna at the cognitive radio node as a result of the transmissions from the radio present in the environment (radio node A in Figure 2.1) received through the corresponding wireless channel. The received signal to noise ratio (SNR) is defined by SNR = Ps /Pn where Ps is the received signal power given by T Ps = T1 ∫ | s(t ) |2dt and Pn is the receiver noise power given by Pn = σ n2. The 0 cognitive radio node then uses the sensed stimuli r(t) to decide on whether a radio user is present or not. In general, the decision between hypotheses H0 and H1 is made by comparing a test statistic x derived from r(t) with a threshold value l. The decision criteria at the cognitive radio node is therefore given by:

0;

d = 

1;

ξ < λ; for deciding on hypothesis H 0 ξ ≥ λ; for deciding on hypothesis H1

(2.2)

where, d is the decision made by the cognitive radio node. As indicated in the decision criteria in (2.2) the cognitive radio node decides that a radio user is not present if the test statistic x is less than the threshold l by assigning d = 0 and decides that a radio user is present if the test statistic x is greater than or equal to the threshold l by assigning d = 1. The equality sign in the decision-making process can also be assigned to the case where x < l which then becomes x £ l. It can be easily observed from the above-mentioned decisionmaking process that the accuracy in making a correct decision depends upon the test statistic x and the decision threshold l as per (2.2) together with the signal to noise ratio. In the subsequent sections we present different methods for deriving the test statistic and the corresponding threshold value for optimum detection which are available from the classical literature on statistical detection [3, 4].

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Cognitive Radio Techiniques

2.2  Statistical Detection Techniques Statistical detection is a well treated problem in the fields of radar, sonar, communications engineering, biomedical engineering, and statistical signal processing. In the recent years, it has been also applied in cognitive radio networks for spectrum sensing and detection. In this section, we present some commonly known detection methodologies that could be used for spectrum sensing and detection in cognitive radio networks. 2.2.1  Maximum A Posteriori Detection

The maximum a posteriori (MAP) detection is a technique that uses the posteriori probabilities under events H0 and H1 for the received signal r(t) to perform the hypothesis testing. The corresponding detector is given by,

0 P ( H1 | r ) ≷H H1 P ( H 0 | r )

(2.3)

where, P(H1|r) and P(H0|r) are the posteriori probabilities of r(t) under the events H1 and H0, respectively. The corresponding detection criteria could be modified as,  P ( H1|r )  H0 ln  (2.4)  = Λ(r ) ≶H1 0 = l P ( H | r ) 0   where, L(r) is known as the log-likelihood function and the corresponding test statistic x(r) may be derived from L(r) itself, depending on the signal and noise models and compared with the threshold l = 0. Moreover, using the Baye’s principle we can rewrite (2.3) as,



0 P (r | H1 )P ( H1 ) ≶H H1 P (r | H 0 )P ( H 0 )

(2.5)

where P(H0) and P(H1) are the prior probabilities of events H0 and H1, respectively, and P(r | H0) and P(r | H1) are the conditional probabilities of r(t) given the events H0 and H1 respectively. By rearranging the terms in (2.5) we come up with, é P (r | H1 ) ù H 0 æ P ( H 0 ) ö (2.6) L(r ) = ln ê ú ≶H1 ln ç P ( H ) ÷ = λ 1 ø è ë P (r | H 0 ) û where L(r) is the redefined log-likelihood function that could be used to derive the test statistic x(r) and compared with the new threshold l as defined



Fundamentals of Spectrum Sensing and Detection

29

in (2.6). In this case, however, we are bound to know the prior probabilities of the events H0 and H1 in order to compute the detection threshold; such detectors are known as the minimum-error probability detectors in ­literature. It should be pointed out here that the minimum-error probability detectors are quite useful when the temporal behavior of the radio users are defined probabilistically with the probabilities P(H0) and P(H1) for the on-off periods, respectively, in order to better design the detectors and also better analyze the detection performance in real-life situations. 2.2.2  Maximum Likelihood Detection

The maximum likelihood (ML) detector is the simplest of all and also could be directly derived from the minimum error probability based detector. The ML detection criteria is given by,

0 P (r | H1 ) ≶H H1 P (r | H 0 )

(2.7)

where, P(r | H0) and P(r | H1) are known as the likelihood functions. If we P (r |H ) define the log-likelihood function of r as L(r ) = ln é P (r |H10 ) ù, the ML detecë û tion criteria then becomes,

0 Λ(r ) ≶H H1 0 = l

(2.8)

The above criteria is a direct result of (2.6) when the prior probabilities of H0 and H1 are assumed to be equal given by P(H0) = P(H1) = 0.5. As we see, the ML detector essentially ignores the prior probabilities of the events H0 and H1 and hence may not perform well when the condition P(H0) = P(H1) is not met. However, implementation of ML detectors, in practice, are less complex than the others, which is an attractive feature of the detector of such class. 2.2.3  The Neyman-Pearson Detector

The Neyman-Pearson detection criteria is based on maximizing the probability of deciding on H1 given that H1 had occurred P[U(r) > l; H1] by selecting the threshold l such that the probability of deciding on H1 given that H0 had occurred Pr[U(r) > l; H0] is a constant y0, where U(x) is the likelihood ratio given by

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Cognitive Radio Techiniques

U (r ) =



P (r | H1 ) P (r | H 0 )

(2.9)

and the corresponding decision criteria is given by 0 U (r ) ≶ H H1 l



(2.10)

with Pr[U(r) > l; H0] = y0. The Neyman-Pearson detector is also know to maximize the detection probability (i.e., P[U(r) > l; H1]) by fixing the false alarm probability (i.e., Pr[U(r) > l; H0]) for a particular detection system, a more detailed definitions of detection and false alarm probabilities are presented later in this chapter under detection performances. 2.2.4  The Bayesian Risk-Based Detector

In the Bayesian risk-based detector, costs are assigned to the decisions for deciding on H0 or H1 depending on whether H0 or H1 had occurred. We define the cost function Cij for deciding on Hi based on the event Hj, where i,j Î {0,1}. The detector is derived by minimizing the Baye’s risk given by

R = å å Cij P ( H i | H j )P ( H j ) i

(2.11)

j

and the corresponding detection criteria is given by

é P (r | H1 ) ù H0 æ (C10 - C00 )P ( H 0 ) ö L(r ) = ln ê = λ ú ≷H1 ln çè (C 01 - C11 )P ( H1 ) ÷ø ë P (r | H 0 ) û

(2.12)

where the test statistic x(r) could be derived from L(r) and compared with the threshold l. The costs are considered such that C10 > C00 and C01 > C11 where, in reality, the penalties for making errors or incorrect decisions have higher costs then making correct decisions. The conditional probabilities P(r | H0) and P(r | H1) and the prior probabilities P(H0) and P(H1) are assumed to be known in making Bayesian decisions.

2.3  Continuous and Discrete Signal Detection In this section, we introduce the concept of using either continuous signals or discrete signals for spectrum sensing and detection purpose purely in an implementation point of view. The mathematical model of the signals and



Fundamentals of Spectrum Sensing and Detection

31

the decision-making strategies presented before are assumed to hold true for both continuous and discrete signals, assuming that the sampling process of the continuous signal does not introduce any correlation in the received signal. The analog signal represented by r(t) over a time of T is represented by the discrete signal r[n] for n = 0,1..(N – 1) with N discrete samples, with a sampling period of Ts = T/N. In an implementation point of view, the continuous signals can be used to perform spectrum sensing and detection at the RF or IF levels and the discrete signals can be used to perform at the base band level. Note that continuous signals can also be used at the base band level, and at the same time discrete signals can also be used at the IF or RF levels with the use of software definable radios with very high sampling rates. Considering a low complexity and low cost receiver, we can assume continuous signals are used to perform spectrum sensing at the RF, IF, or baseband levels and discrete signals are used to perform at the baseband level, as depicted in Figure 2.2. The decision can also be based on the complexity of the spectrum sensing algorithm and technique. A more complex algorithm may only be feasible with advanced signal processing techniques using state-of-the-art digital signal processors or field programmable gate arrays that could perform a high level of number crunching. On the other hand, simple detectors that could be readily implemented using analog circuitries can be directly used at the RF, IF, or based band levels. Again, the choice of requiring a complex or a simple technique spectrum sensing and detection depends on the required detection performance level, which is a very crucial aspect. The detection performance is quite important in order to satisfy the regulatory bodies to maintain a certain degree of assurance for not interfering with the incumbent users of the radio spectrum, which directly relates to the performance of the spectrum sensing technique, thus complexity may have to be introduced to implement high performance techniques.

2.4  Detection Performance The performance measures of statistical detectors are presented in terms of two probabilities known as the detection probability (or probability of detection) and the false alarm probability (or the probability of false alarm). The detection probability PD and the false alarm probability PFA are respectively given by,

PD = Pr[ξ ≥ λ | H1 ] = Pr[deciding on H1 | H1 ]

(2.13)

32

Cognitive Radio Techiniques

RF signal

Spectrum sensing and detection

r(t) Down/upconverter, De/modulator, and transceiver unit

Antenna subsytem and LNA (a)

IF signal

Spectrum sensing and detection

r(t) Antenna subsytem LNA and down/up converter

De/modulator and transceiver Unit

(b)

r(t)

Baseband signal

Antenna subsytem LNA, down/up converter and de/modulator

Spectrum sensing and detection

Baseband transceiver unit

(c) Figure 2.2  S  pectrum sensing and detection functionality implemented at various stages of a transceiver unit.



PFA = Pr[ξ ≥ λ | H 0 ] = Pr[deciding on H1 | H 0 ]

(2.14)

where x is the test statistic and l is the detection threshold. The detection probability is the most important performance metric of any spectrum sensing technique, especially in terms of cognitive radio networks where the regu-



Fundamentals of Spectrum Sensing and Detection

33

latory bodies and standardization bodies require a minimum detection probability guaranteed for the cognitive radios to reliably detect the incumbent users of the spectrum. Therefore, the detection probability is expected to be maximized in a cognitive radio network and hence many spectrum sensing algorithms and techniques are derived to do so. The false alarm probability, on the other hand, is a metric that the cognitive radio would want to minimize in order to avoid any missed opportunity to use the radio spectrum by falsely assuming an incumbent user is present in the environment and wasting the opportunity to utilize the spectrum. The detection performance can also alternatively be expressed in terms of the misdetection probability (or the probability of misdetection) given by PM = Pr[x < l|H1] = Pr[deciding on H0|H1]. The misdetection probability can be expressed directly in terms of the detection probability given by PM = 1 – PD, therefore either one of the two (PD or PM) is sufficient to characterize the detection performance together with the false alarm probability. 2.4.1  Detection Performance Versus the SNR

The detection probability is usually analyzed with respect to the received signal-to-noise ratio. It is well understood that when the power Ps of the received radio signal s(t) gets lower (or equivalently, if the radio transmitter is further away from the cognitive radio node) detecting the radio user becomes much harder. Therefore it is very important to analyze the detection performance of a spectrum sensing algorithm with respect to the received SNR level for a given false alarm probability (or for a given threshold value). Note that the probability of false alarm is calculated when no signal is present (under H0) and therefore it only depends on the detection threshold l and the noise power Pn. 2.4.2  Detection Performance Versus the Signal Observation Length

The detection performance is also analyzed with respect to the length of the observation window or the sensing period T, which is equivalent to the number of samples observed in a discrete system N for a given sampling frequency. When the observation length is increased, in general, the noise can be averaged out when calculating the test statistic which essentially improves the overall SNR for a given false alarm probability (or for a given detection threshold). This, in turn, improves the detection performance of a given spectrum sensing technique.

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Cognitive Radio Techiniques

2.4.3  The ROC Curves

In the previously presented performance analysis methods, we consider the detection probability with respect to either the SNR or the observation length for a fixed value of false alarm probability (or a fixed value of the detection threshold). In this method (ROC curves) we compare the detection probability by varying the false alarm probability (or by varying the detection threshold) for a given SNR level and signal observation length. The receiver operating characteristics (ROC) curves are the plot of false alarm probability values on the x-axis and the corresponding detection probability values on the y-axis (PD vs PFA) by varying the detection threshold l. ROC curve analysis is quite common for analyzing the performance of any standard detectors (for example, in communications engineering applications). The ROC curves can also be used to analyze the performance for different values of SNR, T or N by comparing the curves on the same ROC figure. Moreover, ROC analysis is the best method to compare the detection performances of different detection algorithms and techniques. In the subsequent chapters, when different spectrum sensing and detection techniques are presented, we will use the ROC curves to compare the performances. An alternative performance measure to the ROC curve is the complementary-ROC (C-ROC) curve. The C-ROC curve is the plot of false alarm probability values on the x-axis and the misdetection probabilities on the yaxis (PM vs PFA) by varying the detection threshold. Both ROC and C-ROC convey the same results and considering either one of them is sufficient for analyzing the detection performance of spectrum sensing techniques. 2.4.4  Area Under the ROC Curves

The ROC curves provide relative performance for spectrum sensing considering different techniques and by varying different parameters (such as the SNR, observation length, etc). The area under the ROC curve denoted as AUC is a good figure of merit in order to compare detection performances of different spectrum sensing techniques with different parametric values [5, 6]. The AUC is quite useful, especially in the case when two or more ROC curves crossover each other, in which case comparison can only be made for portions of the ROC curve, with the use of AUC in such situations we are able to compare different ROC curves in overall. The AUC is defined by,

1

AUC (θ ) = ò PD (λ , θ )dPFA ( λ ) 0

(2.15)



Fundamentals of Spectrum Sensing and Detection

35

where q is some parameter that the detection probability PD depends on. Since PFA varies from 0 ® 1 when the detection threshold l is varied from ¥ ® 0, we can rewrite the definition in (2.15) for the AUC as [6],

¥

AUC (θ ) = - ò PD ( λ ,θ ) 0

¶PFA ( λ ) dλ ¶λ

(2.16)

The AUC(q) can be determined either analytically or computationally depending on whether a closed form expression for the integral in (2.16) is obtainable or not.

2.5  Wireless Channel Models The emitted signal from a radio user is transmitted through a wireless channel as depicted in Figure 2.1, which is an important aspect when analyzing the detection performance of spectrum sensing techniques. The communication channel for a wireless medium basically undergoes three types of degradation given by (a) mean pathloss, (b) shadowing on top of the mean path loss and (c) small scale fading on top of mean path loss and shadowing [7, 8]. In this section we briefly discuss such signal degradation in the context of detecting radio user signals in cognitive radio networks. 2.5.1  Mean Pathloss

The mean pathloss in wireless channels increase in proportional to the term da where d is the distance traveled by the signal and a is known as the pathloss exponent. In practice, a is experimentally measured by performing channel measurements over a distance of d. Typical values for the pathloss exponent a could roughly vary from 1.5 – 3.0 for indoor wireless channels and between 2.2 – 4.5 for outdoor wireless channels. α The pathloss at a distance d in meters is given by L(d ) = L(d 0 ) dd0 , where L(d0) is the pathloss at a reference distance d0 in meters which is given by the free-space pathloss [7] L(d0) = (4pfcd0/c)2, where c = 3 ´ 108 is the speed of light and fc is the carrier frequency.

( )

2.5.2  Shadowing

In reality, the pathloss over distance d varies randomly due to the obstacles in the propagating environment. The corresponding random variation in the

36

Cognitive Radio Techiniques

pathloss over larger ranges in the order of 100 – 1000 meters is known as shadowing. The most commonly known shadowing model is the log-normal model where the randomness in the pathloss over the mean pathloss is given by normal distribution in the dB scale, or in other words, the shadowing is modeled as a lognormal distribution. The pathloss based on the lognormal shadowing model is therefore given by,

Lshad (dB ) = L(dB ) + S (dB )

(2.17)

where, S(dB) is a normally distributed random variable with zero mean and variance σ s2(dB). Some of the other shadowing models that are commonly used in literature are the Hata model, the Okamura model, and the LongleyRice model [7]. 2.5.3  Small Scale Fading

The random pathloss effects with short range variations in the order of 1 – 10 meters is known as small scale fading. The small scale random fading is mainly caused by multipath propagation and the relative movements between the transmitter and the receiver units giving rise to the Doppler phenomenon. The two most known small scale fading models are the Rayleigh channel model and the Rice channel model. In the Rayleigh channel model, the received signal envelope R = |r(t)| follows a Rayleigh distributionin time given by,

f R (R ) =

æ R2 ö R exp ç - 2σ 2 ÷ σ2 è ø

(2.18)

for R > 0 and some parameter s 2 > 0. Rayleigh channels are used to model a typical communication channel without a line-of-site (NLOS) component [7]. Another well-known small-scale fading wireless channel model is the Rice channel model used to model wireless channels with line-of-site (LOS) transmissions [7]. In a Rice channel model, the received signal envelope follows a Rice distribution given by

f R (R ) =

æ R 2 + A2 ö æ R A ö R exp ç - 2σ 2 ÷ I 0 çè σ 2 ÷ø σ2 è ø

(2.19)

where, A is the peak amplitude of the dominant (LOS) signal and I0(.) is the modified Bessel function of the first kind and zeroth order.



37

Fundamentals of Spectrum Sensing and Detection

The derivation of various spectrum sensing and detection algorithms depend on the channel model in general. The corresponding detection performance also depends on the propagation effects (different channel models) as we see in the next chapter (Chapter 3). In general, for simplicity and analytical requirements, we consider either a shadowing model or a small-scale fading model together with the mean pathloss such that only one random model is present in the analysis.

2.6  Basic Models for Spectrum Occupancy The modeling of spectrum occupancy in real-life scenarios is very specific to the geographic region and time. Many models have been proposed based on various empirical data collected for the occupancy of spectrum [9–20]. In this section, we present some basic ways to model the spectral occupancy in the context of cognitive radio networks. Note that spectral occupancy models also provide us with the white space evolution models. The occupancy of the spectrum by a radio user basically depends on the two states occupied or notoccupied corresponding to the hypotheses H1 and H0, as defined previously. The spectrum evolutionary models or the spectrum occupancy models that we discuss here are based on the well-known teletraffic models. The traffic that we consider here is simply the traffic in the wireless channel. Some traffic patterns are relatively easier to model than the others, and in general, we take a stochastic modeling approach to be generic. Below we present some basic statistical models for the occupancy of spectrum based on the ON-OFF model. Note that with the ON-OFF model the traffic can be generated by a single radio user or many radio users. The corresponding states are also referred as ON and OFF periods. Figure 2.3 depicts the ON-OFF model of spectrum occupancy with random ON and random OFF periods. Note that better traffic models exist in literature based on self-similarity characteristics that we do not cover in this chapter.



 ON

OFF

ON

OFF

ON

OFF

ON

Time Figure 2.3  The ON-OFF spectral occupancy model.

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Cognitive Radio Techiniques

2.6.1  The Poisson-Exponential Model

The mostly commonly used model in teletraffic theory for analytical simplicity is the Poisson-exponential model. In this model the arrival process is modeled by a Poisson process with an arrival rate of mA. The number of arrivals (number of spectral occupancies) Nt over a period of t is given by a Poisson distribution given by:

Pr[ N t = k ] = f (k , µ At ) =

exp( - µ At )( µAt )k k!

(2.20)

in other words the probability of Nt = k number of spectral occupancies (the number of ON periods) in time t is given by the above probability. For the Poisson arrival model the time between the end of a previous transmission and the beginning of the successive transmission D (i.e., the time between successive spectral occupancies or the OFF periods) is given by an exponentially distributed random process given by:

f D ( D ) = µ A exp( - µA D )

(2.21)

with a mean interarrival time of E[ D ] = D = 1/µ A, where mA is also known as the birth rate. The occupancy time duration t (the duration of the ON period) here is also modeled as an exponentially distributed random process given by:

f τ (τ ) =

1 æ τö exp ç - ÷ è τø τ

(2.22)

with a mean occupancy time of E[τ ] = τ , where µD = 1/τ is known as the rate of the death process, the rate at which the spectral occupancies terminate. The Poisson-exponential model is traditionally used to model the call arrival process and the call duration process in telephony networks with sufficiently large number of subscribers (users). This model may not hold true if there is an insufficient number of users present to generate the traffic. 2.6.2  The Markov Modulated Poisson Process

In real-life situations, the arrival rate (or the mean time between arrivals) and the mean occupancy time are not constants in the longer run; they change with the time of the day, day of the week, and with the geographic location as well. The Markov modulated Poisson process (MMPP) is a better representa-



39

Fundamentals of Spectrum Sensing and Detection

tion of the real-world traffic compared to the previously discussed Poissonexponential process. The MPPP also uses a Poisson arrival process, but with a time-varying arrival rate given by mA(t). The time-varying arrival rate mA(t) is modulated by a Markov process, and hence the title–Markov modulated Poisson process–given to this model. The modulation process introduces correlation between the successive arrival times emulating real-life situations to a greater extent, and it has been used to model both voice and data traffic, as well as mixed traffic. The modulated Markov process can have any number of states and mA(t) depends on the state of the process, or in other words, how many users are using the spectrum at that given time. Correspondingly, the death rate also varies with time given by mD(t) and also depends on the state of the process, or in other words, how many users are currently occupying the spectrum. Suppose we consider an (N + 1)-state Markov model to represent a maximum of N users in the system each user i can have their own birth and i death rates given by µ iA and µD respectively. Using the properties of exponentially distributed random variables, the corresponding aggregated birth and death rates at a particular state n can be expressed as n µA

n

= å µiA i =1



n µD



(2.23)

n

i = å µD i =1

where n = 1,2...N. The corresponding MMPP-based spectrum occupancy is shown in Figure 2.4. If all the users have the same birth and death rates then (2.23) reduces to nmA = nmA and nmD = nmD. Moreover, when the number of



N A

0

(N1) A



1 A

N1

1 1 D





2 A

2 D

(N1) D

N N D

Figure 2.4  T he Markov modulated Poisson process, with birth rate of mA and death rate of mD.

40

Cognitive Radio Techiniques

states in the model is N = 2 then the corresponding model is known as the switched Poisson process. 2.6.3  The Poisson-Pareto Burst Process

Modeling the Internet traffic can be quite different from the standard voice data traffic models presented previously. The Poisson-Pareto Burst Process (PPBP) is a popular model for the Internet traffic as per the literature. In the Poisson-Pareto model, the requests for WEB sessions are modeled as a Poisson arrival process similar to the previously presented models and the packet lengths in time are modeled as a Pareto distributed random process [10]. The Pareto distribution is given by -k

æ τ ö F (τ i ) = 1 - ç i ÷ where τi ³ τ min è τ min ø



(2.24)

where, tmin Î + is a positive value describing the minimum packet length, and k > 0 is a parameter describing the spectral occupancy level of the radio user. Moreover, the mean and variance of t based on the Pareto model is given 2 /[(k - 1)2 (k - 2)] by E[τ ] = τ = kτ min /(k - 1) for k > 1, and E[(τ - τ )2 ] = kτ min for k > 2. Furthermore, during a WEB session, if Tp is the packet request length, TR is the length of the reading time (i.e., the time between the packets), and Np is the total number of packets per session, then Tp follows a Pareto distribution with cutoff [10], TR follows a Geometric distribution, and Np follows a Geometric distribution. Table 2.1 summarizes the spectral occupancy model based on the Poisson-Pareto Burst Process.

2.7  Stochastic Analysis of Radio Signals The radio signals in nature are time varying (nonstationary) and therefore time-frequency analysis of such signals require stochastic treatment. It is Table 2.1 The Spectral Occupancy Model Based on the Poisson-Pareto Burst Process Internet (WEB) Traffic Arrival process Packet length (Tp) Read time (TR) Number of packets per session (Np) Source: [10]

Model Poisson Pareto with cutoff Geometric Geometric



Fundamentals of Spectrum Sensing and Detection

41

important to know the statistical characteristics of the target signals to be detected in order to understand the detection performance when using a particular class of detector. It is hard to predict the signal coherence time that is the time duration where the radio signal remains stationary in real-life scenarios. Therefore, in order to extract the actual time-frequency distribution, many methods have been proposed in literature [21], out of which a wellknown method is the short-term Fourier analysis, giving us the Spectrogram. The time duration for the short-term Fourier transform analysis needs to be such that all the time-varying information is captured in the analysis and, at the same time, it does not lead to a considerable amount of computational overhead. The review article on time-frequency distribution by Cohen [21] provides an extensive overview of the topic, and we refer the readers to this article for further reading. Figure 2.5 depicts a typical time-frequency distribution of nonstationary wireless signal captured in the 2.4 GHz frequency band over a time period of 700 msec. The time-frequency distribution may help one to understand the radio signal power variation in time at a particular frequency band which would, in turn, effect the detection performance of the spectrum sensing technique.

Figure 2.5  A  n example of a time-frequency distribution of a time varying wireless signal at 2.4 GHz.

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Cognitive Radio Techiniques

2.8 Blind, Partial, and Complete Context Aware Signal Detection The spectrum sensing and radio signal detection techniques, in a way, can be classified as blind detection, partial-context aware detection, or complete context aware detection. Statistically, utilizing any known information in the detection process would further improve the detection performance; depending on the knowledge of the target signal to be detected, we could design our algorithm appropriately. 2.8.1  Blind Signal Detection

The spectrum sensing and detection techniques that are used to detect signals with no prior information are known as blind signal detectors. In this category, the target radio signals may be of any form and may have any statistical characteristics in general. 2.8.2  Partial-Context Aware Signal Detection

The spectrum sensing and detection techniques that are used to detect signals with some prior knowledge are known as partial-context aware signal detectors. The detector (i.e., the cognitive radio node performing the spectrum sensing functionality) would have some degree of knowledge about the target radio signals to be detected. For example, such information may include the transmission carrier frequency, symbol time duration or the baud rate, preamble sequences, or channel state information. 2.8.3  Fully Context Aware Signal Detection

When the entire information of the transmitted radio signal is known at the cognitive radio node, the corresponding spectrum sensing and detection techniques utilizing all the signal information to detect the signal are classified as fully context aware signal detectors. One could think of such a scenario where a signal is intended to be transmitted to a particular receiver and thus the receiver would have the complete knowledge of the transmitted signal (apart from the channel state information in some situations). In the fully contextaware category of detectors, the channel state information is also known to the cognitive radio node together with the transmitted signal information.



Fundamentals of Spectrum Sensing and Detection

43

2.9  Summary In this chapter, some prerequisites were presented to follow the subsequent chapters on spectrum sensing techniques in cognitive radio networks. Mainly, the topic on statistical detection methods was summarized, which is a key element of spectrum sensing and detection. Furthermore, the detection performance measures, wireless channel models, and some basic easy-toanalyze spectral occupancy models were covered in the context of detecting real-world radio signals, which are time-varying in nature with a given spatiotemporal spectral occupancy characteristic expected to affect the detection performance in general.

References   [1] Yucek, T., and H. Arslan, “A Survey of Spectrum Sensing Algorithms for Cognitive Radio Applications,” IEEE Communications Surveys and Tutorials, Vol. 11, No. 1, 2009, pp. 116­–130.   [2] Kandeepan, S., et al., Project Report-“D2.1.1: Spectrum Sensing and Monitoring,” EUWB Integrated Project, European Commission funded project (EC: FP7-ICT215669), May 2009, http://www.euwb.eu.   [3] Poor, H. V., An Introduction to Signal Detection and Estimation, Second Edition, New York: Springer-Verlag, 1994.   [4] Kay, S. M., Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory, Englewood Cliffs, NJ: Prentice Hall, 1998.   [5] Hanley, J. A., and B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology, Vol. 143, No. 1, 1982, pp. 29–36.   [6] Atapattu, S., C. Tellambura, and H. Jiang, “Analysis of Area under the ROC Curve of Energy Detection,” IEEE Transactions On Wireless Communications, Vol. 9, No. 3, 2010.   [7] Rappaport, T. S., Wireless Communications: Principles and Practice, Englewood Cliffs, NJ: Prentice-Hall, 1996.   [8] Goldsmith, A., Wireless Communications, New York: Cambridge University Press, 2005.   [9] Adas, A., “Traffic Models in Broadband Networks,” IEEE Communications Magazine, Vol. 35, No. 7, 1997. [10] Janevski, T., Traffic Analysis and Design of Wireless IP Networks, Norwood, MA: Artech House, 2003. [11] Lpez-Bentez, M., A. Umbert, and F. Casadevall, “Evaluation of Spectrum Occupancy in Spain for Cognitive Radio Applications,” IEEE VTC Spring, Barcelona, Spain, 2009.

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[12] Klemm, A., C. Lindemann, and M. Lohmann, “Traffic Modeling and Characterization for UMTS Networks,” IEEE Globecom, San Antonio, TX, 2001, pp. 1741–1746. [13] el Allali, H., and G. Heijenk, “Traffic characterization for a UMTS radio access network,” IEEE Workshop on Mobile and Wireless Communications Network, Stockholm, 2002, pp. 497–501. [14] Janowski, L., T. Ziegler, and E. Hasenleithner, “A Scaling Analysis of UMTS Traffic,” Proceedings of the 6th International Conference on Next Generation Teletraffic and Wired/ Wireless Advanced Networking, May 2006, St. Petersburg, pp. 211–222. [15] Jabbari, B., “Teletraffic aspects of evolving and next-generation wireless communication networks,” IEEE Personal Communications, Vol. 3, No. 6, 1996, pp. 4–9. [16] Yuguang, F., C. Imrich, and L. Yi-Bing, “Modeling PCS Networks Under General Call Holding Time and Cell Residence Time Distributions,” IEEE/ACM Trans. on Networking, Vol. 5, No. 6, 1997. [17] Mah, B.A., “An Empirical Model of HTTP Network Traffic,” IEEE INFOCOM ’97, Kobe, Japan, Vol. 2, 1997, pp. 592–600. [18] Bolotin, V. A., “Modeling Call Holding Time Distributions for CCS Network Design and Performance Analysis,” IEEE Journal on Selected Areas in Communications, Vol. 12, No. 3, 1994. [19] Barcel, F., and S. Bueno, “Idle and Inter-arrival Time Statistics in Public Access Mobile Radio (PAMR) Systems,” IEEE GLOBECOM ’97, Phoenix, AZ, 1997. [20] Kandeepan, S., A. Sierra, J. Campos, and I. Chlamtac, “Periodic Sensing in Cognitive Radios for Detecting UMTS/HSDPA Based on Experimental Spectral Occupancy Statistics,” Proceedings of IEEE Wireless Communications and Networking Conference (WCNC), Sydney, Australia, 2010. [21] Cohen, L., “Time-Frequency Distributions–A Review,” IEEE Proceedings, Vol. 77, No. 7, 1989, pp 941–981.

3 Introduction to Spectrum S­ensing Technique­s The topic of spectrum sensing and primary user detection has gained a great deal of interest in the context of cognitive radios for dynamic spectrum access networks. Spectrum sensing is one of the crucial functionalities of a cognitive radio in order to learn the radio environment. In literature, one, can find various spectrum sensing techniques [1, 2] which, in general, could be classified as (1) energy-based sensing, (2) cyclostationary feature-based sensing, (3) matched filter-based sensing and (4) other sensing techniques. Different techniques serve different purposes based on their advantages and drawbacks. The energy-based sensing is the simplest method to sense the environment in a blind manner; the cyclostationary-based sensing may require some information about the spectraluser signal characteristics; and the matched filter-based sensing requires the complete information of the spectral-user signal, which are presented in detail in this chapter. Some of the other techniques, such as the covariance-based method and the eigenvalue-based method, are also presented.

3.1  Introduction The recent interest in cognitive radio-related research has attracted a great deal of interest in spectrum sensing and detection of radio users in the 45

46

Cognitive Radio Techniques

e­ nvironment. The key objective behind spectrum sensing and detection is to see how reliably one could detect the radio users given a particular scenario with an acceptable payoff or trade-off. In other words, the main objective is to maximize the probability of detection without losing much on the probability of false alarm while minimizing the complexity and time to sense/detect the radio. In this section, we present various methods and techniques to detect the radio users in the environment. Let us define the signal model to be used in the rest of the chapter. Following from the previous chapter, we define two hypothesis H0 and H1 to represent the presence of a radio signal, the corresponding signal model is given by

ν(t ); under H 0 ïî hs(t )+ν(t ); under H1 ì ï

r (t ) = í

(3.1)

where r(t) is the complex baseband of the sensed radio signal, s(t) is the received primary user signal, and n(t) is the additive bandlimited complex Gaussian noise with a noise power of s 2 (including the real and imaginary noise components) over a bandwidth of Bw (Hz). The channel component h has an amplitude and phase shift associated with it given by h = aÐq°. Various models can be adopted for the received radio signal s(t) without the noise component, depending on the considered wireless channel. In the subsequent sections, we consider different channel models and present their corresponding detection performances.

3.2  Spectrum Sensing with Energy Detection The energy based spectrum sensing and detection is the simplest method for detecting primary users in the environment in a blind manner [3]. The energy detector is computationally efficient and could also be used conveniently with analog and digital signals, that is at the RF/IF stages or at the base band. It also has a well-known drawback in the detection performance when the noise variance is unknown to the sensing node. When the signal-to-noise ratio is very low, it would be hard distinguish between the radio signal and noise signal, therefore the knowledge of the noise power can be used to improve the detection performance of the energy detector. 3.2.1  Energy Detector

In energy-based detectors, the energy-metric of the received signal is computed over a given time period T, or equivalently over N samples in the dis-



Introduction to Spectrum S­ensing Technique­s

47

crete domain, and is used as the test statistic for the detection, where T = NTs and Ts is the signal sampling period. From the GLRT in the previous chapter it can be shown that the energy detector is optimum when s(t) is zero mean complex Gaussian [4]. Considering the signal model given by (3.1) the test statistic for the energy detector is given by ξ=ò



t0 +T

t0

r (t )r�(t )dt

(3.2)

where, r�(t ) is the complex conjugate of r(t) and t0 Î R+ is an arbitrary starting time. The signal-to-noise ratio r is then defined based on the received signal s(t) assuming the signal is present throughout within the time period of consideration t1 < t £ t2 for some t1, t2 Î R+, given by

ρ=

t2 α2 s(t )�s (t )dt ò 2 σ [t 2 - t1 ] t1

(3.3)

For the discrete signal r[n] = r(nTs) the energy-based test statistic is given by

ξ » Ts

N -1

å r[n]r�[n]

(3.4)

n=0

where, N is the total number of complex samples and is also known as the time-bandwidth product, which is a metric that defines the performance of the energy based detector [3]. If T is the total sensing duration, then the time-bandwidth product is given by TBw = NTs fs = N, where f s = 1/Ts is the bandwidth of the discrete baseband signal r[n]. Note that in (3.4) there are essentially N number of real component samples and N number of imaginary component samples present, giving us a total of 2N samples. The detection criteria based on the energy-based test statistic is then given by

ì0; d =í î1;

ξ< λ ξ³ λ

(3.5)

Choosing the appropriate value for the threshold l is a challenging task, which we present later in this section. 3.2.2  Energy Detector in Gaussian Channel

In order to compute the detection probability and the false alarm probability, we consider the distribution of the test statistic x. For the Gaussian channel with h = 1 Ð 0°, the energy based test statistic x follows a non central and a

48

Cognitive Radio Techniques

central chi-squared distribution under H0 and H1 respectively with 2N d­egrees of freedom [3]. Using the distributions of the test statistic under H0 and H1, we can derive the detection probability and the false alarm probability as [6],

PD = Pr[ξ > λ ; under H1 ] = Q N ( 2TBw ρ , λ )

(3.6)



PFA = Pr[ξ > λ; under H 0 ] = Γ(TBw , λ / 2)

(3.7)

¥

where, G( a , b ) = G(1N ) ò u a -1 exp( -u )du is the regularized upper incomplete b ¥ Gamma function, G(.) is the Gamma function, Q N (a,b) = ò uN exp(–(u2 + b a2)/2)IN–1(au)/aN–1du is the generalized Marcum Q-function, and IN–1(.) is the modified Bessel function of first kind with order N – 1. Let us look at some results for the detection performance of the energy detector in the additive Gaussian noise channel by plotting the complementary receiver operating characteristics (C-ROC) curve. The C-ROC depicts the probability of false alarm in the x-axis and probability of misdetection in the y-axis. Figure 3.1 shows the C-ROC curves for the energy detector for various values of signal to noise ratio levels r. As we observe from the figure, the detection performance improves with increasing values of r by achieving lower misdetection 10

0

10

-2

10

-4

10

6

10

-8

Prof of Misdetection

ρ = 0dB

ρ = 7dB

ρ = 10dB

N = 10 -10

10

-10

10

-8

10

10

-6

10

-4

10

-2

10

0

Prof of False Alarm

Figure 3.1  C  omplementary ROC curves for the energy detector for various signal to noise ratio levels.



49

Introduction to Spectrum S­ensing Technique­s

Prof of Misdetection

10

0

10

-2

10

-4

10

-6

10

-8

10

-10

N = 10

N = 30

N = 50

ρ = 5 dB 10

-10

10

-8

10

-6

10

-4

10

-2

10

0

Prof of False Alarm

Figure 3.2  C  omplementary ROC curves for the energy detector for various values of timebandwidth product N.

probabilities for lower false alarm probabilities when r increases. Figure 3.2, on the other hand, shows the C-ROC curves for various values of N, and again we observe that the detection performance improves with increasing values of N. Note that the analytical results presented here do not consider the wireless channel effects, such as fading or shadowing. In the subsequent sections, we present the energy detector performance under various wireless channel conditions. Threshold Selection: The detection and false alarm probabilities depend on the threshold l, and hence it is necessary to choose an appropriate value based on our requirements. The detection probability also depends on the signal’s power and the time-bandwidth product, whereas the false alarm probability depends only on the time-bandwidth product apart from the threshold. Therefore, one approach to choose the threshold for a given time-bandwidth product is to select l to meet the desired false alarm probability. 3.2.3  Energy Detector in Fading Channels

The energy detector performance varies when the received signal component s(t) in (3.1) undergoes different types of fading. The authors in [5–7] have

50

Cognitive Radio Techniques

derived the detection performance of energy detector for Rayleigh, Rice, and Nakagami types of fading channels with additive Gaussian noise, which we present here considering no diversity reception. Different types of distributions for the signal-energy-to-noise-power-spectral-density-ratio g = a 2Es / N0 = Nr are considered to derive the detection performance under different channel models. The corresponding probability density functions are then averaged over (3.6) to compute the detection probability, given by, PD = ò Q N ( a ρ , b ) f ρ ( ρ )dρ



(3.8)

R

where a = 2TBw and b = λ . Note that the false alarm probability is unchanged from (3.7) because it does not depend on s(t) under H0. 3.2.3.1  Rayleigh Channel

The probability density function of g in a Rayleigh fading channel is given by æ γö 1 (3.9) f γ (γ ) = exp ç - ÷ for γ ³ 0 γ è γø where γ = E[ γ ] is the mean signal-to-noise ratio. Then by using (3.8) a closed form expression for the detection probability can be derived, given by N-2 1 æ λ ö æ1+ γ ö æ -λ ö PD = exp ç ÷å ç ÷ +ç ÷ 2 n è ø n =0 ! è 2 ø è γ ø n



é ê æ -λ ´ êexp ç 2 + 2γ êë è

N- 2 ö æ -λ ö exp ç ÷ å ÷ è 2 ø n =0 ø

N -1

(

)

λγ nù 2(1+γ ) ú

n!

ú úû

(3.10)

Note that in [6] the authors have considered a total of N samples (N/2 for the inphase and N/2 for the quadrature), whereas we have considered a total of 2N samples (N for the inphase and N for the quadrature). 3.2.3.2  Rice Channel

The probability density function of g in a Rice fading channel is given by æ 1+ K (1 + K )γ ö æç K (1 + K ) γ ö÷ f γ (γ ) = exp ç - K for γ ³ 0 ÷ø I 0 ç 2 ÷ γ γ γ è è ø (3.11) . In [6] and [7], the authors have a considered a different energy-based test statistic which is a scaled version of that presented in (3.2).



Introduction to Spectrum S­ensing Technique­s

51

where, ρ = E[ ρ] is the mean signal-to-noise ratio and K is the Rician factor. Then by using (3.8) authors in [7] have derived a closed form expression for the detection probability for N=1, given by

æ

PD = Q ç ç è

2K γ λ(1 + K ) ö÷ , 1 + K + γ 1 + K + γ ÷ø

(3.12)

3.2.3.3  Nakagami Channel

The probability density function of g in a Nakagami type fading channel is given by m



æ mγ ö 1 æ m ö m -1 f γ (γ ) = γ exp ç for γ ³ 0 ç ÷ G(m ) è γ ø è γ ÷ø

(3.13)

where, m is the Nakagami parameter and γ = E [γ ]. Again, by using (3.8) authors in [6] have derived a closed form expression for the detection probability given by

N -1 (λ /2)u λ(1 - β ) ö æ λö æ PD = A1 + β m exp ç - ÷ å 1F1 ç m;1 + u; ÷ (3.14) è 2ø è u 2 ø u =1

where, β = m/(m + γ ) and 1F1(.;.;.) is the confluent hypergeometric function, and A1 for integer values of m is given by m-2 æ λβ ö é m -1 æ - λ(1 - β ) ö æ - λ(1 - β ) ö ù A1 = exp ç β Lm -1 ç + (1 - β ) å β i Li ç ê ÷ ÷ ÷ø ú è 2m ø ê è ø è 2 2 úû i =0 ë (3.15)

where, Li(.) is the Laguerre polynomial of degree i. The authors in [6, 7] have also presented similar analytical results for the detection performance of the energy detector for the case of diversity reception in fading channels. 3.2.4

Energy Detector in Fading Channels with Shadowing

The detection performance of the energy detector for small scale fading channels were presented in the previous section. Here we present the same for received signals undergoing fading and shadowing simultaneously. The authors in [8] present the detection probability in closed-form considering Gamma distributed shadowing model under Rayleigh and Nakagami fading channels. They show that the detection probability for the shadowing case with fading can derived by considering γ as a Gamma distributed random variable (the shadowing component) in the expressions for PD under fading channels [in

52

Cognitive Radio Techniques

(3.10), (3.12) and (3.14)], and then average it out for all values of γ . The detection probability therefore is given by PD = ∫ Pd f γ |γ (γ )dγ f γ ( γ )d γ = ∫ PD f γ (γ )d γ





(3.16)

where, Pd is the detection probability under Gaussian channel, f γ |γ (γ ) is the probability density function of of g under a given fading channel conditioned on γ , PD is the detection probability under fading and Gaussian noise channel (without shadowing), and f γ (γ ) is probability density function describing the shadowing component modeled as a Gamma distribution given by y k −1 exp( − y /Ω ) (3.17) , for y ≥ 0 Γ(k )Ω k where, k and W are the parameters describing the shadowing model. Considering a Rayleigh fading channel, the detection probability for the energy detector for the Gamma distributed shadowing model then given by fγ ( y) =



λ N -2 1 æ λ ö PD = exp( - ) å ç ÷ 2 n = 0 n! è 2 ø

n

+

¥ 1 1 æ -λ ö 1ö æ G(k - N + 1)U ç k - N + 1; k - n + 1; ÷ ÷ k å n! ç è Ωø G(k )Ω n = 0 è 2 ø

-

exp( -λ /2) N - 2 1 æ λ ö 1ö æ G(n + k - N + 1)U ç n + k - N + 1; k + 1; ÷ ÷ k å n! ç è Ωø G(k )Ω n = 0 è 2 ø

n

n



(3.18)

where, N < k + 1 and U(.;.;.) is the confluent hypergeometric function of the second kind. The authors in [8] also present a closed form expression for the detection probability for the energy detector considering Nakagami fading channel with Gamma distributed shadowing model.

3.3  Energy Detection and Noise Power Uncertainty If the noise power level is perfectly known at the receiver, the energy director (ED) can work with arbitrary values of probability of detection and probability . The authors would like to thank Andrea Mariani (Ph.D. student, University of Bologna) for his contribution to Section 3.3.



Introduction to Spectrum S­ensing Technique­s

53

of false alarm, even in low SNR regimes, by using a sufficiently long observation time. H­owever, in real systems we do not have a perfect knowledge of the noise power level, causing critical implications for energy detection design. The main two problems derived from noise uncertainty are ED threshold setting [9] and the so called SNR wall [10–12]. 3.3.1  ED Threshold Mismatch

The typical approach for setting the threshold in energy detection is given by the constant false alarm rate (CFAR) strategy, in which the threshold value DES is chosen in order to guarantee a target false alarm rate, PFA , and can be obtained inverting the analytical expression of the false alarm probability. From (3.7) we get

(

)

DES λ CFAR = 2 G -1 TBw , PFA

(3.19)

In this approach, the threshold selected depends on the noise power level, s 2. The actual noise power is generally unknown, so we assume that the re­ceiver has 2 its estimate σ� that is typically obtained through a calibration process, and in general, is different from s 2. Therefore, in practical applications, we always must consider the adoption of an ED with estimated noise power (ENP) in 2 place of the ideal ED. The adoption of σ� for threshold setting can cause severe performance degradations. If the uncertain value s 2 is obtained as noise power estimate, threshold mismatch can be avoided including the statistic of the estimator in the probability of false alarm and probability of detection formulas [9, 10, 13]. 3.3.2  SNR Wall

An alternative representation of the performance of the ED is given by the so called design curves [9–11, 13]. The design curve is the relation between the SNR and the number of samples N required to guarantee the desired detecDES tion performance, PFA < PFA and PD > PDDES . Note that, given the sampling frequency, the number of samples is proportional to the time needed for the detection task. Then, the design curve can also be considered as the minimum signal-to-noise ratio, SNRmin, needed to fulfil the detection specification for a given sensing time. The design curve can be derived from the expressions of

54

Cognitive Radio Techniques

the probability of false alarm and probability of detection. For the ideal ED, it can be approximated as [10] SNRmin,ED �



( ) (P )

DES 1 + Q -1 PFA

1 N

1 + Q -1

1 N

DES D

- 1

(3.20)

where Q –1(.) is the inverse of the Gaussian tail function. For the ideal ED, the minimum SNR satisfying the target detection performance can be reduced, increasing the observation time. The ideal ED design curve is plotted DES in Figure 3.3 (continuous curve), with PFA = 0.1 and PDDES = 0.9. Note that, when N is sufficiently high, the design curve has asymptotically a linear trend on a log-log scale, with a slope of –5 dB/decade [13, 14]. In practical implementations however, the noise uncertainty can cause a severe degradation of the detector performance. In particular, in some practical situations, the design curve has a lower SNR limit, under which the detection is impossible even if the observation time tends to infinity. This is the so called SNR wall phenomenon. In presence of noise uncertainty, a very popular design strategy adopted in literature is to consider; the estimated noise variance is constrained into a 20 Ideal ED ENP-ED, ENP-ED, BWB-ED,

SNR min [dB]

10

M = N M = 1000  = 1 dB

0

10

20

30

10

1

10

2

10

3

N

10

4

10

5

PDES = 0.1 and PDPDES = 0.9. The Figure 3.3  D  esign curves for the ideal ED, ENP-ED with PFA 2 2 /σ min = 1 dB is also shown. corresponding BWB curve with ρ = σ max



Introduction to Spectrum S­ensing Technique­s

(

55

)

2 2 , σ max limited range, defined by σ min , that contains also the real noise power 2 level s [11, 12, 14]. This design strategy is called “bounded worse behavior” (BWB). In this situation, the common approach is to consider a worst case strategy, in which the probability of false alarm is evaluated when the esti2 mated noise power assumes the lowest value σ min , while for the probability of 2 detection it assumes the highest value σ max . Then the corresponding design curve is given by



SNRmin,BWB �

( (

DES 2 1 + Q -1 PFA σ max × 2 σ min 1 + Q -1 PDDES

) )

1 N 1 N

- 1

(3.21)

that gives raise to the SNR wall

lim SNRmin,BWB =

N ®¥

2 σ max - 1 > 0 2 σ min

(3.22)

Due to the adoption of this design strategy and noise uncertainty model, an idea that is raised into the spectrum sensing community is that the SNR wall phenomenon is an unavoidable problem in practical applications. 3.3.3  Existence of the SNR Wall

Recently, it has been demonstrated that the SNR wall can be avoided if the ENP has a sufficient accuracy [10, 13]. In particular, the two conditions for avoiding the SNR wall are: 1. The correct statistic of the noise power estimator must be considered in the evaluation of the decision threshold. 2. The variance of the ENP must decrease faster then 1/N when the observation time grows. Note that, even if the second condition cannot be satisfied, the adoption of the correct statistical model of the problem allows to predict the correct value of the SNR wall. In a situation in which the two conditions above cannot be satisfied, the BWB approach is the unique solution; however, not only it always predicts the presence of the wall, but it also generally overestimates its value [10]. Indeed, as we can see from (3.22), in this case the SNR wall value 2 2 ,σ max is determined by the choice of σ min .

(

)

56

Cognitive Radio Techniques

As an example of ENP-ED, assume that M noise only samples, wn with n = 0,…,M – 1, are available at the receiver. Then we can adopt the maximum likelihood noise power estimator defined by 2 σ� = Ts



M −1

∑ w[n]w�[n]

(3.23)

n =0

2

The variance of σ� is s 2/M. In this case, the design curve of the ENP-ED is given by [27]

SNRmin,ENP − ED

DES  2 1 + Q −1  PFA  σ max   � 2 ⋅ − 1 DES σ min 1 + Q  PD  



N +M NM N +M NM

− 1

(3.24)

It is easy to see that, in accordance to the condition ii, the SNR wall does not occur (i.e., limN®¥SNRmin,ENP–ED = 0) only if M is an increasing function of N. Figure 3.3 shows and compares performance of an ideal ED and ENPDES ED with PFA = 0.1 and PDDES = 0.9. As can be seen, when M = N (the number of samples used to estimate noise power) is equal to the number of samples used for detection, the ENP-ED does not exhibit the SNR wall (according to condition ii) and the slope of the design curves is the same. In this situation, only a loss of around 1.5 dB, when N > 100, is noticeable. On the contrary, if M = 1000 is fixed with respect to N, the SNR wall occurs. For comparison, the 2 2 corresponding BWB-ED design curve with ρ = σ max /σ min = 1 dB is also shown. As can be seem, the BWB-based ED design may lead to an incorrect threshold design.

3.4  Spectrum Sensing with Cyclostationary Feature Detection In wireless communications, the transmitted signals show very strong cy­ clostationary features based on the modulation type, carrier frequency, and data rate, especially when excess bandwidth is utilized. Therefore, identifying the unique set of features of a particular radio signal for a given wireless access system can be used to detect the system based on the cyclostationary analysis at the cognitive radio node. The cyclostationary feature analysis is a well developed and treated topic in the literature of signal processing [15, 16]. 3.  These samples can be captured in a signal free time window or in a free frequency band.



Introduction to Spectrum S­ensing Technique­s

57

In the context of cognitive radios, we consider using such analysis for spectrum sensing and primary user detection [17–20], in which case some degree of source signal knowledge may be required. For a sufficient number of samples, this method can perform better than the energy-based detection method when the cyclostationary features are properly identified. However, the main drawback with this method is the complexity associated with it and the requirement for a large sample set for better estimation and precision of the features in the frequency domain. We present some of the fundamentals of cyclostationary feature analysis below and show how it can be used as a spectrum sensing technique to detect primary users in the environment for cognitive radio networks. 3.4.1  Cyclostationarity Analysis

A random process x(t) is classified as a wide sense cyclostationary process if the mean and autocorrelation are periodic in time with some period T, given by

E x (t ) = E x (t + mT ) = E[ x (t )]

(3.25)

Rx (t , τ ) = Rx (t + mT ,τ ) = E[ x(t )x�(t + τ )]

(3.26)

and

where, t is the time variable, t is the lag associated with the autocorrelation function, x�(t ) is the complex conjugate of x(t), and m is an integer. The periodic autocorrelation function can be expressed in terms of the Fourier series given by

¥

å

Rx (t , τ ) =

Rxα (τ )exp(2 π jα t )

(3.27)

α =-¥

where,

Rxα (τ ) = lim

1

ò

T ®¥ T T

τ τ x(t + )x�(t - )exp( -2 π jα t )dt 2 2

(3.28)

The expression in (3.28) is known as the cycle autocorrelation. Using the Wiener relationship, we can define the cyclic power spectrum (CPS) or the spectral correlation function as,

S xα ( f ) = ò

¥

-¥

Rxα (τ )exp( - j 2 π f τ )dτ

(3.29)

58

Cognitive Radio Techniques

The CPS in (3.29) is a function of the frequency f and the cycle frequency a and any cyclostationary features can be detected in the cyclic frequency domain a property that is exploited to be used as a spectrum sensing technique. An alternative expression for (3.28) for the ease of computing the CPS is given by 1 T0 ®¥ T ®¥ T0T

S xα ( f ) = lim lim



T0 / 2

ò-T /2 XT (t , f 0

+

1 1 ) X�T (t , f - )dt (3.30) α α

where, X�T (t , u ) is the complex conjugate of XT (t,u), and XT (t,u) is given by XT (t , u ) = ò



t +T / 2

t -T / 2

x(v )exp( -2 jπ uv )dv

(3.31)

Expression in (3.30) is also known as the time-averaged CPS, which achieves the theoretical CPS when computed over a sufficient number of samples. Frequency-averaged CPS can also be derived similar to the time-averaged one as given in [21]. Let us observe some examples for the CPS. Figure 3.4 depicts a CPS plot for BPSK modulated signal estimated over 2,000 symbols at a signal

0.04



Sx

0.02 0 50 50 f(Hz)

0

0 50

(Hz)

50

Figure 3.4  C  yclic spectral density for BPSK with a signal to noise (power) ratio of 0 dB estimated over 2000 BPSK symbols.



59

Introduction to Spectrum S­ensing Technique­s

0.06

 Sx

0.04 0.02 0 50

50 f(Hz)

0

0 (Hz) 50 50

Figure 3.5  C  yclic spectral density for BPSK with a signal to noise (power) ratio of 0 dB estimated over 20 BPSK symbols.

to noise ratio of 0 dB. Figure 3.5 on the other hand depicts the same for an estimation over 20 BPSK symbols at the same signal-to-noise ratio level. These figures clearly show how the estimate of the CPS varies depending on the number of samples used, and we observe that with a poor estimate of the CPS noise can be seen at cyclic frequencies other than a = 0 (Figure 3.5). With a better estimate of the CPS (Figure 3.4), we can clearly identify the cyclic frequency components and the additive noise component appearing at a = 0. Therefore, using the CPS one could detect the presence of the primary user provided that the CPS is estimated properly. In the next section, we see how the CPS can be used to detect the presence of primary users by cognitive radios. 3.4.2  Cyclostationary Feature-Based Detector

In order to use the cyclostationary features to perform spectrum sensing in wireless communications, we can rewrite the hypothesis equation for the presence of a primary user signal considering the CPS as

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Cognitive Radio Techniques

H 0 : Srα ( f ) = Sνα ( f )

H1 : Srα ( f ) = Ssα ( f ) + Sνα ( f )

(3.32)

where, Sνα ( f ) is the CPS of the additive noise u(t), and Ssα ( f ) is the CPS of the primary user signal s(t). Since n(t) is not a cyclostationary process, the CPS of n for a ¹ 0 is zero. Based on this, we can derive the test statistic for the detector in the discrete domain as

ξ=

å å Srα ( f )S�αr ( f )

(3.33)

α ,α ¹ 0 f

where, S�αr ( f ) is the conjugate of Srα ( f ). The detector is then given by

ì0; d =í î1;

ξ< λ ξ³λ

(3.34)

An important point to note here is that one needs sufficient number of samples to get a good estimate of the CPS and hence this method is not so computationally efficient. Furthermore, when insufficient number of samples are used the detection performance will tend to get worse due to the poor estimate of the CPS. If the target (primary user) signal information is somewhat known a priori (such as the modulation type, code rate, symbol rate, etc.), then the test statistic in (3.33) may be simplified to search for specific values of a corresponding to the target signal. For analog amplitude, phase and frequency modulated signals with a carrier frequency of f 0 the cyclic frequency components are observed at ± 2f 0, and for digital amplitude shift keying and (binary) phase shift keying signals with symbol rate 1/T0 and a carrier frequency of f 0 the cyclic frequency components are observed at k/T0 for k Î, k ¹ 0 and ± 2f 0 + k/T0 for "k Î . Therefore, if the primary user signal falls into one of the signal categories mentioned above, the cognitive radio device can use the signal information to compute its test statistic targeting the specific values of a.

3.5  Spectrum Sensing with Matched Filter Detection The matched filter detection based sensing is exactly the same as the traditional matched filter detection technique deployed in digital receivers. Obviously for match filter based spectrum sensing a complete knowledge



Introduction to Spectrum S­ensing Technique­s

61

t=T r(t)

h(t) = s(T  t)

Figure 3.6  Matched filter based spectrum sensing and detection of primary users.

of the primary user signal is required (such as the modulation format data rate, carrier frequency, pulse shape, etc). The matched filter detection technique is a very well-treated topic in literature, and therefore, we just present the fundamental results on matched filter detection in this section. Given a real transmit signal waveform s(t) defined over 0 £ t £ T the corresponding matched filter maximizing the signal to noise ratio at the output of the filter sampler is given by ì s(T - t ); 0 £ t £ T (3.35) h(t ) = í 0; elsewhere î Figure 3.6 depicts matched filter based spectrum sensing method for primary user detection. Considering that a complete signal information of the primary user signal is required in this case the matched filter method is not really recommended by the system designers to suit our purpose here unless when the complete signal information is known to the secondary user. Then based on the test statistic x(nT ) at the output of the filter sampled every t = nT seconds, the detector is given by ì 0; ξ(nT ) < λ d (nT ) = í (3.36) î 1; ξ(nT ) ³ λ The matched filter-based detector gives better detection probability compared to the previously discussed methods using the energy detector and the cyclostationary feature based detector; however as mentioned, it requires complete signal information and needs to perform the entire receiver operations (such as synchronization, demodulation, etc.) in order to detect the signal.

3.6  Other Spectrum Sensing Techniques Many techniques have been proposed in literature, apart from the ones mentioned before in this chapter. In the rest of this section, we present some of the other known techniques for spectrum sensing and primary user detection in cognitive radio applications.

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3.6.1  Covariance-Based Method

The covariance of wireless signals and the additive noise component are generally different. The difference therefore is used to detect the presence of a wireless signal by distinguishing from the noise signal. Zeng and Liang [22] have proposed test statistics derived from the sample covariance matrix of the received signal to perform signal detection. The sample covariance of the received discrete signal r[n] is given by



é R(0) ê R (1) ê ˆ ( u , v ) = RL ê . ê ë R (L - 1)

R (1) R (2) . R (L - 2)

… … … …

R(L -1) R(L -2) .. R(0)

ù ú ú ú ú û

(3.37)

and for a sample size of N the elements of the sample covariance matrix are given by

R (l ) =

1 N

N -1

å r[n]r�[n - l ] for

l = 0,1,…, L - 1

(3.38)

n =0

In the absence of a primary user signal (under hypothesis H0), the non­ ˆ L is theoretically zero, whereas diagonal element of the covariance matrix R the diagonal elements contain the noise power. In the presence of a primary user signal (under hypothesis H1), the nondiagonal elements would become nonzero, and thus using this property of the covariance matrix, one could detect the presence of the primary user signal. Based on this, Zeng and Liang [22] have proposed the following test statistics given by



T1 =

1 L L å å | Rˆ (u, v ) | L u =1 v =1 L

T2 =

1 L å | Rˆ (u, u ) | L u =1 L



(3.39)

and the detection criteria to make the decisions dˆ to decide on H0 or H1 is given by

ì 0; decide on H 0 ; dˆ = í î 1; decide on H1 ;

if T1/T2 < λ if T1 /T2 ³ λ

(3.40)



Introduction to Spectrum S­ensing Technique­s

63

As per the above-mentioned detection mechanism, it is assumed that the sensed wireless signals are correlated such that the resulting covariance matrix is not diagonal when signal is present (under hypothesis H1). 3.6.2  Eigenvalue-Based Method

The eigenvalue-based method for spectrum sensing and detection is also based on the computation of the covariance matrix of the sensed signal [22]. The eigenvalues of the covariance matrix are computed, and in turn, are used to compute the test statistic as given in [22]. Two test statistics are proposed by Zeng and Liang based on the maximum (Îmax) and the minimum (Îmin) eigenvalues. The first test statistic is given by

T =

∈max ≷ λ1 ∈min

(3.41)

known as the max-min eigenvalue (MME) technique for some threshold l1, and

T =

ξ ∈min



(3.42)

known as the energy with minimum eigenvalue (EME) technique for some threshold l2, where x is the energy of the sensed signal. The detection methods based on the test statistics above do not require the knowledge of the noise power but are based purely on the sensed signal itself, thus considered to be fully blind sensing techniques. 3.6.3  Wavelet-Based Edge Detection

The wavelet transform was proposed for spectrum sensing for detecting edges in a wideband spectrum in the frequency domain for detecting one or more narrowband users [23]. Wavelets transforms in general are used to detect irregularities/singularities in the power spectral density and thus proposed to be used for detecting spectral irregularities or in other words varying power levels in the spectral bands over a wide portion of the spectrum. This method is well suited especially for ultrawideband based cognitive radios that has a frequency band allocation from 3GHz – 10GHz with many narrowband incumbent and other users lying within such as WiMAX, C-band satellite, S-band satellite, Wi-Fi, and DECT. Figure 3.7 depicts the edge detection graphically considering a wide portion of the spectra. The wavelet detection

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Cognitive Radio Techniques

Edges

f(Hz) Figure 3.7  C  oncept of edge detection of narrowband spectral bands using wavelet ­transforms.

method avoids the requirement to have complex bandpass architectures in the receiver for detecting narrowband users for wideband sensing; however, it requires high sampling rate when operating the discrete domain. 3.6.4  Spectral Estimation Methods

Traditional spectral estimation methods can also be used for spectrum sensing and detection in cognitive radio networks [24, 25]. Parametric and nonparametric techniques exist in literature for spectral analysis and estimation. The former method requires a well-defined model for the sensed signal to get good results and thus is not much considered in cognitive radio applications. The nonparametric method is therefore considered to be suitable for spectrum sensing in cognitive radios which we briefly present here. We mainly consider two nonparametric methods, first the multitaper method [26, 27], and second the filter bank based method [28]. 3.6.4.1  Multitaper Method

In the multitaper method–where taper indicating the windowing function of the signal samples–orthonormal Slepian sequences are considered for the tapers. The Slepian sequences have a distinguished property where most of the energy of its Fourier transforms have their energy within a given frequency band for a finitie sample size. This allows one to trade the spectral resolution for reduced variance of the spectral estimate without leaking signal energy into adjacent bands. This, therefore, is considered to be a well-suited technique for spectrum sensing in cognitive radio networks.



Introduction to Spectrum S­ensing Technique­s

65

3.6.4.2  Filter Bank Method

In the filter bank method, a set of bandpass filters with low side-lobes are used to estimate the signal spectra. This is a very conventional method for spectral estimation and could also possibly used for spectrum sensing in cognitive radios. The major disadvantage of this method is obviously the requirement for many bandpass filters in the receiver; on the other hand, considering multicarrier communications with filter bank structure in the receivers this method could be conveniently utilized for spectrum sensing without any additional requirements.

3.7  Summary Spectrum sensing for cognitive radio networks is a very popular topic and many basic techniques that are seen in the literature were presented in this chapter. The presented techniques vary from blind methods, such as the energy detector method, to partial context aware methods, such as the cyclostationary feature detector method, and all the way to complete context aware methods, such as the matched filter detection method. The energy detector is the simplest and is optimal for uncorrelated signal samples with Gaussian distribution. The knowledge of the noise power is also required to get improved detection performance for the energy detector; when the noise power is not known precisely, the energy detector performance is limited by the SNR wall [12]. The covariance and the eigenvalue based methods are more suitable for detecting wireless signals, considering the signals are correlated in nature. The cyclostationary feature-based method has better detection performance than the energy-based method, given that the cyclic features are estimated properly, which requires larger set of samples. Given the short falls of the spectrum sensing methods presented in this chapter, various other strategies are the topics of the next few chapters.

References   [1] Yucek, T., and H. Arslan, “A Survey of Spectrum Sensing Algorithms for Cognitive Radio Applications,” IEEE Communications Surveys and Tutorials, Vol. 11, No. 1, 2009, pp. 116–130.   [2] Kandeepan, S., et al., Project Report–“D2.1.1: Spectrum Sensing and Monitoring,” EUWB Integrated Project, European Commission funded project (EC: FP7-ICT215669), May 2009, http://www.euwb.eu, accessed August 4, 2012.   [3] Urkowitz, H., “Energy Detection of Unknown Deterministic Signals,” Proc. of the IEEE, Vol. 55, No. 4, 1967, pp. 523–531.

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  [4] Lim, T. J., R. Zhang, Y. C. Liang, and Y. Zeng, “GLRT-Based Spectrum Sensing for Cognitive Radio,” Proc. of IEEE GLOBECOM, New Orleans, LA, 2008.   [5] Kostylev, V. I., Energy Detection of a Signal with Random Amplitude,” Proc. IEEE Int. Conf. on Commun. (ICC02), New York, 2002, pp. 1606–1610.   [6] Digham, F., M. S. Alouini, and M. K. Simon, “On the Energy Detection of Unknown Signals over Fading Channels,” IEEE Transactions on Communications, Vol. 55, No. 1, 2007, pp. 21–24.   [7] Digham, F., M. S. Alouini, and M. K. Simon, “On the Energy Detection of Unknown Signals over Fading Channels,” in Proc. of IEEE ICC, Alaska, 2003.   [8] Atapattu, S., C. Tellambura, and H. Jiang, “Performance of an Energy Detector over Channels with Both Multipath Fading and Shadowing,” IEEE Transactions on Wireless Communications, Vol. 9, No. 12, 2010, pp. 3662–3670.   [9] Mariani, A., A. Giorgetti, and M. Chiani, “Energy Detector Design for Cognitive Radio Applications,” Proc. IEEE Int. Waveform Diversity & Design Conference, Niagara, NY, 2010, pp. 53–57. [10] Mariani, A., A. Giorgetti, and M. Chiani, “Effects of Noise Power Estimation on Energy Detection for Cognitive Radio Applications,” IEEE Transactions on Communications, Vol. 59, Issue 12, 2011, pp. 3410–3420. [11] Sonnenschein, A., and P. M. Fishman, “Radiometric detection of spread-spectrum signals in noise of uncertain power,” IEEE Journal on Aerospace Electronic Systems, Vol. 28, Issue 3, 1992, pp. 654–660. [12] Tandra, R., and A. Sahai, “SNR Walls for Signal Detection,” IEEE Journal Of Selected Topics In Signal Processing, Vol. 2, No. 1, 2008. [13] Mariani, A., A. Giorgetti, and M. Chiani, “SNR Wall for Energy Detection with Noise Power Estimation,” Proceeding of IEEE International Conference on Communications (ICC), Kyoto, Japan, 2011. [14] Tandra, R., and A. Sahai, “Fundamental limits on detection in low SNR under noise uncertainty,” Proceedings of IEEE Int. Conference on Wireless Networks, Communication and Mobile Computing, Maui, HI, 2005, pp. 464–469. [15] Gardner, W. A., “Exploitation of spectral redundancy in cyclostationary signals,” IEEE Signal Processing Magazine, Vol. 8, Issue 2, 1991, pp. 14–36. [16] Gardner, W. A., A. Napolitano, and L. Paura, “Cyclostationarity: Half a Century of Research,” Signal Processing, Vol. 86, 2006, pp. 639–697. [17] Sutton, P. D., K. E. Nolan, and L. E. Doyle, “Cyclostationary Signatures in Practical Cognitive Radio Applications,” IEEE Journal on Selected Areas in Communications, Vol. 26, Issue 1, 2008, pp. 13–24. [18] Dandawate, A. V., and G. B. Giannakis, “Statistical Tests for Presence of Cyclostationarity,” IEEE Transactions on Signal Processing, Vol. 42, No. 9, 1994, pp. 2355–2369.



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[19] Kyouwoong, K., I. A. Akbar, K. K. Bae, J-S. Urn, C. M. Spooner, et al., “Cyclostationary Approaches to Signal Detection and Classification in Cognitive Radio,” IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN), Dublin, Ireland, 2007, pp. 212–215. [20] Kandeepan, S., G. Baldini, and R. Piesiewicz, “Experimentally Detecting IEEE 802.11n Wi-Fi Based on Cyclostationarity Features for Ultra-Wide Band Cognitive Radios,” IEEE Personal Indoor and Mobile Radio Communications (PIMRC) Conference, Tokyo, Japan, 2009. [21] Gardner, W. A., “Measurement of Spectral Correlation,” IEEE Transactions On Acoustics, Speech, And Signal Processing, Vol. ASSP-34, No. 5, 1986, pp. 1111–1123. [22] Zeng, Y., and Y. C. Liang, “Spectrum-Sensing Algorithms for Cognitive Radio Based on Statistical Covariances,” IEEE Transactions On Vehicular Technology, Vol. 58, No. 4, 2009, pp. 1804–1815. [23] Zeng, Y., and Y. C. Liang, “Eigenvalue-Based Spectrum Sensing Algorithms for C­ognitive Radio,” IEEE Transactions On Communications, Vol. 57, No. 6, 2009, pp. 1784–1793. [24] Tian, Z., and G. B. Giannakis, “A Wavelet Approach to Wideband Spectrum Sensing for Cognitive Radios,” Proceedings of IEEE/ICST Conference on CROWNCOM, Mykonos, Greece, 2006. [25] Kay, S. M., Modern Spectral Estimation: Theory and Application, Englewood Cliffs, NJ: Prentice Hall, 1999. [26] Stoica, P., and R. Moses, Spectral Analysis of Signals, Pearson/Prentice Hall, 2005. [27] Thomson, D. J., “Spectrum estimation and harmonic analysis,” Proceedings of the IEEE, Vol. 70, No. 9, 1982, pp. 1055–1096. [28] Thomson, D. J., Multitaper Analysis of Nonstationary and Nonlinear Time Series Data, Cambridge University Press, 2000. [29] Farhang-Boroujeny, B., “Filter Bank Spectrum Sensing for Cognitive Radios,” IEEE Transactions on Signal Processing, Vol. 56, No. 5, 2008, pp. 1801–1811.

4 Temporal Spectrum Sensing and P­erformance Analysis Spectrum sensing techniques and performance analysis for cognitive radios are well-treated topics, as presented in the previous chapters. In this chapter, however, we introduce the notion of temporal spectrum sensing and present the corresponding detection performance. In practice, it is not feasible to sense the spectrum continuously in time, as this takes up the receiver resources almost completely, thus periodic spectrum sensing [2–5, 7–11] is proposed to periodically sense the radio environment in time. We devote this entire chapter to temporal periodic spectrum sensing and performance analysis. The performance of periodic sensing very much depends on the temporal transmissions characteristics (spectral occupancy) of the primary user, as well as how fast and how long we sense in time, apart from noise and signal fading phenomena. We provide a basic framework for temporal spectrum sensing analysis in this chapter by considering various spectral occupancy models, based on existing traffic models [1, 6, 12–18] in communications, to analyze the detection performance for periodic sensing.

4.1  Introduction Sensing the spectrum continuously in time is not practical in cognitive radio systems, as it would take up all the receiver resources, leaving no space to 69

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Cognitive Radio Techniques

transmit-receive data. Therefore, periodic sensing is considered for sensing the spectrum for a duration of δt Î + in time with some period Tw Î + as depicted in Figure 4.1. For the periodic sensing technique, the primary user in the environment can be undetected by the cognitive radio node, depending on the spectral occupancy characteristics of the primary user. That is, when the primary user is transmitting while the cognitive radio node is not sensing, it is not possible to detect it. In other words, the cognitive radio node detects the presence of the primary user only when the primary user transmits during the sensing duration (δt) over a given sensing period Tw. In order to study the detection performance using periodic sensing, we provide a generic framework for performance analysis. The framework is then used to study the detection performance of temporal periodic-sensing for different spectral occupancy models of the primary user. In particular, we consider two types of spectral occupancy models for the primary user transmissions for the purpose of analysis based on (1) Poisson arrival process with exponential hold time distribution and (2) Poisson arrival process with Pareto distributed hold time models. The spectral occupancy models are also used to classify the level of occupancy by the primary user in the radio environment, giving us an indica-

Primary user

Sensing period

t

Tw

Periodic sensing

t

Cognitive radio node Figure 4.1  P  eriodic sensing performed by a cognitive radio for detecting primary users in the radio environment.



71

Temporal Spectrum Sensing and P­erformance Analysis

tion of how much white space is available in that particular environment and especially how well the primary user could be detected by using the periodic sensing technique in the cognitive radio node’s point of view. The above-mentioned detection performance study for temporal periodic-sensing is purely based on the spectral occupancy characteristics of the primary user without considering any noise in the received signal or fading. Later in the chapter, we extend the performance analysis of the temporal periodic-sensing technique with a given spectral occupancy model for noisy sensing with signal fading. Finally, based on the analysis that we present throughout the chapter, we derive expressions for the sensing period Tw for detecting the primary user with a given confidence level (detection probability).

4.2  Temporal Periodic-Spectrum Sensing The temporal periodic sensing with primary user ON-OFF transmission characteristics is depicted in Figure 4.2 for a single cognitive radio node and a single primary user network model. As shown in the figure, the cognitive radio node periodically senses the spectrum with a period of Tw seconds for a duration of δt seconds for every period. Using such a periodic sensing process in the noiseless case, the cognitive radio node will detect the presence of the primary user when the primary user transmits anytime between (t0 + t1l ) and (t0 + t 2l ) for some t0 Î  during the lth scanning iteration, where δ t = t 2l - t1l , for all l Î . The analysis performed here for the detection performance in the absence of noise can be interpreted as asymptotic behavior of periodic sensing in the high signal to noise ratio regime. In the rest of the chapter (for i Primary user transmission: temporal behavior 1th scan t11

t

(1 + 1)th scan ... Periodic sensing by cognitive radio

t21

Figure 4.2  Periodic scanning and temporal detection.

t

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Cognitive Radio Techniques

simplicity) we consider t0 = 0. Therefore, based on the temporal statistics, the cognitive radio node will detect the primary user only when the primary user is transmitting while the cognitive radio is sensing the spectrum, as depicted in Figure 4.2. The time between successive spectral occupancies of the primary user is modeled as a random process given by Δi with a mean time between (from the end of a given transmission to the successive beginning) transmissions given by Δm = E[Δi]. The duration of a single occupancy is also modeled as a random process given by τi with a mean hold time (spectral occupancy time) of τm = E[τi] We further elaborate on the primary user’s temporal statistical model that we consider in the next section.

4.3 Primary User Spectral Occupancy Model with Poisson Arrival The temporal spectral occupancy process of the primary user is modeled here by a Poisson arrival process together with (a) exponentially distributed random occupancy time and (b) Pareto distributed random occupancy time. When the Pareto model is used with Poisson arrival, the occupancy model is known as the Poisson-Pareto burst process (PPBP), which better describes a typical (practial) WEB service application compared to the exponential model. The Poisson arrival process describes the WEB requests with an exponentially distributed inter request (arrival) time Δi having a mean request (arrival) rate of λ = 1/Δm, where λ is also known as the spectral occupancy rate. For the Poisson arrival model–in order to perform our analysis–we consider the following axioms. Let N (t) Î  be the number of arrivals at some t Î , then Axiom 1: At time t = 0 the primary user has no occupancy of the spectrum at all. That is, N (0) = 0. Axiom 2: Incremental independency and stationarity of N (t). That is, if  J1 = N(t2) − N(t1) and J2 = N(t4) − N(t3) for some t1, t2, t3, t4, Î  such that t1 < t2 < t3 < t4, then J1 and J2 are independent. Further, if t4 − t3 = t2 − t1, then J1 and J2 have the same statistical properties. Then according to the Poisson arrival model, the probability of having N(t) = n arrivals at time t is given by

P [ N (t ) = n] = exp( - λt )

( λt )n n!

(4.1)



Temporal Spectrum Sensing and P­erformance Analysis

73

where, n Î . It should be noted here that the Poisson arrival model is somewhat limited and does not suit all traffic classes (applications) in the current era; it is mainly suited for telephony type traffic and a limited class of data traffic. As described in Chapter 2, the Markov modulated Poisson model is a better representation of the real-world traffic in the current era. However, we consider the Poisson arrival model here for simplicity of defining a framework for analyzing the detection performance under a given temporal spectrum occupancy profile of a primary user. 4.3.1  Exponential Random Spectral Occupancy Time

The exponential model is traditionally used to describe the random call hold time process. It is useful in modeling voice traffic, as recommended by the ITU [1], and is quite a convenient model for analytical purpose as well. In [2] the exponential model is verified experimentally for aggregated HSDPA data traffic by Telefonica I+D. The exponential model can also be extended to obtain further traffic models based on the type of traffic, such as Erlange and Phase-type models [1]. The exponentially distributed occupancy time τi has a probability density function given by

f τ i (τ i ) = 1/ τm exp( -τi / τm )

(4.2)

for τi > 0, and with a mean hold time of τm. 4.3.2 Pareto Random Spectral Occupancy Time

For the primary user spectral occupancy model that we consider here, the random occupancy time τi is also modeled by a Pareto distribution. The cumulative distribution function of a Pareto random process is given by

 τ  F (τ i ) = 1 −  i   τ min 

−k

where τi ≥ τmin

(4.3)

with τmin Î + is a positive value describing the minimum packet length, and k > 0 is a parameter that describes the primary user spectral occupancy level. Moreover, the expressions for the mean and variance of the random hold time τi are given by E[τi ] = τm = kτmin/(k − 1) for k > 1, and 2 E [(τ i - τm )2 ] = k τ min /[(k - 1)2 (k - 2)] for k > 2. The Pareto model gives us a greater flexibility in modeling different traffic classes compared to the exponential model due, to the presence of the arbitrary value k.

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Cognitive Radio Techniques

4.3.3  Classifying Primary User Spectrum Occupancy Levels

Based on the arrival rate λ and the mean hold time or the mean occupancy duration, τm, we can characterize the spectral occupancy levels of a primary user as light, average, or heavy user of the radio spectrum. Figure 4.3 depicts the classification of spectral occupancy levels of a primary user based on their traffic charH acteristics. We further observe that the pairs { D La , τ L } and {D H a , τ } as shown in Figure 4.3, (which are computed later in this chapter) separate the occupancy level regions of the primary user as light, average, or heavy. Corresponding to the occupancy levels, we also characterize the risk of misdetecting the primary user as high-risk, medium-risk, and low-risk regions, respectively. For analytical purposes the risk regions for misdetecting the primary user are defined by • High-Risk Region (Light User): for 0
τmin is the where, PD¢ (τ ) is given in (4.12), and f τ (τ ) = kτ min probability density function of the Pareto distributed occupancy time τ. We get a closed form expression for the mean probability of detection, by solving the above integration in (4.21), given by

PD² =



+

-k -k 1 é æ Tw - δ t ö ù æ Tw - δ t ö + ê1 - ç ú PO (Tw ) êë è τ min ÷ø úû çè τ min ÷ø

-k ù α é exp( - λ(Tw - δ t ))(Tw - δt )- k exp( - λτ min )τ min ê ú (4.22) PO (Tw ) ë λ(Tw - δt ) + k λτ min + k û

k for τmin £ Tw − δt where, α = kτ min exp( - λδ t ). The detection probability PD² ² for τmin > Tw − δt is given by PD = 1. The corresponding results are depicted in Figure 4.9 for various values of τmin and k(³ 1). From the figure, we observe that the detection probability increases with the arrival rate λ and τmin.

. In equation (8) of [3], the mean detection probability was computed using (4.11), resulting in a different expression to that given in (4.22) with close enough values. . The detection probability in (4.22) does not converge for all values of k < 1, hence care should be taken when using such values for k. We provide examples with k ³ 1.



85

Temporal Spectrum Sensing and P­erformance Analysis 1.00 0.85

min = 0.5 sec

P"D

0.65

0.45

k=1 k=2

min = 0.2 sec

0.25 min = 0.1 sec 0.15

10

2

10

0

 (s 1 )

10

2

Figure 4.9  P  robability of detection for the Poisson-exponential model with Tw = 1 sec, and δt = 0.1 sec.

4.8 Temporal Periodic-Sensing Performance Comparison with Deterministic and Random Occupancies A comparison between the detection probabilities derived under different spectral occupancy models of the primary user transmissions is of interest to us. This would enable us to understand how different spectral occupancy patterns will impact the detection performance given a periodic sensing scheme. We fix the mean occupancy levels in order to compare the relative detection performances between the deterministic, exponential, and Pareto spectral occupancy models. Figure 4.10 depicts the detection performance for the deterministic, exponential, and Pareto distributed spectral occupancy models with Poisson arrival, for a mean hold time of τm = 0.4 seconds. The results show almost similar detection performances at higher arrival rates, giving almost closer to unit probability of detection. However, when the arrival rate λ reduces the differences rise between the models, obviously the random models better represent real world values compared to the deterministic model.

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Cognitive Radio Techniques

1 0.8 0.7

P" D

0.6 0.5 0.4 Deterministic  model

0.3

Exponential  model Pareto  model

0.2

10

2

10  (s

1

0

10

2

)

Figure 4.10  C  omparing the detection probability between the deterministic, exponential and Pareto occupancy model for τ = τm = 0.4 sec with Tw = 1 sec, δt = 0.1 sec and k = 1.0526.

Moreover, we compare the same models for a higher value of mean occupancy time τ and τm equal to 4 seconds representing the case where τ > Tw − δt. For the case of τ > Tw − δt, we saw that the deterministic model gives us a unit probability which is somewhat less realistic when considering real world spectral occupancy characteristics. Figure 4.11 compares the detection probabilities for the different occupancy models for a mean occupancy level of τ = τm = 4 seconds. In summary, the random occupancy models show more realistic results, as expected, compared to the deterministic model, especially when τ exceeds Tw − δt. On the other hand, the deterministic model was used to develop the random models and may also become useful when fixed packet size-based transmissions are used.

4.9  Temporal Periodic-Sensing in Noise So far in this chapter, we have analyzed the detection performance of temporal periodic sensing in the absence of any sensing noise on the physical



87

Temporal Spectrum Sensing and P­erformance Analysis 1 0.8 0.7

P" D

0.6 0.5 0.4 Deterministic  model

0.3

Exponential  model Pareto  model

0.2

10

2

10  (s

1

0

10

2

)

Figure 4.11  C  omparing the detection probability between the deterministic, exponential and Pareto occupancy model, with τ = τm > Tw − δt, for τ = τm = 4 sec with Tw = 1 sec, δt = 0.1 sec and k = 1.0526.

signal and only considering the spectral occupancy characteristics of the primary user. Now we extend the detection performance analysis to sensing with noisy signals, together with the spectral occupancy characteristics of the primary user. We choose the energy detector-based sensing, as presented in Chapter 3, to develop the framework for the corresponding analysis. The detection performance of other spectrum sensing techniques with spectral occupancy characteristics of the primary user can be developed by following a similar framework. The energy of the sensed signal is computed when the cognitive radio node is scanning the spectrum during the interval of [t1l , t 2l ]. The low-pass complex representation of signals are considered. The sensed signal r(t) under the two hypotheses H0 and H1 during the sensing period of [t1l, t 2l ] is given by

ì ν(t ) r (t ) = í îs(t ) + ν(t )

: when primary user is not present (4.23) : when primary user is present

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where, s(t) is the received complex primary user signal, and v(t) is the complex AWGN noise with zero mean and variance s2. The energy ϵ which is used as the test statistic of the sensed signal r(t) is given by t 2l

ϵ = ò l r (t )r�(t )dt



t1

(4.24)

where r�(t ) is the complex conjugate of r(t). For the discrete signal on the other hand, the energy based test statistic is given by ϵ»



N -1

å r[n]r�[n]

(4.25)

n=0

where N is the total number of samples, which is also known as the timebandwidth product as described in Chapter 3. The signal to noise ratio (SNR) based on the received primary user signal s(t) for ta < t £ tb for some ta, tb Î + is defined by

ρ�

1

tb

ò σ 2[tb - t a ] t

a

s(t )�s (t )dt

(4.26)

To simplify the analysis, we assume r to be a constant throughout the period of consideration. In the following analysis we adopt the discrete model in (4.25) as our test statistic. Considering the sensing noise the decisions dl, for a decision threshold m, made by the cognitive radio on the presence of the primary user defined in (4.4), is modified as

0; H 0 dl =   1; H1

for ϵ < µ ; ∀t ∈[t1l , t2l ] for ϵ ≥ µ; form some t ∈[t1l , t2l ]

(4.27)

Now let us define the following probabilities P00, P01, P10 and P11 when AWGN is not present (i.e., considering the temporal statistics only) P01 = P[d l = 0 | E ^CB ]

P01 = P[d l = 0 | E B ]

P01 = P[d l = 0 | E ^CB ]

(4.28)

P01 = P[d l = 0 | E B ] where E^CB¢ is the complementary event of EB defined above (4.9). Based on the definitions of the detection probabilities PD¢ , PD² and PF¢ for the noiseless case presented earlier in this chapter, the above probabilities can be rewritten as



Temporal Spectrum Sensing and P­erformance Analysis

89

P00 = 1 - Prob of false alarm = 1 - PF¢ = 1 P10 = Prob of false alarm = PF¢ = 0



ìï PD¢ ; P11 = Prob of detection = í ïî PD² ;

for deterministic τ

ìï 1 - PD¢ ; P01 = Prob of misdetection = í ïî 1 - PD² ;

for deterministic τ

for random τ

(4.29)

for random τ

Then the overall probability of detection and the probability of false alarm, for noisy sensing, together with the temporal spectral occupancy characteristics of the primary user, are given by

PD = P[ ϵ ≥ µ | H 0 ]P01 + P[ ϵ ≥ µ | H1 ]P11

(4.30)



PF = P[ ϵ ≥ µ | H 0 ]P00 + P[ ϵ ≥ µ | H1 ]P10

(4.31)

where P[ϵ ³ m|H0] and P[ϵ ³ m|H1] are specific probabilities based on the spectrum sensing technique that is used for sensing in AWGN without considering the temporal occupancy characteristics of the primary user. For the energy-based sensing technique that we consider in this example, these probabilities are derived in Chapter 3, Section 3.2. Then, the overall detection and false alarm probabilities are given by

PD = G( N, µ /2)(1 - PD² ) + Q N ( 2 N ρ , µ )PD²

(4.32)



PF = G(N, µ /2)

(4.33)

¥

where, G( a , b ) = G(1N ) ò u a -1 exp( -u )du is the upper incomplete regularized b ¥ Gamma function, and Q N ( a , b ) = ò u N exp( -(u 2 + a 2 )/2)I N -1( au )/a N -1du b is the generalized Marcum Q-function with IN−1(.) being the modified Bessel function of first kind with order N − 1. Note that the false alarm probability only depends on sensing noise since PF¢ = 0. Let us consider the exponential random occupancy model as an example to observe the detection performance, using the energy detector, when both sensing noise and temporal spectral occupancy characteristics are considered for the primary user detection. For the exponential model, the term PD² in (4.32) is given by (4.20).

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Figure 4.12 depicts the complementary-ROC curves for the noisy detection case with various values of Poisson arrival rates λ for a given signalto-noise ratio (SNR) r and τm. We observe improvements in the detection performance when the arrival rate is increased, as expected, and for larger values of λ the detection performance is limited by the sensing noise. The complementary-ROC curve for higher values of λ is similar to the energy detector’s performance curve for the given signal-to-noise ratio and N where the influence of the spectral occupancy characteristics becomes negligible. At lower values of λ, however, the detection performance is very much limited by the temporal spectral occupancy characteristics of the primary user. Figure 4.13 depicts the complementary-ROC for various signal-to-noise ratio levels for a given λ and τm. We see that the detection probability is dominated by the sensing noise at low signal-to-noise ratio levels whereas the temporal occupancy characteristics of the primary user significantly affects the performance at higher signal-to-noise ratio levels. Note that the sensing time Tw also affects the detection performance; the smaller the value of Tw, the better the detection performance. The sensing duration δt improves the noisy

Probability of misdetection

10

10

0

–2

λ = 0.1 s –1

λ = 5 s –1 λ = 10 s –1

10

–4

λ = 20 s

–1

λ = 50 s –1 10

–6

λ = 80 s –1 Noise only C-ROC (i.e., λ = ¥)

10

–8

10

–8

10

–6

–4

10 10 Probability of false alarm

–2

10

0

Figure 4.12  C  omplementary ROC curves for various values of Poisson arrival rates λ, with N = 4, δt = 0.1 s, Tw = 1 s, r = 10 dB and and exponential mean occupancy time τm = 0.5 s.



91

Temporal Spectrum Sensing and P­erformance Analysis

10

Prob of Misdetection

10

0

2

SNR = 10dB SNR = 8dB

10

4

10

6

10

8

SNR = 5dB SNR = 0dB

Noise and temporal characteristics performance Noise onlyperformance

10

8

10

6

4

10 Prob of False Alarm

10

2

10

0

Figure 4.13  C  omplementary ROC curves for various values of signal to noise ratio levels r, with N = 4, δt = 0.1 s, Tw = 1 s, λ = 10 s−1 and an exponential mean occupancy time τm = 0.5 s.

detection performance where increasing δt will essentially increase N for a given bandwidth.

4.10 Temporal Periodic-Sensing in Noise with Signal Fading/Shadowing The detection performance of periodic sensing with a given temporal spectrum occupancy characteristics of the primary user with fading/shadowing signals and additive noise is of interest to us, since the model closely describes a real world scenario for primary user detection. In Chapter 3, the detection performance of the energy detector under various fading/shadowing channels was presented without considering any spectral occupancy characteristics of the primary user. Here, we use them to derive the detection performance for temporal periodic sensing. Following from (4.32) one could derive the detection probability for a fading primary user signal by averaging out the signal-to-noise ratio for a given fading model, given by

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Cognitive Radio Techniques ¥

PD = ò éëG( N, µ /2)(1 - PD² ) + Q N ( 2 N ρ, µ )PD² ùû f ρ ( ρ)d ρ (4.34) 0

where fr(r) is the probability density function of the signal to noise ratio r. The solution to the above integral results in fad

PD = G( N, µ /2)(1 - PD² ) + PD PD²



(4.35)

fad

where PD is the detection probability for fading primary user signals. Exfad pressions for PD were derived in Chapter 3 for various fading/shadowing models, such as Rayleigh, Rice, and Nakagami. For example, the detection probability derived in (4.35) for a Rayleigh fading channel with a mean s­ignal-to-noise ratio of ρ is given by N −2 1µ  −µ  PD = Γ( N, µ/ 2)(1 − PD′′ ) + PD′′ exp  ∑   +  2  n =0 n!  2  n



1+ ρ  PD′′    ρ 

N −1 

N −2   −µ   −µ  exp − exp  ∑   2 + 2 ρ  2  n =0   

(

)

n µρ 2(1+ ρ ) 

n!

 

(4.36)

The probability of detection expressions for other fading/showing channels, such as Rice and Nakagami, can also be derived in a similar manner by fad replacing the term PD in (4.35) with the respective expression derived in Chapter 3 for the energy detector.

4.11  Optimum Sensing Period Based on the analysis presented in this chapter, we could derive the optimum sensing period Tw given by Tˆw for the periodic sensing technique in order to achieve the required detection probability based on the other parameters, such as λ, τm, r. In practice, to satisfy the regulatory requirements for performing secondary communications one needs to detect the primary user with a specified minimum detection probability PDmin. By identifying the sensing period requirements, we can avoid over-scannin­g (i.e., avoid faster scanning by having smaller Tw) and save energy at the sensing node, and at the same time avoid under-scanning (i.e., avoid slower scanning by having larger Tw) and achieve the required minimum detection probability.



Temporal Spectrum Sensing and P­erformance Analysis

93

We consider the noisy sensing performance with the energy detector for the deterministic occupancy time model with Poisson arrival to derive a closed form solution for the optimum sensing time Tˆw. The detection probability, from (4.32) is given by,

PD = G(N, µ /2)(1 - PD¢ ) + Q N ( 2N ρ, µ )PD¢

(4.37)

where PD¢ is the detection probability for the deterministic τ case given in (4.11). Then, for a given detection probability PD = PDmin by substituting for PD¢ in (4.37) and rearranging terms we have Tˆw = -

ö 1 æ é Q N ( 2 N ρ - G( N, µ /2) ù ln ç1 - ê ú (1 - exp( - λ(τ + δ t )))÷ min λ è ëê PD - G( N, µ / 2) ûú ø

(4.38)

The optimum sensing period Tˆw is just an indictor of for the scanning period Tw to be used that is near optimum. The true optimum value very much depends on how well the true spectrum occupancy of the primary users follows the prescribed model (i.e. Poisson-Deterministic model in this case). For dynamically varying conditions, however, when the temporal statistics and the signal power are varying—which is the case in reality—the cognitive radio node needs to estimate the relevant parameters in order to make use of (4.38).

4.12  Reality of Spectrum Occupancy Models The detection performance and the analytical framework provided in this chapter are done by assuming certain models for the spectrum occupancy by the primary user. The models do not necessarily reflect real-world scenarios in most of the cases, especially with the modern era of a mixture of traffic types and the related applications, such as video, multimedia, voice, and data. In general, there exist no generic models to analyze such traffic classes (spectral occupancies); the models used in this chapter and the corresponding results are a good indication of how the spectrum sensing techniques would perform under varying primary user temporal characteristics, as well as noisy sensing with fading signals.

4.13  Summary In this chapter, the performance of detecting primary users by cognitive radios using periodic sensing of the spectrum was presented. The temporal

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spectrum occupancy statistics of the primary user were considered for the performance analysis, and were later on extended to noisy sensing together with occupancy statistics. The detection probability depends on the primary user’s occupancy rate of the spectrum, occupancy duration of the spectrum, the sensing period, the time-bandwidth product, and the signal-to-noise ratio. The probability of false alarm however does not depend on the temporal statistics but depends only on the time-bandwidth product and the noise power. Two random spectral occupancy models were considered for the analysis based on the Poisson exponential model and the Poisson-Pareto burst model. Results show that the detection performance very much depends on the type of model considered especially at low arrival rates. Moreover, the sensing noise dominates the detection performance at low signal-to-noise ratio levels and the spectral occupancy characteristics dominates at higher signal-to-noise ratio levels.

References   [1] ITU Handbook: Teletraffic Engineering, ITU-D, Study Group2, June 2006, www.itu.int   [2] Kandeepan, S., A. Siera, J. Campos, and I. Chlamtac, “Periodic Sensing in Cognitive Radios for Detecting UMTS/HSDPA Based on Experimental Spectral Occupancy Statistics,” In Proceedings of IEEE Wireless Communications and Networking Conference (WCNC), April 2010, Sydney.   [3] Kandeepan, S., A. Giorgetti, and M. Chiani, “Periodic Spectrum Sensing Performance and Requirements for DetectingLegacyUsers withTemporal and Noise Statisticsin Cognitive Radios,” Proceedings of IEEE Globecom/Workshop, Hawaii, 2009.   [4] Kandeepan, S., et al., Project Report–“D2.1.1:Spectrum Sensing and Monitoring,” EUWB Integrated Project, European Commission funded project (EC: FP7-ICT215669), May 2009, http://www.euwb.eu, accessed August 4, 2012.   [5] Kandeepan, S., et al., “Spectrum Sensing for Cognitive Radios with Transmission Statistics: Considering Linear Frequency Sweeping,” EURASIP Journal on Wireless Communications and Networking, Vol. 2010, No. 1, Article ID 123674, doi:10.1155/2010/123674, April 2010, pp. 1–13.   [6] Matthias, W., A. de Baynast, and M. Petri, “On the Performance of Dynamic Spectrum Access based on Spectrum Occupancy Statistics,” Communications, IET, Vol. 2, I­ssue 6, 2008, pp. 772–782.   [7] Kim, H., and K. G. Shin, “In-band Spectrum Sensing in Cognitive Radio Networks: Energy Detection or Feature Detection?,” MobiCom08, San Francisco, CA, 2008.



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  [8] Cordeiro, C., K. Challapali, and M. Ghosh, “Cognitive PHY and MAC layers for dynamic spectrum access and sharing of TV bands,” In Proceedings of ACM First International Workshop on Technology and Policy for Accessing Spectrum, Article No. 3, 5 August 2006, Boston.   [9] Zhao, Q., et al., “Optimal Dynamic Spectrum Access via Periodic Channel Sensing,” IEEE WCNC 2007, Kowloon, Hong Kong, 2007, pp. 33–37. [10] Geirhofer, S., L. Tong, and M. S. Brian, “Dynamic Spectrum Access in the Time Domain: Modeling and Exploiting White Space,” IEEE Communications Magazine, Vol. 45, No. 5, 2007, pp. 66–72. [11] Zhao, Q., L. Tong, and A. Swami, “Decentralized Cognitive Mac for Dynamic Spectrum Access,” IEEE DySPAN, Baltimore, MD, 2005. [12] Toni, J., Traffic Analysis and Design of Wireless IP Networks, Norwood, MA: Artech House, 2003. [13] Allen, A. O., Probability Statistics, and Queuing Theory with Computer Science Applications, San Diego, CA: Academic Press, 1990. [14] Jabbari, B., “Teletraffic aspects of evolving and next-generation wireless communication networks,” IEEE Personal Communications, Vol. 3, Issue 6, 1996, pp. 4–9. [15] Fang, Y., I. Chlamtac, and Y. Lin, “Modeling PCS Networks Under General Call Holding Time and Cell Residence Time Distributions,” IEEE/ACM Trans. on Networking, Vol. 5, No. 6, 1997. [16] Mah, B. A., “An Empirical Model of HTTP Network Traffic,” IEEE INFOCOM 97, Kobe, Japan, Vol. 2, 1997, pp. 592–600. [17] Bolotin, V. A., “Modeling Call Holding Time Distributions for CCS Network Design and Performance Analysis,” IEEE Journal on Selected Areas in Communications, Vol. 12, No. 3, 1994. [18] Barcel, F., and S. Bueno, “Idle and Inter-arrival Time Statistics in Public Access Mobile Radio (PAMR) Systems,” IEEE GLOBECOM 97, Phoenix, AZ, 1997.

5 Cooperative Spectrum Sensing The spectrum sensing techniques discussed so far have a need to address the hidden node problem where a spatially separated primary user can go undetected­ depending on the received signal strength at the cognitive radio node. One of the ways to combat the hidden node problem in cognitive ­radio networks is to have many cognitive radio nodes cooperating together to detect the presence of a primary user in the environment [1]. Depending on the cooperation strategy used [2] a distant primary user can be detected by a given cognitive radio node even when it is unable to be detected locally by that particular cognitive radio node. Such a cooperative effort for detecting primary users is known as cooperative spectrum sensing in the cognitive radio­ literature [3–24]. In this chapter we elaborate the concept of cooperative spectrum sensing, present various cooperative sensing techniques and strategies and analyse their detection performances. The detection performance of cooperative sensing in general becomes far superior than the noncooperative (single cognitive radio-based local) sensing.

5.1  Introduction Cooperative spectrum sensing is performed to address the hidden node ­problem in cognitive radio networks for detecting distant primary users by a cognitive radio node. In cooperative spectrum sensing, a group of N nodes 97

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cooperate together by sharing their own local sensing decisions on the presence of a primary user. The local decisions made by the cognitive radios can be either soft or hard decisions, depending on the capabilities of the local node. A global decision on the presence of the primary user is then made by fusing the information from all the N cognitive radio nodes. Through a reporting channel, the cognitive radio nodes inform a central unit known as the fusion center or the cognitive base station (CBS) about their local decisions, as depicted in Figure 5.1. The cognitive base station then fuses the gathered decisions by using an appropriate fusion strategy and comes up with a global decision on the presence of the primary user in the environment. The global decision is then reported back to the cognitive radio nodes. As shown in Figure 5.1, the cognitive radio nodes closer to the primary user in the region will detect its presence better than the cognitive radio nodes that are further away from the primary user. Therefore, using the cooperative sensing strategy the cognitive radio network can better detect a primary user. Suppose uk(i) is the local decision at some time instance k at the cognitive radio node i, then the fusion decision made at the fusion center (cognitive base station) is given by d k = L({uk (1), uk (2)..uk ( N )})



(5.1)

CR

PU

CR

CR

CR

CR CBS

Figure 5.1  C  ooperative spectrum sensing in cognitive radio networks for better detection of a primary user in the environment.



Cooperative Spectrum Sensing

99

where, Uk = {uk(1), uk(2)..uk (N)} is the set of local cognitive radio decisions and L (.) is the fusion decision strategy that is used at the fusion center to fuse the data. The local decisions uk (i) can be either soft or hard decisions and the corresponding techniques are presented later in this chapter. One of the main advantages of cooperative spectrum sensing—apart from getting better detection performance—is the reduction in spectrum sensing time. Since the detection performance is improved, the time duration for sniffing the spectrum per cognitive radio node can be reduced. Another advantage is the ability to localize the primary user (or multiple primary ­users) by performing appropriate localization techniques by cooperating with the other cognitive radio nodes. This is not an explicit advantage of cooperative sensing; however, some of the functionalities in cooperative sensing can also be used for localization. The topic on localization of primary users is addressed in the latter part of this book. On the other hand, there are a few drawbacks associated with the cooperative sensing scheme. Some of the main drawbacks are the overheads associated with the cooperative sensing logistics (trusting another cognitive radio node with its spectrum sensing decision), need for additional communications resources for the reporting process, errors involved in the reporting process. Throughout the chapter, we consider error-free reporting channels in analyzing the performance of various cooperative sensing techniques, and at the end of the chapter, we treat the topic of noisy reporting channels leading bit errors in the received reports. The survey article on cooperative spectrum sensing [1] presents a thorough literature study on the topic, while in this chapter, we treat the same from a beginners’ perspective. The rest of the chapter is organized as follows. In Section 5.2, the fusion strategies are introduced for cooperative sensing in the spatial and the temporal domains. In Section 5.3 and Section 5.4 the hard decision-based and the soft decision-based cooperatives spectrum sensing are presented respectively. In Section 5.5 cluster-based cooperative sensing is discussed, followed by the study of noisy reporting channels in Section 5.6. In Section 5.7, we provide some of the issues to be considered in cooperative sensing, and finally we summarize the chapter in Section 5.8.

5.2  Spatio-Temporal Fusion Strategy From Figure 5.1 it is clear that the cooperation is based in the spatial domain with spatially distributed cognitive radio nodes. The temporal domain for

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cooperation should also be considered in order to make sure that the cognitive radio nodes cooperate in a timely manner. 5.2.1  Synchronized Reporting

Suppose the cognitive base station makes a fusion decision every ΔF seconds, then all the cognitive radio nodes need to report their decisions within this time duration to the cognitive base station. Such an approach can be considered as synchronized cooperation as depicted in Figure 5.2. As depicted in the figure, the reports from the cognitive radios may arrive any time within a particular decision period by the cognitive base station. In this sense, the cognitive radio terminals – in order to keep up with timely reporting – need to make sure that the delay for sensing, processing, and report-transmissions are all quantified for. The synchronized reporting can have some slight timing-jitter for reporting (with jitter being much less than ΔF) but will have a mean reporting period of ΔF. There can also be another level of timing synchronization for sensing the environment, which is discussed later in the chapter under the topic of time-divisional cooperative spectrum sensing. 5.2.2  Nonsynchronized Reporting

Maintaining synchronous reporting can be a bit of a burden at the cognitive radio terminal. Therefore, a nonsynchronous reporting strategy can be adopted by the network. With nonsynchronous reporting, cognitive radio nodes are not required to maintain synchronism for reporting their decisions to the cognitive base station. As a result, varying numbers of reports K (£ N) can arrive at the cognitive bases station in a given reporting period ΔF, as depicted in Figure 5.3. The main drawback, however, with this scheme is that it is hard to predict the detection performance theoretically unless some a priori knowledge on the time for sending the reports by the cognitive radios is known. It is reasonable, in this case, to assume some statistical model on the timing for sending the reports by the cognitive radio nodes with a very high jitter compared to the synchronized scheme and a mean reporting time of ΔF. The jitter in this case can be modeled to be much greater than ΔF. . Assuming the processing time to make the decisions at the cognitive radio base station is negligible.



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Cooperative Spectrum Sensing CBS decision making instances

F t

Arival of local reports from CR at the CBS

Figure 5.2  Synchronized reporting for cooperative spectrum sensing.

5.3  Hard Decision Fusion The hard decision-based fusion strategy for cooperative spectrum sensing is basically a two-level decision process to decide on the presence of a primary user in the environment. The first level of decision-making is at the cognitive radio node known as the local decisions where the cognitive radio nodes CBS decision making instances

F t

Arival of local reports from CR at the CBS Figure 5.3  Nonsynchronized random reporting for cooperative spectrum sensing.

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p­erform their own decisions on the presence of the primary user. The local decisions made by the cognitive radio nodes uk(i) are hard decisions with a binary representation of −1 (for binary 0) for the case of deciding on H0 and 1 for the case of deciding on H1. The techniques and strategies used for making such hard decisions are purely up to the cognitive radio nodes. The local threshold selection is also up to the cognitive radio node to decide upon. Suppose li is the decision threshold at the ith cognitive radio node, then the corresponding decision uk(i) is given by

ì -1; uk (i ) = í î 1;

ξ< λ ξ³λ

(5.2)

where ξ is the test statistic used for the detection. Once the cognitive radio node makes a decision, it then reports it to the cognitive base station. Note that the binary decision uk(i) has a value of −1 to represent the logic 0 in order to be conveniently used in the fusion strategies as explained later. The second decision process in cooperative spectrum sensing is performed at the cognitive base station after receiving all (depending on the reporting strategy) the local decisions from the cognitive radios. The second level of detection is basically performed by fusing the received data and deciding upon the presence of the primary user. There are basically two commonly used fusion strategies for hard decision-based data fusion as presented subsequently. 5.3.1  Chair-Varshney Fusion Strategy

The optimum rule for fusing the received data from the cognitive radio nodes is given by the Chair-Varshney criteria based on the log-likelihood test, as presented in [2]. In order to use this fusion strategy, the cognitive base station requires the information on the reliability of the individual nodes that send the local decisions in terms of their respective false alarm [PFA(i)] and misdetection [PM(i)] probabilities, as well as the a priori probabilities of the events H0 and H1 given by P{H0} and P{H1}, respectively. The Chair-­Varshney criteria for optimal fusion detection is given by

ì 1; dk = í î -1;

µ ³0 µ