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Tecnolog´ıas de la Informaci´on, Comunicaciones y Matem´atica Computacional

Universidad de Valencia

Non-convex Distributed Power

Allocation Games in Cognitive Radio

Networks

Xiaoge Huang

Advisors

Prof. Baltasar Beferull Lozano

Dr. Carmen Botella Mascarell

Thesis submitted for the Degree of Philosophiae Doctor (Ph.D.) Valencia, May 2013

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Resumen

Motivaci´

on y objetivos

En las ´ultimas d´ecadas, las comunicaciones inal´ambricas han experimen-tado un desarrollo espectacular, con el objetivo de proporcionar una experiencia de usuario similar a los sistemas cableados, pero bajo la filosof´ıa de poder comunicarse “en cualquier lugar y en cualquier mo-mento”. El desarrollo de los sistemas comerciales ha sido posible gracias a la aparici´on de nuevas tecnolog´ıas, que, en general, requieren cada vez de canales con un mayor ancho de banda. Sin embargo, el espec-tro elecespec-tromagn´etico es un recurso limitado, cuyo uso viene regulado por el gobierno de cada pa´ıs. En el caso particular de Estados Unidos, los ´ultimos resultados publicados por la Comisi´on Federal de Comunica-ciones (FCC,Federal Communications Commission) muestran que el

es-pectro electromagn´etico est´a infrautilizado actualmente; algunas bandas de frecuencias son muy utilizadas, mientras que otras est´an s´olo parcial-mente ocupadas. De hecho, la ocupaci´on var´ıa en espacio y tiempo, es decir, estas bandas est´an desocupadas en diferente regiones del espacio durante ciertos intervalos de tiempo. La tecnolog´ıa de radios cognitivas se propone recientemente como una soluci´on para promover un uso efi-caz del espectro, ya que la base de su funcionamiento es la detecci´on en un determinado lugar y momento de “agujeros en el espectro” o bandas de frecuencias desocupadas por el usuario primario o principal con la correspondiente licencia. Gracias a esta detecci´on, un usuario secun-dario o sin licencia para ocupar esa banda de frecuencias o canal, puede transmitir/recibir temporalmente en esas frecuencias utilizando una ra-dio cognitiva sin perturbar las comunicaciones entre usuarios primarios. El hecho de compartir el espectro es beneficioso para los usuarios

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secun-Sin embargo, desde el punto de vista pr´actico, esta tecnolog´ıa presenta muchos retos que o bien siguen sin resolverse, o bien todav´ıa no se han resuelto de una forma eficiente. Por un lado, uno de los principales retos es la implementaci´on de un m´etodo de detecci´on fiable para en-contrar agujeros en el espectro, identificando as´ı las oportunidades de transmisi´on del usuario secundario sin comprometer la integridad de las comunicaciones entre usuarios primarios. Hay que tener en cuenta que si un usuario secundario detecta err´oneamente que un canal de frecuencias est´a libre y puede transmitir, cuando no lo est´a en realidad, producir´a una interferencia que degradar´a la experiencia del usuario primario. Por tanto, es imprescindible mantener una probabilidad de detecci´on err´onea lo suficientemente peque˜na. Por otra parte, otro criterio de dise˜no es disminuir la probabilidad de falsa alarma tanto como sea posible, ya que ´esta refleja el porcentaje de espectro vacante que est´a clasificado err´oneamente como ocupado, aumentando as´ı el uso oportunista del es-pectro de los usuarios secundarios de radio cognitiva. Por otro lado, con el fin de limitar la probabilidad de interferir con los usuarios primar-ios, es deseable mantener la probabilidad de fallo de detecci´on tan baja como sea necesario para cumplir las restricciones exigidas para proteger a los usuarios primarios. El umbral de detecci´on es el par´ametro que determina el equilibrio entre la probabilidad de falsa alarma y la prob-abilidad de fallo de detecci´on: un umbral bajo aumenta la probprob-abilidad de falsa alarma, disminuyendo la probabilidad de fallo (aumentando la probabilidad de detecci´on), y viceversa.

Otro par´ametro que influye en el proceso de detecci´on es el tiempo de de-tecci´on, es decir, el tiempo que el usuario secundario emplea en el proceso de detecci´on. La elecci´on de este tiempo ofrece una soluci´on de compro-miso entre la calidad y la velocidad de detecci´on: aumentar el tiempo de detecci´on disminuye tanto la probabilidad de falsa alarma como la prob-abilidad de detecci´on, pero reduce tambi´en el tiempo disponible para las transmisiones secundarias, lo que reduce el rendimiento en transmisi´on de la radio cognitiva. Esta dependencia entre los par´ametros es la que justifica el dise˜no conjunto de los par´ametros de detecci´on y transmisi´on de la radio cognitiva, siempre suponiendo que estas radios presentan una naturaleza ego´ısta y por lo tanto, no est´an dispuestas a cooperar entre ellas.

Esta tesis se centra en las tecnolog´ıas de comunicaciones relacionadas con la radio cognitiva, tomando como base un sistema de

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comunica-ciones de tipo OFDM (Orthogonal Frequency Division Multiplexing),

como los propuestos en los futuros sistemas de comunicaciones de cuarta generaci´on (LTE,Long Term Evolution). Concretamente, a lo largo de

la tesis, se investigan sistemas de comunicaciones con un solo usuario secundario o con varios usuarios secundarios (caso multiusuario). En el caso de los sistemas con un solo usuario secundario, el objetivo es resolver el problema de asignaci´on de potencias de transmisi´on sobre diferentes canales en base a la informaci´on de detecci´on disponible bajo el modelo de acceso oportunista al espectro. En el caso de los sistemas con m´ultiples usuarios secundarios, el comportamiento no cooperativo entre las radios cognitivas se modela utilizando teor´ıa de juegos. El principal objetivo de este segundo caso es modelar y analizar el prob-lema de optimizaci´on multiusuario competitivo, teniendo en cuenta la incertidumbre asociada con el proceso de detecci´on.

Metodolog´ıa

En esta tesis, se combinan los m´etodos de an´alisis te´orico y la simulaci´on por ordenador.

En el an´alisis te´orico de los casos de un usuario y de m´ultiples usuarios secundarios, se ha seguido la metodolog´ıa cl´asica de construir el nuevo concepto te´orico como un sistema l´ogico con definiciones y operaciones para demostrar los distintos teoremas. En primer lugar, el problema se modela como un problema de optimizaci´on matem´atica. Despu´es, se aplican m´etodos de optimizaci´on para analizar y resolver este prob-lema. Especialmente, la tesis se centra en el problema de optimizaci´on de recursos, tanto para sistemas de comunicaciones con una sola radio cog-nitiva como para el caso multiusuario. Para el caso de un solo usuario, la funci´on objetivo, as´ı como las restricciones para el problema de op-timizaci´on de recursos son no convexas, lo que da lugar a un problema complejo de resolver que motiva la utilizaci´on del m´etodo alternante para resolver el problema. Para los sistemas multiusuario, el problema de optimizaci´on consiste en un juego no cooperativo, donde se utiliza el concepto nuevo de cuasi-equilibrio de Nash.

Tras el an´alisis te´orico, los algoritmos propuestos para los dos casos considerados (un ´unico usuario y m´ultiples usuarios), se simulan por ordenador mediante el programa Matlab. Es importante destacar que tanto para el caso de un usuario como para el caso multiusuario, los

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es-laci´on est´andar, propuestos por organismos de estandarizaci´on o por la comunidad cient´ıfica, con el objetivo de facilitar la reproducci´on de los resultados obtenidos en esta tesis. Del mismo modo, los algoritmos prop-uestos se han comparado en todos los casos con los mejores algoritmos de optimizaci´on propuestos en la literatura de radios cognitivas. Aunque las simulaciones se han realizado con el programa Matlab, ser´ıa posible utilizar otras plataformas de simulaci´on y lenguajes de programaci´on.

Conclusiones y Contribuciones

En esta tesis, se considera un sistema de comunicaciones de tipo

inter-weave con radios cognitivas donde el objetivo general es maximizar la

tasa de cada usuario secundario mediante la optimizaci´on conjunta de la operaci´on de detecci´on y la asignaci´on de potencias de transmisi´on en diferentes canales, teniendo en cuenta la influencia de la incertidumbre en el proceso de detecci´on y el hecho de que la potencia de interferen-cia que puede aceptar un usuario primario est´a limitada. Este prob-lema se plantea tanto para sistemas de comunicaciones con un ´unico usuario secundario como para sistemas con m´ultiples usuarios secundar-ios. Adem´as, en el caso multiusuario, tambi´en se contempla el escenario donde tanto el usuario primario como los usuarios secundarios disponen de m´ultiples antenas (canal MIMO, Multi-Input Multi-Output).

En primer lugar, se estudia el problema de optimizaci´on de la asignaci´on de recursos para sistemas de comunicaciones con un ´unico usuario secun-dario, donde tanto el usuario primario como el usuario secundario dispo-nen de una ´unica antena (canal SISO, Single-Input Single-Output). El

usuario primario dispone de varios canales para transmitir. El objetivo del usuario secundario es maximizar su tasa mediante la optimizaci´on de forma conjunta de la informaci´on de detecci´on (el resultado del proceso de detecci´on es com´un a todos los canales) y de la asignaci´on de potencia para cada canal.

En este escenario, se considera que el sistema de comunicaciones es de

tipo interweave, con un acceso oportunista al espectro, donde la radio

cognitiva detecta si hay transmisi´on del usuario primario en todos los canales, y decide transmitir si los resultados de la detecci´on indican que el usuario primario est´a inactivo en ese canal. Sin embargo, debido a los errores de detecci´on, la radio cognitiva podr´ıa acceder a un canal

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cuando todav´ıa est´a ocupado por el usuario primario, provocando inter-ferencias perjudiciales tanto para los usuarios secundarios como para los usuarios primarios. Por este motivo, en el algoritmo de asignaci´on de potencia se propone una restricci´on en la potencia de interferencia in-troducida por el usuario secundario, llamadarate-loss gap, que asegura

que la degradaci´on experimentada por el usuario primario est´a acotada. El problema de optimizaci´on resultante es no convexo. Para resolverlo, se proponen un algoritmo de optimizaci´on exhaustivo y un algoritmo de optimizaci´on de direcci´on alternante. El an´alisis de la complejidad del algoritmo de optimizaci´on de direcci´on alternante, junto con los resulta-dos de las simulaciones, prueban que este algoritmo resuelve el problema de forma eficaz.

En segundo lugar, la tesis se centra en el problema de la asignaci´on de recursos en sistemas de comunicaciones con m´ultiples usuarios primarios y secundarios, pero con una ´unica antena por usuario. En este escenario, se asume que cada usuario primario dispone de un canal distinto en el que transmitir. En este caso, el esquema de acceso al espectro es de tipo espectro compartido, y el problema de asignaci´on de recursos se plantea como un juego de estrategia no cooperativa, donde cada radio cognitiva es ego´ısta y se esfuerza por utilizar tantos canales como sea posible con el fin de maximizar su propia tasa, considerando tambi´en el impacto de disponer de informaci´on de detecci´on imperfecta. En el esquema de espectro compartido, las radios cognitivas pueden coexistir con los usuarios primarios y ajustar la potencia de transmisi´on en cada canal en funci´on del resultado de la detecci´on.

Cuando se aplica la teor´ıa de juegos a este escenario, el juego resultante pertenece a la clase de juegos no convexos. La no convexidad se debe tanto a las funciones objetivo como al conjunto de resultados posibles resultantes de los problemas de optimizaci´on individual de cada radio cognitiva. En un primer paso, se propone utilizar un esquema distribuido de detecci´on cooperativa, basado en un algoritmo de consenso, donde las radios cognitivas comparten su informaci´on de detecci´on ´unicamente a nivel local. Tras la detecci´on, para resolver el problema de asignaci´on de recursos, se propone el algoritmo de optimizaci´on de direcci´on alter-nante, demostrando que es posible alcanzar un equilibrio local de Nash. A continuaci´on, se utiliza el nuevo concepto de equilibrio relajado o cuasi-equilibrio de Nash. Se realiza el an´alisis de las condiciones sufi-cientes para demostrar la existencia del cuasi-equilibrio de Nash para el juego bajo consideraci´on. Tras este an´alisis, se propone un algoritmo

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de Nash del juego considerado. A partir de los resultados de las simula-ciones, se comprueba que el m´etodo propuesto mejora considerablemente la tasa de las radios cognitivas con respecto a distintos m´etodos alter-nativos propuestos en la literatura.

Finalmente, se investiga un escenario con m´ultiples usuarios primarios y secundarios, que adem´as disponen de m´ultiples antenas. El esquema de acceso al espectro considerado es el de acceso oportunista. En este ´ultimo caso, el problema a resolver sigue siendo la asignaci´on de recur-sos de las radios cognitivas cuando cada usuario primario dispone de una canal distinto en el que transmitir. El problema de optimizaci´on se analiza como un juego no cooperativo estrat´egico, donde la matriz de covarianza de transmisi´on, el tiempo de detecci´on y el umbral de de-tecci´on son las variables a optimizar conjuntamente. El juego resultante es no convexo, por lo tanto, se utiliza nuevamente el concepto de cuasi-equilibrio de Nash, y se demuestra anal´ıticamente que el juego propuesto puede lograr un cuasi-equilibrio de Nash bajo ciertas condiciones, medi-ante la utilizaci´on del m´etodo deVariational Inequality (VI). En

partic-ular, se demuestra te´oricamente la condici´on suficiente de la existencia y la unicidad del cuasi-equilibrio de Nash para el juego propuesto. Por otra parte, se presenta una posible extensi´on de este trabajo teniendo en cuenta el tiempo de detecci´on para las radios cognitivas. A partir de los resultados de las simulaciones, se demuestra que el algoritmo iterativo de punto interior primal-dual converge de forma eficiente al cuasi-equilibrio de Nash.

Como trabajo futuro, se contempla el desarrollo de la introducci´on del factor de precio en el escenario con m´ultiples usuarios primarios y se-cundarios. Otra extensi´on futura es la introducci´on de un m´etodo de detecci´on robusto basado en detecci´on cooperativa. Una alternativa a la detecci´on, es la utilizaci´on de mapas de interferencia, que actuar´ıan como

soft info. Por ´ultimo, todos los algoritmos y esquemas presentados en

esta tesis se han analizado mediante simulaciones. Su implementaci´on en un testbed ser´ıa de gran utilidad de cara a su posible aplicaci´on pr´actica.

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Acknowledgement

This dissertation could never have been written without help and sup-port from many people around me.

First of all, I would like to thank my supervisor Prof. Baltasar Befer-ull Lozano for hiring me as a PhD student in GSIC and providing me such a good working environment. Your work as my advisor not only shaped the student I am today, but the professor I aspire to become. You managed to provide me the freedom to think and explore, while simultaneously giving me the guidance I needed to stay focused. Spe-cially, I would like to thank your for not assigning me heavy tasks in the funding projects so that I could finish my thesis writing on time. I would also like to thank my other advisor and friend Prof. Carmen Botella Mascarell, who not only constantly fueled me with strength, hope and support to take on challenges and go through frustrations, but also helped me a lot during all the period of my research with guidance and stimulating suggestions. Thank you for believing in me and for your advice and friendship. Specially, I would like to thank your mother and your family for their thoughtful kindness to me, which warmed my heart and greatly eased my homesickness.

To my colleagues and friends in the Group of Information and Commu-nication Systems: Eugenio Celada, C´esar Asensio, Santosh Shah, Ibra Khalife, Fernando Camaro Nogues, Daniel Alonso, Vinay Prasad, and Gustavo Hernandez. We had many valuable discussions and glad co-operations. Special thanks goes to Eugenio Celada, who is not just a friend, but also a free driver, Spanish teacher, and the guy who is always helpful. It is truly a pleasure to get to know each of you. Thank you for your help during my life in Spain and I will treasure this wonderful memory during my whole life.

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helped me. I consider myself lucky that I could meet you guys in Spain. Thanks for your support, encouragement and friendship. I will never forget those happy days we spent together. Looking forward to meeting you guys again in the world, someday, somewhere, so stay in touch and I hope our paths will cross again soon.

Finally, I owe an enormous debt of gratitude to my parents Chao Huang, Junxuan Jiang, Aiping Tang, Xuemei Peng. Your unconditional love, understanding, and unwavering support are the origin of the power for me to keep on moving in my research. I am extremely indebted to my husband Weifan Tang who gives me deep love and the continuous en-couragement. Thank you for listening to my complaints and frustrations about study and research, and for believing in me. Without all of this, I would not have completed this thesis. A special thanks to my forthcom-ing baby for comforthcom-ing to my life at this remarkable moment, and makforthcom-ing everyday so beautiful.

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Publications

Journal Articles

• Xiaoge Huang, Baltasar Beferull-Lozano, and Carmen Botella,

“Quasi-nash equilibria for non-convex distributed power alloca-tion games in cognitive radios,” Wireless Communicaalloca-tions, IEEE Transactions on. To be published. Accepted May, 2013.

• Xiaoge Huang, Baltasar Beferull-Lozano, and Carmen Botella,

“Joint sensing and power allocation in non-convex power allocation games in MIMO cognitive radio networks,” Wireless Communica-tions, IEEE Transactions on. To be submitted, 2013.

Conference Proceedings

• Xiaoge Huang and Baltasar Beferull-Lozano, “Joint optimization

of detection and power allocation for OFDM-based cognitive ra-dios,” In IEEE Global Telecommunications Conference (GLOBE-COM 2010), pages 1-5, December, 2010.

• Xiaoge Huang and Baltasar Beferull-Lozano, “Power allocation

op-timization in OFDM-based cognitive radios based on sensing infor-mation,” In IEEE International Conference on Acoustics, Speech and Signal Process (ICASSP 2011), pages 3192-3195, May, 2011.

• Xiaoge Huang and Baltasar Beferull-Lozano, “Non-cooperative power

allocation game with imperfect sensing information for cognitive radio,” In IEEE International Conference on Communications (ICC 2012), pages 1666-1671, June, 2012.

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“Non-convex power allocation games in MIMO cognitive radio networks,” In IEEE International Workshop on Signal Process-ing Advances for Wireless Communications (SPAWC 2013), June, 2013.

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Abstract

In this thesis, we explore interweave communication systems in cognitive radio networks where the overall objective is to maximize the sum-rate of each cognitive radio user by optimizing jointly both the detection oper-ation based on sensing and the power allocoper-ation across channels, taking into account the influence of the sensing accuracy and the interference limitation to the primary users. The optimization problem is addressed in single and multiuser cognitive radio networks for both single-input single-output and multi-input multi-output channels.

Firstly, we study the resource allocation optimization problem for single-input single-output single user cognitive radio networks, wherein the cognitive radio aims at maximizing its own sum-rate by jointly optimiz-ing the sensoptimiz-ing information and power allocation over all the channels. In this framework, we consider an opportunistic spectrum access model under interweave systems, where a cognitive radio user detects active primary user transmissions over all the channels, and decides to trans-mit if the sensing results indicate that the primary user is inactive at this channel. However, due to the sensing errors, the cognitive users might access the channel when it is still occupied by active primary users, which causes harmful interference to both cognitive radio users and primary users. This motivates the introduction of a novel interfer-ence constraint, denoted as rate-loss gap constraint, which is proposed to design the power allocation, ensuring that the performance degradation of the primary user is bounded. The resulting problem is non-convex, thus, an exhaustive optimization algorithm and an alternating direction optimization algorithm are proposed to solve the problem efficiently. Secondly, the resource allocation problem for a single-input single-output multiuser cognitive radio network under a sensing-based spectrum shar-ing scheme is analyzed as a strategic non-cooperative game, where each

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order to maximize its own sum-rate by considering the effect of imper-fect sensing information. The resulting game-theoretical formulations belong to the class of non-convex games, where the non-convexity oc-curs at both the objective functions and feasible constraint sets of the cognitive radio users’ optimization problems. A distributed cooperative sensing scheme based on a consensus algorithm is considered in the pro-posed game, where all the cognitive radio users can share their sensing information locally. We start with the alternating direction optimiza-tion algorithm, and prove that the local Nash equilibrium is achieved by the alternating direction optimization algorithm. In the next step, we use a new relaxed equilibrium concept, namely, quasi-Nash equilibrium for the non-convex game instead of the traditional Nash equilibrium for the convex game. The analysis of the sufficient conditions for the existence of the quasi-Nash equilibrium for the proposed game is pro-vided. Furthermore, an iterative primal-dual interior point algorithm that converges to a quasi-Nash equilibrium of the proposed game is also proposed. From the simulation results, the proposed algorithm is shown to yield a considerable performance improvement in terms of the sum-rate of each cognitive radio user, with respect to previous state-of-the-art algorithms.

Finally, we investigate a multiple-input multiple-output multiuser cog-nitive radio network under the opportunistic spectrum access scheme. We focus on the throughput of each cognitive radio user under correct sensing information, and exclude the throughput due to the erroneous decision of the cognitive radio users to transmit over occupied channels. The optimization problem is analyzed as a strategic non-cooperative game, where the transmit covariance matrix, sensing time, and detec-tion threshold are considered as multidimensional variables to be opti-mized jointly. The resulting game is non-convex, hence, we also use the new relaxed equilibrium concept quasi-Nash equilibrium and prove that the proposed game can achieve a quasi-Nash equilibrium under certain conditions, by making use of the variational inequality method. In par-ticular, we prove theoretically the sufficient condition of the existence and the uniqueness of the quasi-Nash equilibrium for this game. Further-more, a possible extension of this work considering equal sensing time is also discussed. Simulation results show that the iterative primal-dual interior point algorithm is an efficient solution that converges to the quasi-Nash equilibrium of the proposed game.

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Contents

List of Figures xxi

List of Tables xxiii

List of Abbreviations xxv

1 Introduction 1

1.1 Motivation . . . 3

1.2 Contributions . . . 4

1.2.1 Joint optimization of detection and power alloca-tion in single user CRNs . . . 4

1.2.2 Joint optimization of detection and power alloca-tion in multiuser CRNs . . . 5

1.3 Thesis Organization . . . 7

2 State of the Art 9 2.1 Cognitive Radio, a Brief Introduction . . . 9

2.1.1 Definition of CR . . . 9

2.1.2 Main tasks and key technologies . . . 10

2.1.3 The main challenges . . . 16

2.2 Game Theory in CRNs . . . 18

2.2.1 Basic concepts of game theory . . . 19

2.2.2 Nash equilibrium . . . 19

2.3 The Main Challenges in This Thesis . . . 20

2.3.1 Spectrum sensing . . . 20

2.3.2 Power allocation . . . 21

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2.4.1 Power allocation in single user CRNs . . . 22

2.4.2 Power allocation in multiuser CRNs . . . 23

2.5 Conclusions . . . 24

3 Joint Optimization of Detection and Power Allocation in Single User CRNs 27 3.1 System Model . . . 30

3.2 Problem Formulation . . . 32

3.3 Joint Optimization of Detection and Power Allocation . . 35

3.3.1 Exhaustive optimization of power allocation and detection . . . 36

3.3.2 Complexity analysis of the EPD algorithm . . . . 40

3.3.3 Alternating direction optimization of power allo-cation and detection . . . 40

3.3.4 Complexity analysis of the APD algorithm . . . . 42

3.4 Simulation Results . . . 43

3.4.1 Scenario description . . . 44

3.4.2 Simulation results analysis . . . 44

3.5 Conclusions . . . 50

4 Joint Optimization of Detection and Power Allocation in Multiuser SISO CRNs 51 4.1 System Model . . . 53

4.1.1 System model for multiuser CRNs . . . 54

4.1.2 Spectrum sensing . . . 55

4.2 Problem Formulation . . . 57

4.2.1 Total achievable rate of the CR users . . . 57

4.2.2 Constraints for the CR users . . . 58

4.2.3 Optimization problem . . . 61

4.3 Local Nash Equilibrium and Alternating Optimization . . 62

4.3.1 Alternating direction optimization in SISO CRNs . 62 4.3.2 Local power allocation optimization . . . 63

4.3.3 Local threshold optimization . . . 65

4.3.4 Local Nash equilibrium . . . 66

4.3.5 Complexity analysis of the ADOS algorithm . . . . 67

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CONTENTS

4.4.1 Equivalent reformulation of game theory . . . 69

4.4.2 VI method and KKT conditions . . . 70

4.4.3 Definition and basic concepts of QNE . . . 73

4.4.4 The existence of the QNE . . . 74

4.5 Primal-Dual Interior Point Optimization in SISO CRNs . 76 4.5.1 Line search iterations . . . 78

4.5.2 Trust region iterations . . . 80

4.5.3 Complexity analysis of the PDIPS algorithm . . . 82

4.6 Simulation Results . . . 84

4.6.1 Scenario description . . . 84

4.6.2 Simulation results analysis . . . 85

4.7 Conclusions . . . 90

5 Joint Optimization of Detection and Power Allocation in Multiuser MIMO CRNs 91 5.1 System Model . . . 94

5.1.1 System model for multiuser MIMO CRNs . . . 94

5.1.2 Spectrum sensing . . . 95

5.2 Problem Formulation . . . 97

5.2.1 Total achievable throughput of the CR users . . . 98

5.2.2 Constraints for the CR users . . . 98

5.2.3 Optimization problem . . . 100

5.3 QNE for Non-Convex Game in MIMO CRNs . . . 100

5.3.1 Equivalent reformulation of game theory . . . 101

5.3.2 VI method and KKT conditions . . . 102

5.3.3 The existence and the uniqueness of QNE . . . 104

5.3.4 Equi-sensing time for all the CR users . . . 105

5.4 Primal-Dual Interior Point Optimization in MIMO CRNs 107 5.4.1 Complexity analysis of the PDIPM algorithm . . . 108

5.5 Simulation Results . . . 110

5.5.1 Scenario description . . . 110

5.5.2 Simulation results analysis . . . 112

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6 Conclusion and Future Work 117 6.1 Conclusions . . . 117

6.1.1 Joint optimization of detection and power alloca-tion in single user SISO CRNs . . . 117 6.1.2 Joint optimization of detection and power

alloca-tion in multiuser SISO CRNs . . . 118 6.1.3 Joint optimization of detection and power

alloca-tion in multiuser MIMO CRNs . . . 119 6.2 Future Work . . . 120

Appendices 122

A Definition of the Tangent Cone 123

B Basic Concepts of Variational Inequality Theory 125

C Proof of Theorem 2 129

D Proof of Theorem 3 133

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List of Figures

1.1 Spectrum allocation table from FCC [1] . . . 2

2.1 Cognitive radio operation cycle [2] . . . 12

2.2 Energy detection [3] . . . 14

3.1 OFDM modulation [4] . . . 28

3.2 System Model: one pair of PU Tx-Rx and one pair of CR Tx-Rx . . . 30

3.3 The optimal solutionP? k . . . 39

3.4 EPD algorithm: sum-rate versus threshold for different values of rate-loss gap Γk, withPmax=6W . . . 45

3.5 EPD algorithm: sum-rate versus threshold for different values of power budgetPmax, with Γk=0.1% . . . 46

3.6 APD algorithm: sum-rate versus power budget Pmax for different values of rate-loss gap Γk=0.1%,0.2%,0.3% . . . 47

3.7 APD algorithm: sum-rate versus rate-loss gap Γk for dif-ferent values of power budgetPmax=3W,6W,9W . . . 48

3.8 Sum-rate versus power budget Pmax for different algo-rithms, with Γk=0.1% . . . 49

4.1 System model: N PUs and M CR Tx-Rx pairs. PU k uses channelk,k= 1, ..., N. . . 54

4.2 Frame structure of conventional sensing-based spectrum sharing. . . 55

4.3 Network topology: location of two PUs and three CR Tx-Rx pairs. . . 85

4.4 Sum-rate achieved at the QNE with differentPi max . . . . 86

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4.5 Sum-rate achieved at the QNE versus Pi

max; comparison

between DG, ADOS and PDIPS algorithms. . . 87 4.6 Sum-rate achieved at the QNE versus Pi

max; comparison

betweenP(Hk,1) = 0.5 and P(Hk,1) = 0.9. . . 88

4.7 Sum-rate achieved at the QNE versus Pi

max; comparison

between global constraint and individual constraint. . . . 89 4.8 Average-rate gap for PU achieved at the QNE versus

Pi

max; comparison between constraints (4.17) and (4.19). . 90

5.1 System model for MIMO CRNs. . . 94 5.2 Frame structure of conventional sensing-based spectrum

sharing withL antennas for MIMO CRi. . . 95

5.3 Radio environment map of two PUs and six CR Tx-Rx pairs . . . 110 5.4 Throughput versus iteration number for different CR users111 5.5 Throughput versus optimal sensing time for different CR

users . . . 112 5.6 Throughput versus sensing time for different values ofPmask113

5.7 Throughput gain U

Ud versus normalized interference

Pi mask

Pi

max . 114

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List of Tables

1.1 Scenarios addressed in each chapter . . . 7 3.1 Notation for single user SISO CRNs . . . 29 3.2 Simulation parameters . . . 44 4.1 Notation for multiuser SISO CRNs . . . 53 4.2 Four instantaneous rates at CR-Rx i . . . 57

4.3 Notation of quasi-Nash equilibrium . . . 69 4.4 Notation of PDIPS . . . 77 4.5 Simulation parameters . . . 84 5.1 Notation for multiuser MIMO CRNs . . . 93 5.2 Simulation parameters . . . 110

(24)
(25)

List of Abbreviations

ADO Alternating Direction Optimization

ADOS ADO for SISO CRNs

APD Alternating Optimization of Power Allocation and Detection

CR Cognitive Radio

CRNs Cognitive Radio Networks

CCC Common Control Channel

CSI Channel State Information

DG Deterministic Game

DSA Dynamic Spectrum Access

ECC Electronic Communications Committee

EPD Exhaustive Optimization of Power Allocation and Detection

FCC Federal Communications Commission

ISM Industrial, Scientific and Medical

KKT Karush-Kuhn-Tucker

LICQ Linear Independent Constraint Qualification

MIMO Multiple-Input Multiple-Output

MUI Multiuser Interference

NCG Non-Cooperative Game

NE Nash Equilibrium

NNPG Non-Convex Non-Cooperative Power Allocation Game

OFDM Orthogonal Frequency Division Multiplexing

(26)

PDIP Primal-Dual Interior Point

PDIPM Primal-Dual Interior Point Optimization in MIMO CRNs PDIPS Primal-Dual Interior Point Optimization in SISO CRNs

PLR Power Budget Limited Regime

PU Primary User

QNE Quasi-Nash Equilibrium

Rx Receiver

RLR Rate-Loss Limited Regime

SNR Signal to Noise Radio

SISO Single-Input Single-Output

SSS Sensing-Based Spectrum Sharing

Tx Transmitter

VI Variational Inequality

WF Water-Filling

WLANs Wireless Local Area Networks WPANs Wireless Personal Area Networks WRANs Wireless Regional Area Networks

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Chapter 1

Introduction

The science is nothing more than a refinement of everyday thinking.

——Albert Einstein(1879-1955)

During the last decade, wireless communication networks have been greatly developed including third generation 3G, fourth generation cel-lular networks, IEEE 802.11 Wireless Local Area Networks (WLANs), IEEE 802.15.4 WPANs, Bluetooth, etc. The radio spectrum ranging from 3KHz to 300GHz is the basic resource to carry data in wireless networks. In each region, spectrum is regulated by its radio regulatory agency, such as Federal Communications Commission (FCC) in USA [6], Electronic Communications Committee (ECC) in Europe [7], and Ofcom in UK [8]. Spectrum is traditionally assigned via a fixed frequency al-location policy. For example, the spectrum alal-location table by FCC is shown in Figure 1.1, where each portion of spectrum is exclusively al-located to a specific wireless system, and all subscribers to a wireless system should be granted to access the exclusive spectrum. Following this traditional approach, the spectrum resource is in danger of being exhausted. Obtaining a license on a spectrum band is becoming more and more difficult and expensive.

The Industrial, Scientific and Medical (ISM) spectrum band, which is mostly located around 2.4 GHz and 5 GHz, is the only spectrum that can be shared by different networks. WLANs, WPANs, cordless phones, and even microwave ovens are operating simultaneously in the ISM spectrum band, and thus experiencing interference from each other. Therefore, the

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U.S. DEPARTMENT OF COMMERCE N A TIO NA L T ELECOMMUN ICATIONS & INFORMATION ADMIN

ISTR

A

TIO

N

MOBILE (AERONAUTICAL TELEMETERING)

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5.685.735.905.95 6.2 6.5256.6856.7657.07.17.37.35 8.18.195 8.8158.9659.0409.49.5 9.99.99510.00310.00510.110.15 11.17511.27511.411.611.6512.0512.1012.2313.213.2613.3613.4113.5713.613.813.8714.014.2514.3514.99015.00515.01015.1015.615.816.36 17.4117.4817.5517.917.9718.0318.06818.16818.7818.919.0219.6819.8019.99019.99520.00520.01021.021.4521.8521.92422.022.85523.023.223.3524.8924.9925.00525.0125.0725.2125.3325.5525.6726.126.17526.4826.9526.9627.2327.4127.5428.029.729.829.8929.9130.0

UNITED

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THE RADIO SPECTRUM

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STANDARD FREQ. AND TIME SIGNAL

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Space Research

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Space Research

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STD. FREQ. & TIME SIGNAL SAT. (400.1 MHz)

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SPACE RES.(S-E) Earth Expl.Satellite (E-S)

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SPACE RESEARCH (S-E)

AERONAUTICALRADIONAVIGATION

RADIOLOCATION

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RADIO-LOCATIONRadiolocation

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)

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RADIO-LOCATION

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StandardFrequency andTime SignalSatellite (E-S)

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StandardFrequency andTime SignalSatellite (S-E)Stand. Frequencyand Time SignalSatellite (S-E)

FIXED MOBILE RADIO ASTRONOMY SPACERESEARCH(Passive) EARTH

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RADIONAVIGATION RADIONAVIGATION INTER-SATELLITE RADIONAVIGATION RADIOLOCATION Radiolocation SPACE RE..(Passive)

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FIXED MOBILE FIXED MOBILE FIXED MOBILE Mobile Fixed FIXED SATELLITE (S-E) BROAD-CASTING BCSTSAT. FIXED MOBILE FX SAT(E-S) MOBILE FIXED EARTHEXPLORATIONSATELLITE FI XEDSATELLITE (E-S) MOBILE SATELLITE (E-S) MOBILE FIXED SPACERESEARCH(Passive) EARTH EXPLORATIONSATELLITE(Passive) EARTH

EXPLORATION SAT. (Passive) SPACERESEARCH(Passive) INTER-SATELLITE RADIO-LOCATION SPACERESEARCH FIXED MOBILE F I X E D MOBILE SATELLITE (E-S) MOBILESATELLITE RADIONAVIGATION RADIO-NAVIGATIONSATELLITE EARTHEXPLORATIONSATELLITE F I X E D SATELLITE (E-S) MOBILE FIXED FIXED SATELLITE (E-S) AMATEUR AMATEUR SATELLITE AMATEUR AMATEUR SATELLITE AmateurSatellite Amateur RADIO-LOCATION MOBILE FIXED MOBILESATELLITE(S-E) FIXEDSATELLITE(S-E) MOBILE FIXED BROAD-CASTINGSATELLITE BROAD-CASTINGSPACE

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RADIONAV. SATELLITE (Space to Earth)

AERONAUTICAL MOBILE SATELLITE (R)

(space to Earth)

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300 325335 405415 435 495505510 525535 16051615 1705 1800 1900 20002065210721702173.52190.52194 2495250125022505 2850 3000 RADIO-LOCATION BROADCASTING FIXED MOBILE AMATEUR RADIOLOCATION MOBILE FIXED MARITIMEMOBILE

MARITIME MOBILE (TELEPHONY)

MARITIMEMOBILE

LANDMOBILE

MOBILE

FIXED

30.030.56 32.033.0 34.0 35.0 36.037.037.538.038.2539.040.0 42.0 43.69 46.647.0 49.650.0 54.0 72.073.074.674.875.275.476.0 88.0 108.0 117.975121.9375123.0875123.5875 128.8125132.0125136.0137.0137.025137.175137.825138.0144.0146.0148.0149.9150.05150.8152.855154.0156.2475157.0375157.1875157.45161.575161.625161.775162.0125 173.2173.4174.0 216.0220.0222.0225.0 235.0 300

ISM – 6.78 ± .015 MHz ISM – 13.560 ± .007 MHz ISM – 27.12 ± .163 MHz

ISM – 40.68 ± .02 MHz ISM – 24.125 ± 0.125 GHz 30 GHz ISM – 245.0 ± 1GHz ISM – 122.5 ± .500 GHz ISM – 61.25 ± .250 GHz 300.0 322.0328.6335.4 399.9400.05400.15401.0402.0403.0406.0406.1410.0420.0 450.0454.0455.0456.0460.0462.5375462.7375467.5375467.7375470.0 512.0 608.0614.0 698746764776 794806821824849851866869894896901 901 902928929930931932935940941944960 12151240 13001350139013921395140014271429.5143014321435152515301535154415451549.51558.5155916101610.61613.81626.5 16601660.51668.4167016751700171017551850200020202025211021552160218022002290230023052310232023452360238523902400241724502483.52500265526902700 29003000

MARITIME MOBILE SATELLITE

(space to Earth)

MOBILE SATELLITE (S-E)

RADIOLOCATION

RADIONAVIGATIONSATELLITE (S-E)RADIOLOCATION

Amateur

Radiolocation

AERONAUTICALRADIONAVIGATION

SPA CE RESEARCH ( Passive)

EARTH EXPL SAT (Passive)

RADIO ASTRONOMY MOBILEMOBILE ** FIXED-SAT (E-S) FIXED FIXED FIXED** LAND MOBILE (TLM)

MOBILE SAT. (Space to Earth) MARITIME MOBILE SAT.(Space to Earth) Mobile(Aero. TLM)

MOBILE SATELLITE (S-E)

MOBILE SATELLITE(Space to Earth)

AERONAUTICAL MOBILE SATELLITE (R)

(space to Earth) 3.0 3.1 3.3 3.53.63.653.7 4.2 4.44.5 4.84.944.995.05.155.255.355.465.475.65.655.835.855.9256.4256.5256.706.8757.0257.0757.125 7.197.2357.257.307.457.557.757.908.0258.1758.2158.48.458.59.09.29.39.5 10.010.4510.510.5510.610.6810.7 11.7 12.2 12.712.7513.2513.413.7514.014.214.414.4714.514.714515.136515.3515.415.4315.6315.716.617.117.217.317.717.818.318.618.819.319.720.120.221.221.422.022.2122.522.5523.5523.624.0 24.0524.2524.4524.6524.75 25.0525.2525.527.027.529.529.930.0 ISM – 2450.0 ± 50 MHz 30.031.031.331.832.032.333.033.4 36.037.037.638.038.639.540.040.541.042.543.545.546.947.047.248.250.250.451.452.6 54.2555.7856.957.058.259.059.3 64.065.066.0 71.0 74.075.576.077.077.578.081.0 84.0 86.0 92.095.0 100.0102.0105.0 116.0119.98120.02126.0 134.0 142.0144.0149.0150.0151.0 164.0168.0170.0174.5176.5182.0185.0190.0 200.0202.0 217.0 231.0235.0238.0241.0248.0250.0252.0 265.0 275.0 300.0 ISM – 5.8 ± .075 GHz ISM – 915.0 ± 13 MHz INTER-SATELLITE

RADIOLOCATION SATELLITE (E-S)

AERONAUTICALRADIONAV.

PLEASE NOTE: THE SPACING ALLOTTED THE SERVICES IN THE SPEC-TRUM SEGMENTS SHOWN IS NOT PROPORTIONAL TO THE ACTUAL AMOUNT OF SPECTRUM OCCUPIED. AERONAUTICAL MOBILE AERONAUTICAL MOBILE SATELLITE AERONAUTICAL RADIONAVIGATION AMATEUR AMATEUR SATELLITE BROADCASTING BROADCASTING SATELLITE EARTH EXPLORATION SATELLITE FIXED FIXED SATELLITE INTER-SATELLITE LAND MOBILE LAND MOBILE SATELLITE MARITIME MOBILE MARITIME MOBILE SATELLITE MARITIME RADIONAVIGATION METEOROLOGICAL AIDS METEOROLOGICAL SATELLITE MOBILE MOBILE SATELLITE RADIO ASTRONOMY RADIODETERMINATION SATELLITE RADIOLOCATION RADIOLOCATION SATELLITE RADIONAVIGATION RADIONAVIGATION SATELLITE SPACE OPERATION SPACE RESEARCH STANDARD FREQUENCY AND TIME SIGNAL STANDARD FREQUENCY AND TIME SIGNAL SATELLITE

RADIO ASTRONOMY FIXED MARITIME MOBILE FIXED MARITIME MOBILE Aeronautical Mobile

STANDARD FREQ. AND TIME SIGNAL (60 kHz)

FIXED

Mobile*

STAND. FREQ. & TIME SIG

.

MET. AIDS (Radiosonde)

Space Opn. (S-E)

MOBILE.SAT. (S-E)

Fixed

StandardFreq. andTime SignalSatellite (E-S)

FIXED

STANDARD FREQ. AND TIME SIGNAL (20 kHz)

Amateur

MOBILE

FIXED SAT. (E-S)

SpaceResearch

ALLOCATION USAGE DESIGNATION

SERVICE EXAMPLE DESCRIPTION Primary FIXED Capital Letters S e c o n d a r yMobile 1st Capital with lower case letters

U.S. DEPARTMENT OF COMMERCE National Telecommunications and Information Administration

Office of Spectrum Management October 2003

MOBILE

BROADCASTING

TRAVELERS INFORMATION STATIONS (G) AT 1610 kHz

59-64 GHz IS DESIGNATED FORUNLICENSED DEVICES

Fixed

AERONAUTICALRADIONAVIGATION

SPACE RESEARCH (Passive)

* EXCEPT AERO MOBILE (R)

** EXCEPT AERO MOBILE WAVELENGTH

BAND DESIGNATIONS ACTIVITIES FREQUENCY 3 x 107m3 x 106m3 x 105m30,000 m3,000 m 300 m 30 m 3 m 30 cm 3 cm 0.3 cm 0.03 cm3 x 105Å3 x 104Å3 x 10Å33 x 102Å 3 x 10Å 3Å 3 x 10-1Å3 x 10-2Å3 x 10-3Å3 x 10-4Å3 x 10-5Å3 x 10-6Å 3 x 10-7Å 0 10 Hz 100 Hz1 kHz 10 kHz100 kHz 1 MHz 10 MHz100 MHz1 GHz 10 GHz 100 GHz1 THz1013Hz 1014Hz 1015Hz 1016Hz 1017Hz 1018Hz 1019Hz 1020Hz 10Hz21 1022Hz 1023Hz 1024Hz 1025Hz

THE RADIO SPECTRUM MAGNIFIED ABOVE

3 kHz 300 GHz

VERY LOW FREQUENCY (VLF)

Audible Range AM Broadcast FM Broadcast RadarSub-Millimeter Visible Ultraviolet Gamma-ray Cosmic-ray

Infra-sonics Sonics Ultra-sonics Microwaves Infrared

PLSCX RadarBands

LF MF HF VHF UHF SHF EHF INFRARED VISIBLE ULTRAVIOLET X-RAY GAMMA-RAY COSMIC-RAY

X-ray ALLOCATIONS FREQUENCY BROADCASTING FIXED MOBILE* BROADCASTING FIXED BROADCASTING FIXED Mobile FIXED BROADCASTING BROADCASTING FIXED FIXED BROADCASTING FIXED BROADCASTING FIXED BROADCASTING FIXED BROADCASTING FIXED BROADCASTING FIXED BROADCASTING FIXED FIXED

FIXED FIXEDFIXED FIXED LANDMOBILE

FIXED AERONAUTICAL MOBILE (R)

AMATEUR SATELLITE

AMATEUR

MOBILE SATELLITE (E-S)

FIXED Fixed Mobile Radio-location FIXED MOBILE LAND MOBILE MARITIME MOBILE FIXED LAND MOBILE FIXED LAND MOBILE RADIONAV-SATELLITE FIXED MOBILE FIXED LAND MOBILE

MET. AIDS (Radio- sonde)

SPACE OPN. (S-E)

Earth Expl Sat(E-S)

Met-Satellite (E-S) MET-SAT. (E-S)

EARTH EXPLSAT. (E-S)

Earth Expl Sat(E-S)

Met-Satellite (E-S)

EARTH EXPLSAT. (E-S)

MET-SAT. (E-S) LAND MOBILE

LAND MOBILE FIXED LAND MOBILE FIXED FIXED FIXED LAND MOBILE LAND MOBILE FIXED LAND MOBILE LAND MOBILE LAND MOBILE LAND MOBILE MOBILE FIXED MOBILE FIXED BROADCAST MOBILE FIXED MOBILE FIXED FIXED LAND MOBILE LAND MOBILE FIXED LAND MOBILE AERONAUTICAL MOBILE AERONAUTICAL MOBILE FIXED LAND MOBILE LAND MOBILE LAND MOBILE FIXED LAND MOBILE FIXED MOBILE FIXED FIXED FIXED MOBILE FIXEDFIXED FIXED BROADCAST

LAND MOBILELAND MOBILE

FIXED

LAND MOBILE METEOROLOGICAL

AIDS FX Space res. Radio Ast E-Expl Sat FIXED MOBILE**

MOBILE SATELLITE (S-E)

RADIODETERMINATION SAT. (S-E)

Radiolocation MOBILE FIXED Amateur Radiolocation AMATEUR FIXED MOBILE B-SAT FX MOB Fixed Mobile Radiolocation RADIOLOCATION MOBILE ** Fixed (TLM) LAND MOBILE FIXED (TLM) LAND MOBILE (TLM) FIXED-SAT (S-E) FIXED (TLM)

MOBILEMOBILE SAT. (Space to Earth) Mobile ** MOBILE**

FIXED

MOBILE

MOBILE SATELLITE (E-S)

SPACE OP.(E-S)(s-s)

EARTH EXPL. SAT. (E-S)(s-s)

SPACE RES.(E-S)(s-s) FX. MOB. MOBILE FIXED Mobile R- LOC. BCST-SATELLITE Fixed Radio-location B-SAT R- LOC. FX MOB Fixed Mobile Radiolocation FIXED MOBILE** Amateur RADIOLOCATION SPACE RES..(S-E) MOBILE

FIXEDMOBILE SATELLITE (S-E)

MARITIME MOBILE Mobile FIXED FIXED BROADCAST MOBILE FIXED

MOBILE SATELLITE (E-S)

FIXED F IXED MARITIME MOBILE FIXED FIXED MOBILE** FIXED MOBILE**

FIXED SAT (S-E)

AERO. RADIONAV.

FIXED

SATELLITE (E-S)

Amateur- sat (s-e)

Amateur

MOBILE

FIXED SAT(E-S)

FIXED

FIXED SATELLITE (S-E)(E-S)

FIXED

FIXED SAT (E-S)

MOBILE Radio- location RADIO-LOCATION FIXED SAT.(E-S ) Mobile**Fixed Mobile FX SAT.(E-S) L M Sat(E-S) AERO RADIONAV

FIXED SAT (E-S)

AERONAUTICAL RADIONAVIGATION RADIOLOCATION Space Res.(act.) RADIOLOCATION Radiolocation Radioloc. RADIOLOC.

Earth Expl Sat

Space

Res.

Radiolocation

BCST SAT.

FIXED

FIXED SATELLITE (S-E)

FIXED SATELLITE (S-E)

EARTH EXPL. SAT.

FX SAT (S-E)

SPACE RES.

FIXED SATELLITE (S-E)

FIXED SATELLITE (S-E)FIXED SATELLITE (S-E)

MOBILE SAT. (S-E)

FX SAT (S-E)

MOBILE SATELLITE (S-E)FX SAT (S-E)

STD FREQ. & TIME

MOBILE SAT (S-E)EARTH EXPL. SAT.

MOBILE FIXED SPACE RES. FIXED MOBILEMOBILE** FIXED

EARTH EXPL. SAT.

FIXED MOBIL E** RAD.AST SPACE RES. FIXED MOBILE INTER-SATELLITE FIXED RADIO ASTRONOMY SPACE RES.(Passive) AMATEUR AMATEUR SATELLITE Radio-location Amateur RADIO-LOCATION Earth Expl.Satellite (Active)

FIXED

INTER-SATELLITE

RADIONAVIGATION

RADIOLOCATION SATELLITE (E-S)

INTER-SATELLITE FIXED SATELLITE (E-S) RADIONAVIGATION FIXED SATELLITE (E-S) FIXED MOBILE SATELLITE (E-S)

FIXED SATELLITE (E-S)

MOBILE

FIXED

Earth ExplorationSatellite (S-S) std freq & time

e-e-sat (s-s) MOBILE FIXED e-e-sat MOBILE SPACE

RESEARCH (deep space)

RADIONAVIGATION

INTER- SAT

SPACE RES. FIXED

MOBILE SPACE RESEARCH (space-to-Earth) SPACERES. FIXEDSAT. (S-E) MOBILE FIXED FIXED-SATELLITE MOBILE FIXED FIXED SATELLITE MOBILESAT. FIXEDSAT MOBILESAT.

EARTH EXPL SAT (E-S) Earth Expl.Sat (s - e)

SPACE RES. (E-S)

FX-SAT(S-E) FIXED MOBILE BROAD-CASTING BCSTSAT. RADIOASTRONOMY FIXED MOBILE* * FIXED

SATELLITE (E-S)MOBILE

SATELLITE (E-S) FIXED SATELLITE (E-S) MOBILE RADIONAV.SATELLITE FIXED MOBILE MOB. SAT(E-S) RADIONAV.SAT.

MOBILESAT (E-S).

FIXED MOBILE FX SAT(E-S) MOBILE FIXED INTER- SAT

EARTH EXPL-SAT (Passive)

SPACE RES. INTER- SAT SPACE RES. EARTH-ESINTER- SAT EARTH-ES SPACE RES. MOBILE FIXED EARTH

EXPLORATION SAT. (Passive)

SPACE RES. MOBILE FIXED INTER- SAT FIXED MOBILE INTER-SAT RADIO- LOC. MOBILE FIXED EARTH

EXPLORATION SAT. (Passive)

MOBILE FIXED INTER-SATELLITE FIXED MOBILE** MOBILE** INTER-SATELLITE MOBILE INTER-SATELLITE RADIOLOC. Amateur Amateur Sat. Amateur RADIOLOC. AMATEUR SAT AMATEUR RADIOLOC. SPACERESEARCH(Passive) EARTHEXPL SAT.(Passive)

FIXED

MOBILE

INTER-SATELLITE SPACERESEARCH(Passive) EARTHEXPL SAT.(Passive)Amatuer

FIXED MO-BILE INTER- SAT. SPACERES. E A R T H EXPL . SAT INTER-SATELLITE INTER-SAT.INTER-SAT. MOBILE FIXED FX-SAT (S - E) BCST - SAT. B- SAT. MOB** FX-SAT SPACE RESEARCH SPACE RES..

This chart is a graphic single-point-in-time portrayal of the Table of Frequency Allocations used by the FCC and NTIA. As such, it does not completely reflect all aspects, i.e., footnotes and recent changes made to the Table of Frequency Allocations. Therefore, for complete information, users should consult the Table to determine the current status of U.S. allocations.

Figure 1.1: Spectrum allocation table from FCC [1]

performance of wireless networks working in the ISM spectrum band is highly limited by the coexistence of other nearby wireless networks. In addition, the licensed spectrum utilization is highly dependent on the location and time. For instance, during some time periods in a certain geographic area, the allocated spectrum bands may be seldom used. In November 2002, the FCC published a report to indicate that during 90% of the time, many licensed frequency bands remain unused [1]. Fur-thermore, the Shared Spectrum Company (SCC) has published a bunch of spectrum measurement results of USA and some European Countries since 2004 [9]. From their spectrum reports [10, 11], the average uti-lization of many licensed frequency bands in many cities is less than 25%. This means that it is not an actual spectrum scarcity what is worrisome, but rather the inefficient spectrum usage. As a result, since 2004, FCC has recommended to consider authorizing new devices in the TV broadcast spectrum at locations where TV channels are not being used for authorized services, including broadcast television, broadcast auxiliary services such as wireless microphones, and private land mobile radio [12]. The IEEE 802.22 Working Group on Wireless Regional Area

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1.1 Motivation Networks (WRANs) was formed in October 2004, and has been working on the standardization for the rural broadband wireless access using the TV broadcast spectrum by Cognitive Radio (CR) technologies [13]. The basic idea behind IEEE 802.22 is to exploit the unused or not fully utilized licensed spectrum, which is called “spectrum hole”. Actually, this idea was proposed in the light of the concept of CR by Joseph Mitola III at Royal Institute of Technology (KTH), Sweden, in 1999 [14]. In essence, CR technology differs from conventional radio devices in that a CR can equip users with cognitive capability and reconfigurability (e.g., frequency, power, modulation), allowing for Dynamic Spectrum Access (DSA). Following this concept, many national regulatory bodies (i.e., the FCC in the USA) have recently proposed expanding the unli-censed spectral bands to obtain more flexible utilization of the available spectrum through the use of CR technology. As such, CR is foreseen as one of the most viable technical paradigms to improve the spectrum uti-lization significantly, and contribute to solving the problem of spectrum shortage.

1.1

Motivation

Although spectrum sharing brings opportunities for CR users to access the licensed channels∗, many new challenges come up when deploying

CR in practice. On the one hand, the challenge for a reliable sensing method to find the “spectrum hole” is to identify suitable transmis-sion opportunities without compromising the integrity of the Primary User (PU). One of the design criteria is to make the probability of false alarm as low as possible, since it measures the percentage of vacant spectrum that is misclassified as busy, increasing thus the opportunistic usage of the spectrum from the CR users. On the other hand, in or-der to limit the probability of having CR users interfering with PUs, it is desirable to keep the missed detection probability as low as possible. The detection thresholds are the trade-off factor between the false alarm and the missed detection probabilities: generally speaking, low thresh-olds will result in high false alarm rates in favor of low missed detection probability and vice versa. Alternatively, the choice of the sensing time offers a trade-off between the quality and speed of sensing: increasing

In this thesis, a channel means a frequency subband or an aggregation of fre-quency subbands (frefre-quency bands) for spectrum sensing and transmitting.

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the sensing time permits to decrease both false alarm and miss detection probability values, however, it reduces the time available for secondary transmissions, which decreases CR throughput. The above trade-off calls naturally for a joint determination of the sensing and transmission parameters of the CR users, assuming a paradigm of selfish behavior among these CR users, where the CR users have no willing to cooperate with each other.

In this thesis, for the application of CR technology, we investigate ap-plications for both single user and multiuser Cognitive Radio Networks (CRNs). In the case of single user CRNs, we study the problem of power allocation making use of the detection information under an op-portunistic spectrum access model. For multiuser CRNs, we analyze the noncooperative behavior of the CR users based on game theory. The modeling and analysis of the competitive multiuser optimization, taken into consideration the sensing accuracy, is the main overall subject of this thesis.

1.2

Contributions

In [15–19], we have explored a sensing-based access scheme in CRNs where the overall objective is to maximize the sum-rate (sum-throughput) of each CR user by optimizing jointly both the detection operation based on sensing and the power allocation, taking into account the influence of the sensing accuracy and the interference limitation to the PUs. The optimization problem is addressed in single and multiuser CRNs for both Single-Input Single-Output (SISO) and Input Multiple-Output (MIMO) channel. In the following, we enumerate the main topics where this thesis provides contributions.

1.2.1 Joint optimization of detection and power

alloca-tion in single user CRNs

We start with the resource allocation and optimization problem for single user CRNs [15,16], where joint power allocation and spectrum detection are key issues. In single user CRNs, the CR-Transmitter (Tx) has to perform the spectrum sensing before accessing the channel. We consider the Opportunistic Spectrum Access (OSA) model under the

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opportunis-1.2 Contributions tic spectrum access scheme. In the OSA model, CR users are allowed to transmit over the channel of interest when all the PUs are detected as not transmitting at this channel. One essential enabling technique for OSA-based CRNs is spectrum sensing, where the CR users individually or collaboratively detect active PU transmissions over the channel, and decide to transmit if the sensing results indicate that all the PUs are inactive in this channel. The main contributions of Chapter 3 are the following:

• We consider an Orthogonal Frequency Division Multiplexing (OFDM)

based communication system and present efficient algorithms to maximize the sum-rate of the CR by optimizing jointly both the detection operation and the power allocation. The problem is non-convex, and can be formulated as a two-variable problem and solved by the alternating direction optimization method operating sequentially over the power allocation and the detection threshold.

• We show that the algorithm operates basically in two regimes

de-pending on the constraints involved. As compared to previous work, a novel interference constraint is proposed to design the power allocation scheme, ensuring that the performance degrada-tion of the PU is bounded.

1.2.2 Joint optimization of detection and power

alloca-tion in multiuser CRNs

In [17], we analyze the resource allocation problem among CR users for the Sensing-Based Spectrum Sharing (SSS) scheme as a strategic Non-Cooperative Game (NCG), where each CR user is selfish and strives to use the available spectrum in order to maximize its own sum-rate by considering the effect of imperfect sensing information. The resulting game-theoretical formulations belong to the class of non-convex games, where the non-convexity occurs at both the objective functions and the feasible sets of the CR users’ optimization problems. Therefore, tra-ditional mathematical tools from [20] are not applicable to show the existence of an equilibrium for this game. We analyze our Non-Convex Non-Cooperative Power Allocation Game (NNPG) based on the new relaxed mathematical equilibria concept introduced in [21], namely, the Quasi-Nash Equilibrium (QNE). The main contributions of Chapter 4

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are the following:

• We propose a NNPG, where each CR user aims at maximizing its

own sum-rate by jointly optimizing the sensing operation as well as the transmit power over all channels, which differs from the disjoint case, called deterministic game where the sensing parameters are not considered as a part of the optimization, as shown in [22–26].

• Deviating from the constraints considered in previous work [22–

33] (such as interference temperature and outage probability con-straints), we introduce a rate-loss constraint in order to effectively protect the PU from harmful interference caused due to the imper-fect sensing information. We analyze the optimization problem in two different limited regimes, namely, power budget limited regime and rate-loss limited regime. The performance of the CR users in these regimes are evaluated extensively through simulation.

• In addition, a distributed cooperative sensing scheme based on a

consensus algorithm is considered in the proposed game for a SSS scenario. Compared with the OSA scenario discussed in [31–33], in our scenario, the CR users can coexist with PUs, and adjust the transmit power on each channel based on the sensing result.

• The fourth major contribution of this chapter is to prove that

the proposed NNPG can achieve a QNE under certain conditions, by making use of the Variational Inequality (VI) method. Mean-while, we show that, under the so-called linear independent con-straint qualification, the achieved QNE coincides with the Nash Equilibrium (NE).

• Finally, an iterative Primal-Dual Interior Point (PDIP) algorithm

that converges to a QNE of the proposed game is provided here. The PDIP algorithm can run at each node in parallel, since it re-quires only the local information of each CR user (e.g. its own transmit power and the channel gain), and hence, it can be re-garded as a distributed solution. Simulation results show that the PDIP algorithm yields a considerable performance improvement, in terms of the sum-rate of each CR user, with respect to previous state-of-the-art algorithms, such as alternating direction optimiza-tion algorithm [16] and the deterministic game proposed in [26].

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1.3 Thesis Organization In Chapter 5, we move a step ahead from Chapter 4, and consider an OSA scenario in multiuser MIMO CRNs [19]. The optimization problem is analyzed as a strategic NCG, where the transmit covariance matrix, sensing time, and detection threshold are considered as variables to be optimized. The resulting game is non-convex, hence, we also use the new relaxed equilibria concept QNE, and prove that the proposed game can achieve a QNE under certain conditions, by making use of the VI method. Simulations show that the proposed game can achieve a consid-erable performance improvement with respect to the deterministic game in [34].

1.3

Thesis Organization

This thesis is organized as follows. Chapter 2 introduces the background of CRNs, and summarizes the related works in optimization of power allocation and game theory in CRNs. Chapter 3 describes the proposed joint optimization of detection and power allocation schemes for single user CRNs. The proposed joint optimization of detection and power al-location schemes for multiuser SISO CRNs is given in Chapter 4. Chap-ter 5 provides the proposed joint optimization of detection and power allocation schemes for multiuser MIMO CRNs. Chapter 6 concludes our study in this thesis and points out several future directions in the research on CRNs. The relationship between the major chapters from Chapter 3 to Chapter 5 can be seen from Table 1.1, where we summarize the scenarios addressed in the different chapters.

Table 1.1: Scenarios addressed in each chapter

Chapter Number of CR Spectrum Share Mode Channel Mode

3 single user OSA SISO

4 multiuser SSS SISO

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Chapter 2

State of the Art

Cognitive radio (CR) is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spec-trum. The ultimate goal for the CR is to accommodate the increasing demand for wireless data transmission by using the radio spectrum more efficiently.

In this chapter, we introduce the background of CR technologies, a brief description of game theory and present the related work. We first intro-duce in Section 2.1 and Section 2.2 the background of CR technologies

including the definition, key technologies, and main topic in CRNs, re-spectively. The main concepts of game theory that are used in our optimization problem, are presented in Section 2.3. Finally, the related

work in Section 2.4 is organized around two main themes of our research

in CRNs: (i). Resource allocation in single user CRNs; (ii). Resource allocation in multiuser CRNs. In Section 2.5, we provide the conclusion.

2.1

Cognitive Radio, a Brief Introduction

2.1.1 Definition of CR

The ever-increasing demand for higher data rates in wireless communi-cations in the face of under utilization of the electromagnetic spectrum motivated the detection and exploitation of spectrum holes, which are defined as [35]: “a spectrum hole is a frequency band assigned to a PU,

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at a particular time and specific geographic location, where the band is not being utilized by that user.” Spectrum utilization can be improved significantly by making it possible for an unlicensed secondary user (who is not being served) to access a spectrum hole unoccupied by the PU at the right location and time in question. The concept of CR, which is based on the software-defined radio, has been proposed as the means to promote the efficient use of the spectrum by exploiting the existence of spectrum holes.

The term “CR” was firstly introduced by Joseph Mitola in his paper in 1999, where he defined CR as: “A radio that employs model based reasoning to achieve a specified level of competence in radio related domains [14].” In 2005, Professor Simon Haykin defined CR as [36]: “an intelligent wireless communication system that is awa

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