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1. Fundamental Limitsof Cognitive RadiosGoochul Chung

2. OutlineMotivationIntroductionPart I ( Overlay Cognitive Radio )Capacity Analysis of Overlay Cognitive Radio Part II ( Interweave Cognitive Radio )Resource AllocationPart III ( Sensing in Interweave Cognitive Radio )Sensing Strategy in Cooperative SensingFrequency AllocationLegitimate RadioLicensed Radio with Primary Use of the Channel

3. Stringent Regulation on Interference to Legitimate RadioInterferenceInterference to Legitimate Radio

4. Active Legitimate Radio

5. Transmission over Legitimate Channel (Without Cooperation)Legitimate RadioSecondary Network

7. Motivation for Cognitive RadioScarcity of ChannelAlmost all wireless channels have licensed user with utmost privilege

8. Constraint for new wireless applicationsCognitive RadioPossess Cognitive Information about Legitimate User

9. Interference Avoidance

10. Compensation Use legitimate channel without performance degradation of legitimate userNew Wireless Application with Cognitive Radio can Share the Channel with Legitimate UserCognitive Radio TypeUnderlay Cognitive RadioCognitive Information

11. Interference Level ( Channel Gain )

12. Simultaneous Transmission with Limited InterferenceInterweave Cognitive RadioCognitive Information

13. Channel Availability

14. No Simultaneous Transmission Overlay Cognitive RadioCognitive Information

15. Messages of Legitimate User

16. Simultaneous Transmission Underlay Cognitive RadioUnderlay Cognitive RadioUltra Wide Band

17. Spread its message over ultra wide band ( 3 – 10 GHz )

18. Small Power

19. Use small power to limit interference1N3 GHz10 GHzLegitimate Radio NLegitimate Radio 1CognitiveRadio

20. Interweave Cognitive RadioInterweave Cognitive RadioNo Simultaneous Transmission

21. Sense if there is legitimate radio

22. Transmit only if legitimate radio is not detectedLegitimate ReceiverLegitimate TransmitterDetectionNo TransmissionCognitive TransmitterCognitive Receiver

23. Overlay Cognitive RadioKnowledge of Legitimate Users Message

24. Obtain legitimate user’s message sets

25. Unidirectional CooperationOverlay Cognitive RadioLegitimate TransmitterBackbone NetworkLegitimate ReceiverUnidirectional CooperationCognitive ReceiverCognitive Transmitter

26. QuestionCognitive Information Acquisition Selective Information Acquisition

27. Can information be efficiently collected to increase spectral efficiency? ( Channel Selection )

28. Sensing

29. How can sensing increase spectral efficiency with sensing accuracy?Utilization of Cognitive Information Resource Allocation

30. How can the resource (power) be allocated to increase average capacity?

31. Coding

32. What is the good coding strategy?Contribution Capacity Analysis of Cognitive RadioInformation Theoretic Understanding on different types of Cognitive Radio

33. Limits of Cognitive Radio

34. Overlay Cognitive Radio

35. Interweave Cognitive Radio

36. Underlay Cognitive RadioSystem Design of Cognitive RadioBuild a Spectrally Efficient Cognitive Radio System

37. Coding Strategy for Overlay Cognitive Radio

38. Resource Allocation Algorithm for Interweave Cognitive Radio

39. Sensing Strategy for Interweave Cognitive Radio Part ICapacity of Overlay Cognitive Radio

40. Previous WorksFully Cognitive Radio Cognitive of the entire message set of legitimate user

41. Capacity of strong interference case (I. Maricet. al.)

42. Capacity of general interference case (W. Wu et. al.) Partially Cognitive RadioCognitive of portion of the message set of legitimate user

43. Capacity of strong interference case (I. Maricet. al.)Partially Cognitive RadioPartially Cognitive RadioNot fully cognitive of licensed user’s message sets

44. : message set known to cognitive radio

45. : message set unknown to cognitive radioLegitimate TransmitterCognitive TransmitterPartially Cognitive RadioInterference ChannelFully Cognitive Radio

46. MotivationLimited Cognitive InformationPracticality

47. Knowledge of full non-causal message set is not guaranteed

48. Generalization

49. Partially Cognitive Radio generalize the channel model in between - Interference Channel - Fully Cognitive Radio Channel Capacity Analysis Information Theoretical Understanding

50. Knowledge of limits of the channel

51. Coding Design

52. Knowledge of effective coding strategySystem ModelEncoder1Decoder1Legitimate TransmitterLegitimate ReceiverEncoder2Decoder2Cognitive TransmitterCognitive ReceiverWeak InterferenceWeak Interference to Legitimate ReceiverRate Region : Rate Triplet for Partially Cognitive Radio Constraint : determines ratio of two rates

53. : Fully Cognitive Radio Channel

54. : Interference Channel ( Capacity : Still Open Problem )Key FeatureCommon Message at the Cognitive Transmitter : Detected only at Legitimate Receiver

55. Unidirectional cooperation from the cognitive transmitter

56. Side Information for Cognitive Radio Encoder1Decoder1Legitimate TransmitterLegitimate ReceiverEncoder2Decoder2Cognitive TransmitterCognitive Receiver

57. Outer Bound (Discrete Memoryless Channel)Outer bound of capacity regionOuter bound: Convex closure of the following inequality for the probability distribution

58. Outer Bound (Discrete Memoryless Channel)Encoder1Decoder1Discrete Memoryless ChannelLegitimate TransmitterLegitimate ReceiverEncoder2Decoder2Cognitive ReceiverCognitive Transmitter: Auxiliary Random Variable from:Transmitter side information on : Decoded from at decoder1

59. Outer Bound (Discrete Memoryless Channel)Discrete Memoryless ChannelEncoder1Decoder1Legitimate TransmitterLegitimate ReceiverEncoder2Decoder2Cognitive TransmitterCognitive Receiver : Auxiliary Random Variable from Independent with : Decoded from at decoder1

60. Discrete Memoryless ChannelEncoder1Decoder1Legitimate TransmitterLegitimate ReceiverEncoder2Decoder2Cognitive TransmitterCognitive ReceiverOuter Bound (Discrete Memoryless Channel): Encoded into: Decoded from at decoder 2 : Independent with

61. Discrete Memoryless ChannelEncoder1Decoder1Legitimate TransmitterLegitimate ReceiverEncoder2Decoder2Cognitive TransmitterCognitive ReceiverOuter Bound (Discrete Memoryless Channel): Encoded into: Decoded from at decoder 2 : Independent with: Given to encoder 2 as side information

62. Outer Bound (Gaussian Channel)Gaussian ChannelCondition : weak interference to licensed receiverEncoder1Decoder1Legitimate TransmitterLegitimate ReceiverEncoder2Decoder2Cognitive TransmitterCognitive Receiver

63. Outer Bound (Gaussian Channel)Outer bound of capacity region : convex closure of set : Transmit powers

64. Outer Bound (Gaussian Channel)Encoding With Power SplitConstraint on : Transmit cooperation with power split

65. Same codeword for

66. Constraint on : Interference free for transmission

67. Interference cancellation at the transmitter Decoder1Decoder2Encoding With Power Split & Interference Cancellation

68. Achievable Scheme (General Idea)Support Legitimate TransmissionSuperposition coding with allocation of power to shared messageInterference CancellationDirty paper coding to cancel interference Support Interference Channel TransmissionHan & Kobayashi coding to cope with interference like channelCoding Legitimate TransmitterLegitimate ReceiverCodebook1Joint DecoderCodebook2Rate SplitCodebook3Codebook1Joint DecoderDPCRate SplitCodebook4SICCognitive TransmitterCognitive Receiver

69. Numerical ResultPerformance of achievable scheme is compared to the outer bound Interference gainb = 0.5

70. a = 2Power constraintsPower constraint for legitimate transmitter: 10

71. Power constraint for cognitive transmitter: 10Numerical Result : Approaches Capacity Region of Fully Cognitive Radio : Good Inner and Outer Bound for Interference Channel

72. ContributionCapacity of Partially Cognitive Radio‘Good’ Outer Bound

73. Tight in one extreme: Fully Cognitive Radio

74. Gradual decrease with loss of cognitive information

75. ‘Good’ Achievable Scheme

76. Capacity Achieving in one extreme: Fully Cognitive Radio

77. Best Known Capacity Achieving Coding : Interference Channel

78. Gradual decrease with loss of cognitive informationFuture WorkSum Capacity with Constant GapInterference Channel : 1 Bit Gap ( R. Etkin et. al. )

79. Capacity with 1 Bit gap in Gaussian interference channel

80. Fully Cognitive Channel : Capacity Achieving

81. Capacity achieving in Gaussian interference channel with Fully Cognitive RadioPartially Cognitive RadioGeneralize the Sum Capacity Result

82. Establish sum capacity with constant gap in two extremes

83. Establish sum capacity with a gap corresponding to ReferencesJ.Mitola, “Cognitive Radio,” Ph.D. dissertation, Royal Institute of Technology (KTH),Stockholm, Sweden, 2000.S. Haykin, Cognitive radio: brain-empowered wireless communications, IEEE J. Sel. Areas in Commun., vol. 23, pp. 201-220, Feb. 2005.N. Devroye, P. Mitran and V. Tarokh, “Achievable Rates in Cognitive Rado Channels,” IEEE Trans. Inform. Theory, vol. 52, pp. 1813-1827, May 2006.I. Maric, A. Goldsmith, G. Kramer, S. Shamai (Shitz), “On the Capacity of Interference Channel with a Partially-Cognitive Traansmitter,”IEEE Trans. Inform. Theory.I. Maric, R. Yates, “The Strong Interference Channel with Common Information,” Allerton Conf. Communications, Monticello, Il, Sep. 2005.I. Maric, R. Yates, G. Kramer, “The strong interference channel with unidirectional cooperation,” presented at the Information Theory and Applications (ITA) Inaugural Workshop, Feb. 2006.W. Wu, S. Vishwanath and A. Arapostathis, “On the Capacity of Interference Channel with degraded Message Sets,”IEEE Trans. Inform. Theory.T. S. Han and K. Kobayashi, “A new achievable rate region for the interference channel,”IEEE Trans. Inform. Theory, vol. 27, pp. 49-60, Jan. 1981.H. Sato, “Two-user communication channels,” IEEE Trans. Inform. Theory, vol. 23, pp. 295-304, May 1977.A. B. Carleial, “Outer bounds on the capacity of interference channels,” IEEE Trans. Inform. Theory, vol. 29, pp. 602-606, Jul. 1983. vol. IT-24,J. A. Thomas, “Feedback can at most double Gaussian multiple access channel capacity,” IEEE Trans. Inform. Theory, vol. 33, pp. 711-716, Sep. 1987.H. Weingarten, Y. Steinberg and S. Shamai (Shitz), “The Capacity region of the Gaussian MIMO broadcast channel,” IEEE Trans. Inform. Theory, vol. 52, pp. 3936-3964, Sep. 2006.M. Costa, “Writing on dirty paper,” IEEE Trans. Inform. Theory, vol. 29, pp. 439-441, May 1983.T. M Cover and J.A. Thomas, Elements of information theory, ser. Wiley Series in Telecommunications. New York: John Wiley & Sons Inc., 1991, a Wiley-Interscience Publication.

84. Part IICapacity of Interweave Cognitive Radio

85. MotivationLow Utilization FCC Report

86. Several unused 6MHz channel everywhere

87. Possibility of opening the channel near futureInterweave Cognitive Radio Opportunistic Access

88. Increase spectral efficiency

89. Channel Selection & Power allocation

90. Establish maximum increase in spectral efficiencyMultiple ChannelsensesensesenseMultiple Channel in Interweave Cognitive RadioTotal legitimate channels : N

91. Number of Simultaneous Sensing : L

92. Selection of L channels to sense from N legitimate channels

93. Transmission over available channelsExample when N=4 and L=2: Licensed user: Cognitive user

94. Channel EnvironmentDissimilarity between Channels Noise Variances:

95. Different noise variances

96. Represents fading states

97. Probability of Channel Being Available:

98. Different probabilities

99. Low indicates frequently used channelGraphical Representation of Channel, N=4

100. QuestionSelection of Channel Sensing Low Noise Variance

101. High Probability of Being Available What is a good channel in the mixture?Power Allocation Dependent on Channel Sensing

102. No power allocation on unavailable channel How do we allocate power?Joint Optimization Power Allocation and Channel Selection

103. Maximize Average Capacity Limit of interweave cognitive radio & Building of efficient systemProbability of Channel Being Available:

104. Different probabilities

105. Low indicates frequently used channelJoint Optimization ProblemOptimization Parameter Channel Selection:

106. Power Allocation :Average Capacity Maximization

107. Power Allocation with given

108. Find power allocation when channel selection is given

109. Graphically represented by “modified water-filling”Optimal Power AllocationExample when N=4, L=3

110. Exhaustive Search

111. Exhaustive search of channels with the highest capacity

112. Combinatorial times “modified water-filling”

113. Require more efficient method to select channelsOptimal Channel Selection

114. Objective

115. Approximate the optimal channel selection and power allocation

116. Reduce complexity

117. Two Step Approximation

118. Coarse Optimization

119. Lowest water-level

120. Fine Optimization

121. Neglect poor channels

122. Use lowest water-levelSub-Optimal Channel SelectionCoarse OptimizationOptimal?YesLowest water-levelCoarse Optimization

124. Find channels that minimize water-level of modified water-filling

125. Iteratively find channels which lower the water-level

126. maximum N-L iteration

127. Optimal if water-level is lower than any unselected channelCoarse OptimizationArbitrary L channels & modified water-fillingCompare area under water-levelL largest channels & modified water-fillingTerminate if no larger areaExample when N=5, L=2

128. Intuition

129. Existence of unselected channel with low noise variance

130. Channel selection can be improved

131. Existence of channel with very high noise variance

132. Useless ( Does not increase capacity )

133. Method

134. Exclude useless channels

135. Relax integer condition on channel selection

136. Find convex functionFine OptimizationCoarse OptimizationUseless ChannelFine Optimization Needed

137. Fine OptimizationOptimization Problem Find channel selection & power allocation to maximize capacity

138. : Minimum water level from coarse optimization

139. k : Constant which makes the objective function convex2010년 4월 18일Fine OptimizationSolutionSolution from KKT conditionOptimality Performs the same with the exhaustive searchComplexity Order N iterationNumerical ResultPerformance ComparisonExhaustive Search

141. Fine OptimizationParameter N=8

142. L=4Coarse Optimization

143. Optimal in low SNR

144. Fine Optimization

145. Same performance with exhaustive search in all SNR regionNumerical Result

146. ContributionAverage Capacity of Interweave Cognitive RadioJoint Optimization to maximize average capacity

147. Channel Selection

148. Power Allocation

149. Limits of Interweave Cognitive Radio is verifiedPractical Maximum Capacity Achieving System Computationally practical algorithm

151. Fine Optimization Practical interweave cognitive radio system is built Contribution to Spectral Efficiency

152. Future WorkInterweave Cognitive Radio with LearningExact Knowledge on Channel Availability Probability

153. In practice, Cognitive may not know the exact probability

154. Understanding of the probability can be enhanced by observationExploitation & Exploration Exploitation

155. With the sensing result, cognitive radio makes a transmission

156. Exploration

157. With the sensing result, cognitive radio updates the probability of channel being availableJoint Power Allocation & Channel Selection with LearningsensesensesenseInterweave Cognitive Radio with Learning ( L. Lei et. al. )Channel Selection with fixed power allocation

158. Multi arm bandit solution: Licensed user: Cognitive userFrequency Time Power Allocation & Channel selection

159. ReferencesS. Srivasa and S. Jafar, “The Throughput Potential of Cognitive Radio: A Theoretical Perspective,” Asilomar Conf. on Signals, Systems, and Computers, Asilomar, CA, Oct. 2006.N. Devroye, P. Mitran, and V. Tarokh, “Achievable Rates in Cognitive Rado Channels,” IEEE Trans. Inform. Theory, vol. 52, pp. 1813-1827, May 2006.W. Wu, S. Vishwanath, and A. Arapostathis, “Capacity of a Class of Cognitive Radio Channels: Interference Channels With Degraded Message Sets,” IEEE Trans. Inform. Theory, vol. 53, pp. 4391-4399, Nov. 2007.W. Wang, T. Peng and W. Wang, “Optimal Power Control under Interference Temperature Constraints in Cognitive Radio Network,” IEEE Wireless Comm. & Networking Conf., Hong Kong, Mar. 2007.A. Goldsmith and P. Varaiya, “Capacity of fading channels with channel side information,” IEEE Trans. Inform. Theory, vol. 43, pp. 1986-1992, Nov. 1997.Y. Song, Y. Fang, and Y. Zhang, “Stochastic Channel Selection in Cognitive Radio Networks,” IEEE Global Communications Conf., Washington, DC, Nov. 2007.X. Yang, Z. Yang, and D. Liao, “Adaptive Spectrum Selection for Cognitive Radio Networks,” International Conf. on Computer Science and Software Engineering, Wuhan, China, Dec. 2008.D. Huang, C. Miao, C. Leung and Z. Shen, “Resource Allocation of MU-OFDM Based Cognitive Radio Systems Under Partial Channel State Information,” http://arxiv.org/abs/0808.0549G. Chung, S. Vishwanath, and C. S. Hwang, “On the Fundamental Limits of Interweaved Cognitive Radios,” http://arxiv.org/abs/0910.1639

160. Part IIISensing of Interweave Cognitive Radio

161. MotivationSensing AccuracyAccurate Cognitive Information

162. Guarantee Legitimate User’s Reliable TransmissionCooperative Sensing Firm Requirement on Interference to Legitimate User

163. Cooperative sensing increases sensing abilitySpectral Efficiency Trade offs between spectral efficiency and detection error

164. Design sensing system to maximize spectral efficiency

165. Keep detection error in tolerable levelCooperative SensingLegitimate RadioSensing Network Energy Detection

166. Each sensor detects energy level

167. Underlay Network

168. Unaware of existence of legitimate user

169. No dedicated channel exists

170. Limited bit and distanceSensing Network

171. Cooperative SensingEnergy DetectorDecisionParameter and Variables Detection Time at each Detector

172. Mapping to LegitimateTransmitterEnergy Detector& MappingEnergy Detector& Mapping

173. Previous WorkDistributed Computation ( Tsisikliset. al.) General Model on Distributed Computation

174. Solution to Sensing ErrorSensing Algorithm Probability of Detection

175. Probability of False AlarmFuture WorkBuild Cooperative Sensing System Spectrally Efficient System

176. Limit on Detection ErrorExpected ContributionCombined work of Sensing Network and Spectrally Efficient System

177. Spectrally Efficient System with Constraint on Cognitive RadioSummary Capacity Analysis of Cognitive RadioCapacity of Overlay Cognitive Radio

178. ‘Good’ Outer Bound

179. ‘Good’ Inner Bound

180. Capacity with a Reasonable Gap

181. Maximum Average Capacity of Interweave Cognitive RadioSystem Design of Cognitive RadioBuild a Spectrally Efficient Cognitive Radio System

182. Coding Strategy for Overlay Cognitive Radio

183. Resource Allocation Algorithm for Interweave Cognitive Radio - Exact Knowledge of probability - With LearningSensing Strategy for Interweave Cognitive Radio Appendix (1)Proof of outer bound (IFC-DMS)(a)from conditional markov chain (b)from identifying

184. Appendix (2)(a)from identifying

185. Appendix (3)(a)from markov chain (c)from identifying (b)from conditional markov chain

186. Appendix (4)(a)from identifying

187. Appendix (5)(a)from markov chain (c)from identifying (b)from conditional markov chain

188. Appendix (6)Proof of outer bound (Gaussian)Lemma: Let be arbitrarily distributed zero-mean random variables with covariance matrix , where are independent of each other. Let be the zero-mean Gaussian distributed random variables with the same covariance matrix. Then, Lemma: Let be arbitrarily distributed zero-mean random variables , and be the Gaussian distributed random variables with the same covariance matrix. Let be any subset of {1,2,…,k} and be its complement. Then, With help of EPI and above Lemma, outer bound can be proven

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