Qualifying exam

1. Fundamental Limitsof Cognitive Radios Goochul Chung

4. Active Legitimate Radio

5. Transmission over Legitimate Channel (Without Cooperation)Legitimate Radio Secondary Network

9. Interference Avoidance

11. Interference Level ( Channel Gain )

13. Channel Availability

15. Messages of Legitimate User

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

18. Small Power

19. Use small power to limit interference1 N 3 GHz 10 GHz Legitimate Radio N Legitimate Radio 1 Cognitive Radio

21. Sense if there is legitimate radio

22. Transmit only if legitimate radio is not detectedLegitimate Receiver Legitimate Transmitter Detection No Transmission Cognitive Transmitter Cognitive Receiver

24. Obtain legitimate user’s message sets

25. Unidirectional CooperationOverlay Cognitive Radio Legitimate Transmitter Backbone Network Legitimate Receiver Unidirectional Cooperation Cognitive Receiver Cognitive Transmitter

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

28. Sensing

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

31. Coding

33. Limits of Cognitive Radio

34. Overlay Cognitive Radio

35. Interweave Cognitive Radio

37. Coding Strategy for Overlay Cognitive Radio

38. Resource Allocation Algorithm for Interweave Cognitive Radio

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

44. : message set known to cognitive radio

45. : message set unknown to cognitive radioLegitimate Transmitter Cognitive Transmitter Partially Cognitive Radio Interference Channel Fully Cognitive Radio

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

48. Generalization

50. Knowledge of limits of the channel

51. Coding Design

53. : Fully Cognitive Radio Channel

55. Unidirectional cooperation from the cognitive transmitter

56. Side Information for Cognitive Radio Encoder1 Decoder1 Legitimate Transmitter Legitimate Receiver Encoder2 Decoder2 Cognitive Transmitter Cognitive Receiver

58. Outer Bound (Discrete Memoryless Channel) Encoder1 Decoder1 Discrete Memoryless Channel Legitimate Transmitter Legitimate Receiver Encoder2 Decoder2 Cognitive Receiver Cognitive Transmitter : Auxiliary Random Variable from :Transmitter side information on : Decoded from at decoder1

59. Outer Bound (Discrete Memoryless Channel) Discrete Memoryless Channel Encoder1 Decoder1 Legitimate Transmitter Legitimate Receiver Encoder2 Decoder2 Cognitive Transmitter Cognitive Receiver : Auxiliary Random Variable from Independent with : Decoded from at decoder1

60. Discrete Memoryless Channel Encoder1 Decoder1 Legitimate Transmitter Legitimate Receiver Encoder2 Decoder2 Cognitive Transmitter Cognitive Receiver Outer Bound (Discrete Memoryless Channel) : Encoded into : Decoded from at decoder 2 : Independent with

61. Discrete Memoryless Channel Encoder1 Decoder1 Legitimate Transmitter Legitimate Receiver Encoder2 Decoder2 Cognitive Transmitter Cognitive Receiver Outer Bound (Discrete Memoryless Channel) : Encoded into : Decoded from at decoder 2 : Independent with : Given to encoder 2 as side information

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

65. Same codeword for

66. Constraint on : Interference free for transmission

67. Interference cancellation at the transmitter Decoder1 Decoder2 Encoding With Power Split & Interference Cancellation

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

79. Capacity with 1 Bit gap in Gaussian interference channel

80. Fully Cognitive Channel : Capacity Achieving

82. Establish sum capacity with constant gap in two extremes

84. Part IICapacity of Interweave Cognitive Radio

86. Several unused 6MHz channel everywhere

88. Increase spectral efficiency

89. Channel Selection & Power allocation

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

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

104. Different probabilities

106. Power Allocation :Average Capacity Maximization

108. Find power allocation when channel selection is given

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

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

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 Selection Coarse Optimization Optimal? Yes Lowest water-level Coarse 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 Optimization Arbitrary L channels & modified water-filling Compare area under water-level L largest channels & modified water-filling Terminate if no larger area Example when N=5, L=2

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 Optimization Coarse Optimization Useless Channel Fine Optimization Needed

138. : Minimum water level from coarse optimization

140. Coarse Optimization

143. Optimal in low SNR

144. Fine Optimization

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

147. Channel Selection

148. Power Allocation

150. Coarse Optimization

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

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

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

156. Exploration

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

159. References S. 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/0808.0549 G. 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

164. Design sensing system to maximize spectral efficiency

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

172. Mapping to Legitimate Transmitter Energy Detector & Mapping Energy Detector & Mapping

178. ‘Good’ Outer Bound

179. ‘Good’ Inner Bound

180. Capacity with a Reasonable Gap

182. Coding Strategy for Overlay Cognitive Radio

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