认知无线电网络频谱感知策略与拥塞博弈算法研究
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摘要
本文考虑了认知无线电网络中的自私频谱感知和分配策略问题:M个自私的次用户寻找恰当的时机接入N个授权频段。受限于硬件条件,每个次用户能且仅能选择一个授权频段进行频谱感知,并根据感知结果适时竞争接入授权频段。不同的授权频段可能给次用户带来不同的效用值。出于自私性,每个次用户总是做能够带来最大效用值的频段选择。我们的目标是设计一种最优网络频谱感知策略在满足各次用户自私性前提下兼顾网络整体性能,也即最大化网络吞吐量。我们将这一问题描述为一个非合作频谱感知博弈,其稳定的频谱感知决策就对应于一个Nash均衡。我们提出了一种新颖的贪婪算法,该算法可以高效地计算出所有的纯策略Nash均衡,并且对效用函数的具体形式没有过多要求。基于该算法,我们随后提出了其改进版本,并从理论上证明了该改进算法可以计算出最优纯策略Nash均衡,即具有最大的网络吞吐量。同时,我们给出了改进算法的分布式MAC协议。大量的仿真数据和实验结果验证了理论推导的正确性,并展示了所提出的算法的优异性能。进一步的,我们证明了所提出的贪婪算法具有普适性:对所有拥有严格单调效用函数的单拥塞博弈问题均可适用。进而对此类博弈,所有的纯策略Nash均衡均可以在O(nlogm)内求解出。所提出的算法解决了该类博弈问题,因而具有一定的理论价值。
In this paper, we consider a noncooperative cognitive radio network with M self-ish secondary users (SUs) opportunistically access N licensed channels. Every SUchooses one channel to sense and subsequently compete to access (based on the sens-ing outcome) to obtain the channel utility. Different channels may have different utili-ties. Each SU selfishly makes a sensing decision to maximize its obtained utility. Theobjective is to design an optimal sensing policy with maximum network throughput.This problem is formulated as a noncooperative game where a stable sensing policyreaches a Nash Equilibrium (NE). A novel greedy algorithm with great efficiency isproposed to calculate all pure-strategy NE for a large class of utility functions. Byslight modification, the algorithm is able to reach an optimal pure-strategy NE withthe maximum network throughput. The algorithm can be practically implemented asa MAC protocol in a distributed way with negligible communication overhead. In-tensive simulation experiments verify the correctness of the theorems and reveal theeffectiveness of our algorithm. Furthermore, we have shown that our algorithm canbe extended to all singleton congestion games with strict monotonic utility functions.And for these games, all NE can be calculated within O(n log m).
In this paper, we consider a noncooperative cognitive radio network with M self-ish secondary users (SUs) opportunistically access N licensed channels. Every SUchooses one channel to sense and subsequently compete to access (based on the sens-ing outcome) to obtain the channel utility. Different channels may have different utili-ties. Each SU selfishly makes a sensing decision to maximize its obtained utility. Theobjective is to design an optimal sensing policy with maximum network throughput.This problem is formulated as a noncooperative game where a stable sensing policyreaches a Nash Equilibrium (NE). A novel greedy algorithm with great efficiency isproposed to calculate all pure-strategy NE for a large class of utility functions. Byslight modification, the algorithm is able to reach an optimal pure-strategy NE withthe maximum network throughput. The algorithm can be practically implemented asa MAC protocol in a distributed way with negligible communication overhead. In-tensive simulation experiments verify the correctness of the theorems and reveal theeffectiveness of our algorithm. Furthermore, we have shown that our algorithm canbe extended to all singleton congestion games with strict monotonic utility functions.And for these games, all NE can be calculated within O(n log m).
引文
[1] KOLODZY P, AVOIDANCE I, MODELS S. Spectrum policy task force[J]. FederalCommunications Commission, 2002.
[2] MCHENRY M. Report on spectrum occupancy measurements[J]. Shared Spec-trum Company.
[3] MCHENRY M. Spectrum white space measurements[C]//New America Founda-tion Broadband Forum. .[S.l.]: [s.n.] , 2003.
[4] HAYKIN S. Cognitive radio: brain-empowered wireless communications[J].IEEE Journal on Selected Areas in Communications, 2005, 23(2):201–220.
[5] MITOLA J, MAGUIRE G. Cognitive radio: making software radios more per-sonal[J]. IEEE personal communications, 1999, 6(4):13–18.
[6] MITOLA J, et al. Cognitive radio: an integrated agent architecture for softwaredefined radio[D].[S.l.]: Royal Inst. Technol.(KTH), Stockholm, Sweden, 2000.
[7] KRENIK W, BATRA A. Cognitive radio techniques for wide area net-works[C]//Proceedings of the 42nd annual conference on Design automation..[S.l.]: [s.n.] , 2005:409–412.
[8] FCC E. Notice of proposed rule making and order[J]. Docket No. 03, 2003, 222.
[9] THOMAS R, DASILVA L, MACKENZIE A. Cognitive networks[C]//Proc. IEEEDySPAN. .[S.l.]: [s.n.] :352–360.
[10] MITOLA III J. Cognitive radio for ?exible mobile multimedia communica-tions[J]. Mobile Networks and Applications, 2001, 6(5):435–441.
[11] AKYILDIZ I, LEE W, VURAN M, et al. NeXt generation/dynamic spectrum ac-cess/cognitive radio wireless networks: a survey[J]. Computer Networks, 2006,50(13):2127–2159.
[12] BUDDHIKOT M, KOLODZY P, MILLER S, et al. DIMSUMNet: New directionsin wireless networking using coordinated dynamic spectrum access[C]//IEEEWoWMoM. .[S.l.]: [s.n.] , 2005,5.
[13] ILERI O, SAMARDZIJA D, MANDAYAM N. Demand responsive pricing andcompetitive spectrum allocation via a spectrum server[C]//Proc. of IEEE DyS-PAN. .[S.l.]: [s.n.] , 2005:194–202.
[14] BRIK V, ROZNER E, BANERJEE S, et al. DSAP: a protocol for coordinatedspectrum access[C]//IEEE DySPAN. .[S.l.]: [s.n.] , 2005:611–614.
[15] PENG C, ZHENG H, ZHAO B. Utilization and fairness in spectrum assignmentfor opportunistic spectrum access[J]. Mobile Networks and Applications, 2006,11(4):555–576.
[16] CAO L, ZHENG H. Distributed spectrum allocation via local bargain-ing[C]//IEEE SECON. .[S.l.]: [s.n.] , 2005,5.
[17] HUANG J, BERRY R, HONIG M. Spectrum sharing with distributed interferencecompensation[C]//Proc. IEEE DySPAN. .[S.l.]: [s.n.] , 2005:88–93.
[18] MA L, HAN X, SHEN C. Dynamic open spectrum sharing MAC protocol forwireless ad hoc networks[C]//IEEE DySPAN. .[S.l.]: [s.n.] , 2005:203–213.
[19] SANKARANARAYANAN S, PAPADIMITRATOS P, MISHRA A, et al. A bandwidthsharing approach to improve licensed spectrum utilization[C]//Proceedings ofthe first IEEE Symposium on New Frontiers in Dynamic Spectrum Access Net-works. .[S.l.]: [s.n.] , 2005.
[20] ZHAO Q, TONG L, SWAMI A. Decentralized cognitive MAC for dynamic spec-trum access[C]//New Frontiers in Dynamic Spectrum Access Networks, 2005.DySPAN 2005. 2005 First IEEE International Symposium on. .[S.l.]: [s.n.] ,2005:224–232.
[21] ZHENG H, CAO L. Device-centric spectrum management[C]//Proc. IEEE DyS-PAN. .[S.l.]: [s.n.] , 2005,2005:56–65.
[22] ZHENG H, PENG C. Collaboration and fairness in opportunistic spectrumaccess[C]//Proceedings of IEEE International Conference on Communications(ICC). .[S.l.]: [s.n.] , 2005.
[23] NIE N, COMANICIU C. Adaptive channel allocation spectrum etiquette for cog-nitive radio networks[J]. Mobile Networks and Applications, 2006, 11(6):779–797.
[24] ETKIN R, PAREKH A, TSE D. Spectrum sharing for unlicensed bands[J]. IEEEJournal on selected areas in communications, 2007, 25(3):517.
[25] MENON R, BUEHRER R, REED J. Outage probability based comparison of un-derlay and overlay spectrum sharing techniques[C]//Proc. IEEE DySPAN. .[S.l.]:[s.n.] , 2005:101–109.
[26] WANG B, JI Z, LIU K. Self-learning repeated game framework for distributedprimary-prioritized dynamic spectrum access[J]. Proc. IEEE SECON 2007:631–638.
[27] HAN Z, PANDANA C, LIU K. Distributive opportunistic spectrum ac-cess for cognitive radio using correlated equilibrium and no-regret learn-ing[C]//Proceedings of IEEE Wireless Communications and Networking Con-ference. .[S.l.]: [s.n.] , 2007.
[28] HUANG J, BERRY R, HONIG M. Auction-based spectrum sharing[J]. MobileNetworks and Applications, 2006, 11(3):405–408.
[29] GANDHI S, BURAGOHAIN C, CAO L, et al. A general framework for wirelessspectrum auctions[C]//Proc. of IEEE DySPAN. .[S.l.]: [s.n.] , 2007.
[30] ACCESS W. Integration of WiMAX and WiFi: Optimal Pricing for BandwidthSharing[J]. IEEE Communications Magazine, 2007:141.
[31] JI Z, LIU K. Belief-assisted pricing for dynamic spectrum allocation in wirelessnetworks with selfish users[C]//Proc. IEEE Int’l Conference on Sensor, Mesh,and Ad Hoc Communications and Networks (SECON). .[S.l.]: [s.n.] :119–127.
[32] JI Z, LIU K. Dynamic spectrum sharing: a game theoretical overview[J]. IEEECommunications Magazine, 2007, 45(5):88.
[33] WANG B, WU Y, JI Z, et al. Game theoretical mechanism design for cognitiveradio networks with selfish users[J]. IEEE Signal Processing Magazine, 2008,25(6):74–84.
[34] HURWICZ L. The design of mechanisms for resource allocation[J]. The Ameri-can Economic Review, 1973, 63(2):1–30.
[35] FUDENBERG D, TIROLE J. Game theory[M].[S.l.]: MIT Press, 1991.
[36] NASH J. Equilibrium points in n-person games[J]. Proceedings of the NationalAcademy of Sciences of the United States of America, 1950:48–49.
[37] CHEN X, DENG X. Settling the complexity of 2-player Nash-equilibrium[C]//Electronic Colloquium on Computational Complexity. .[S.l.]:[s.n.] , 2005,140.
[38] JOHNSON D, PAPADIMITRIOU C, YANNAKAKIS M. How easy is localsearch?[J]. JCSS, 1988, 37(1):79–100.
[39] DASKALAKIS C, GOLDBERG P, PAPADIMITRIOU C. The complexity of com-puting a Nash equilibrium[J]. 2009.
[40] CHEN X, DENG X. 3-Nash is PPAD-complete[C]//Electronic Colloquium onComputational Complexity. .[S.l.]: [s.n.] , 2005.
[41] ZHAO W, TONG L, SWAMI A, et al. Decentralized cognitive MAC for oppor-tunistic spectrum access in ad hoc networks: A POMDP framework[J]. IEEEJournal on Selected Areas in Communications, 2007, 25(3):589.
[42] JIA J, ZHANG Q, SHEN X. HC-MAC: a hardware-constrained cognitive MACfor efficient spectrum management[J]. IEEE journal on selected areas in com-munications, 2008, 26(1):106–117.
[43] CHANG N, LIU M. Optimal channel probing and transmission scheduling foropportunistic spectrum access[C]//Proceedings of the 13th annual ACM interna-tional conference on Mobile computing and networking. .[S.l.]: [s.n.] , 2007:38.
[44] ZHAO Q, KRISHNAMACHARI B, LIU K. On myopic sensing for multi-channelopportunistic access: Structure, optimality, and performance[J]. IEEE Transac-tions on Wireless Communications, 2008, 7(12):5431–5440.
[45] JAVIDI T, KRISHNAMACHARI B, ZHAO Q, et al. Optimality of myopic sens-ing in multi-channel opportunistic access[C]//IEEE International Conference onCommunications, 2008. ICC’08. .[S.l.]: [s.n.] , 2008:2107–2112.
[46] SU H, ZHANG X. Cross-layer based opportunistic MAC protocols for QoS pro-visionings over cognitive radio wireless networks[J]. IEEE Journal on SelectedAreas in Communications, 2008, 26(1):118–129.
[47] XU D, JUNG E, LIU X. Optimal bandwidth selection in multi-channel cogni-tive radio networks: how much is too much?[C]//3rd IEEE Symposium on NewFrontiers in Dynamic Spectrum Access Networks. DySPAN 2008. .[S.l.]: [s.n.], 2008.
[48] LIU K, ZHAO Q, CHEN Y. Distributed sensing and access in cognitive radionetworks[C]//Proc. of 10th International Symposium on Spread Spectrum Tech-niques and Applications (ISSSTA). .[S.l.]: [s.n.] , 2008.
[49] LIU K, ZHAO Q, CHEN Y. Distributed sensing and access in cognitive radio net-works[C]//10th International Symposium on Spread Spectrum Techniques andApplications (ISSSTA). .[S.l.]: [s.n.] , 2008.
[50] WANG F, KRUNZ M, CUI S. Spectrum sharing in cognitive radio net-works[C]//Proc. of IEEE INFOCOM. .[S.l.]: [s.n.] , 2008:1885–1893.
[51] HUANG J, BERRY R, HONIG M. Distributed interference compensation forwireless networks[J]. IEEE Journal on Selected Areas in Communications, 2006,24(5):1074–1084.
[52] LIU H, HUANG L, KRISHNAMACHARI B, et al. A negotiation game for mul-tichannel access in cognitive radio networks[C]//Proceedings of the 4th AnnualInternational Conference on Wireless Internet. .[S.l.]: [s.n.] , 2008.
[53] CORDEIRO C, CHALLAPALI K, BIRRU D, et al. IEEE 802.22: an introductionto the first wireless standard based on cognitive radios[J]. Journal of communi-cations, 2006, 1(1):38–47.
[54] CORDEIRO C, CHALLAPALI K, BIRRU D, et al. IEEE 802.22: the first world-wide wireless standard based on cognitive radios[C]//New Frontiers in DynamicSpectrum Access Networks, 2005. DySPAN 2005. 2005 First IEEE InternationalSymposium on. .[S.l.]: [s.n.] , 2005:328–337.
[55] FABRIKANT A, PAPADIMITRIOU C, TALWAR K. The complexity of pure Nashequilibria[C]//Proceedings of the thirty-sixth annual ACM symposium on Theoryof computing. .[S.l.]: [s.n.] , 2004:612.
[56] ROSENTHAL R. A class of games possessing pure-strategy Nash equilibria[J].International Journal of Game Theory, 1973, 2(1):65–67.
[57] MONDERER D, SHAPLEY L. Potential games[J]. Games and economic behav-ior, 1996, 14(1):124–143.
[58] VOCKING B. Congestion games: Optimization in competition[C]//Proceedingsof the 2nd Algorithms and Complexity in Durham Workshop. .[S.l.]: [s.n.] ,2006:9–20.
[59] LIU M, WU Y. Spectum sharing as congestion games[C]//Allerton conference..[S.l.]: [s.n.] , 2008:2005–2007.
[60] LIU M, AHMAD S, WU Y. Congestion Games with Resource Reuse and Appli-cations in Spectrum Sharing[J]. Proc. ACM GAMENETS, 2009.
[61] MILCHTAICH I. Congestion games with player-specific payoff functions[J].Games and economic behavior, 1996, 13(1):111–124.
[62] ACKERMANN H, ROGLIN H, VOCKING B. Pure Nash equilibria in player-specific and weighted congestion games[J]. Theoretical Computer Science,2009, 410(17):1552–1563.
[2] MCHENRY M. Report on spectrum occupancy measurements[J]. Shared Spec-trum Company.
[3] MCHENRY M. Spectrum white space measurements[C]//New America Founda-tion Broadband Forum. .[S.l.]: [s.n.] , 2003.
[4] HAYKIN S. Cognitive radio: brain-empowered wireless communications[J].IEEE Journal on Selected Areas in Communications, 2005, 23(2):201–220.
[5] MITOLA J, MAGUIRE G. Cognitive radio: making software radios more per-sonal[J]. IEEE personal communications, 1999, 6(4):13–18.
[6] MITOLA J, et al. Cognitive radio: an integrated agent architecture for softwaredefined radio[D].[S.l.]: Royal Inst. Technol.(KTH), Stockholm, Sweden, 2000.
[7] KRENIK W, BATRA A. Cognitive radio techniques for wide area net-works[C]//Proceedings of the 42nd annual conference on Design automation..[S.l.]: [s.n.] , 2005:409–412.
[8] FCC E. Notice of proposed rule making and order[J]. Docket No. 03, 2003, 222.
[9] THOMAS R, DASILVA L, MACKENZIE A. Cognitive networks[C]//Proc. IEEEDySPAN. .[S.l.]: [s.n.] :352–360.
[10] MITOLA III J. Cognitive radio for ?exible mobile multimedia communica-tions[J]. Mobile Networks and Applications, 2001, 6(5):435–441.
[11] AKYILDIZ I, LEE W, VURAN M, et al. NeXt generation/dynamic spectrum ac-cess/cognitive radio wireless networks: a survey[J]. Computer Networks, 2006,50(13):2127–2159.
[12] BUDDHIKOT M, KOLODZY P, MILLER S, et al. DIMSUMNet: New directionsin wireless networking using coordinated dynamic spectrum access[C]//IEEEWoWMoM. .[S.l.]: [s.n.] , 2005,5.
[13] ILERI O, SAMARDZIJA D, MANDAYAM N. Demand responsive pricing andcompetitive spectrum allocation via a spectrum server[C]//Proc. of IEEE DyS-PAN. .[S.l.]: [s.n.] , 2005:194–202.
[14] BRIK V, ROZNER E, BANERJEE S, et al. DSAP: a protocol for coordinatedspectrum access[C]//IEEE DySPAN. .[S.l.]: [s.n.] , 2005:611–614.
[15] PENG C, ZHENG H, ZHAO B. Utilization and fairness in spectrum assignmentfor opportunistic spectrum access[J]. Mobile Networks and Applications, 2006,11(4):555–576.
[16] CAO L, ZHENG H. Distributed spectrum allocation via local bargain-ing[C]//IEEE SECON. .[S.l.]: [s.n.] , 2005,5.
[17] HUANG J, BERRY R, HONIG M. Spectrum sharing with distributed interferencecompensation[C]//Proc. IEEE DySPAN. .[S.l.]: [s.n.] , 2005:88–93.
[18] MA L, HAN X, SHEN C. Dynamic open spectrum sharing MAC protocol forwireless ad hoc networks[C]//IEEE DySPAN. .[S.l.]: [s.n.] , 2005:203–213.
[19] SANKARANARAYANAN S, PAPADIMITRATOS P, MISHRA A, et al. A bandwidthsharing approach to improve licensed spectrum utilization[C]//Proceedings ofthe first IEEE Symposium on New Frontiers in Dynamic Spectrum Access Net-works. .[S.l.]: [s.n.] , 2005.
[20] ZHAO Q, TONG L, SWAMI A. Decentralized cognitive MAC for dynamic spec-trum access[C]//New Frontiers in Dynamic Spectrum Access Networks, 2005.DySPAN 2005. 2005 First IEEE International Symposium on. .[S.l.]: [s.n.] ,2005:224–232.
[21] ZHENG H, CAO L. Device-centric spectrum management[C]//Proc. IEEE DyS-PAN. .[S.l.]: [s.n.] , 2005,2005:56–65.
[22] ZHENG H, PENG C. Collaboration and fairness in opportunistic spectrumaccess[C]//Proceedings of IEEE International Conference on Communications(ICC). .[S.l.]: [s.n.] , 2005.
[23] NIE N, COMANICIU C. Adaptive channel allocation spectrum etiquette for cog-nitive radio networks[J]. Mobile Networks and Applications, 2006, 11(6):779–797.
[24] ETKIN R, PAREKH A, TSE D. Spectrum sharing for unlicensed bands[J]. IEEEJournal on selected areas in communications, 2007, 25(3):517.
[25] MENON R, BUEHRER R, REED J. Outage probability based comparison of un-derlay and overlay spectrum sharing techniques[C]//Proc. IEEE DySPAN. .[S.l.]:[s.n.] , 2005:101–109.
[26] WANG B, JI Z, LIU K. Self-learning repeated game framework for distributedprimary-prioritized dynamic spectrum access[J]. Proc. IEEE SECON 2007:631–638.
[27] HAN Z, PANDANA C, LIU K. Distributive opportunistic spectrum ac-cess for cognitive radio using correlated equilibrium and no-regret learn-ing[C]//Proceedings of IEEE Wireless Communications and Networking Con-ference. .[S.l.]: [s.n.] , 2007.
[28] HUANG J, BERRY R, HONIG M. Auction-based spectrum sharing[J]. MobileNetworks and Applications, 2006, 11(3):405–408.
[29] GANDHI S, BURAGOHAIN C, CAO L, et al. A general framework for wirelessspectrum auctions[C]//Proc. of IEEE DySPAN. .[S.l.]: [s.n.] , 2007.
[30] ACCESS W. Integration of WiMAX and WiFi: Optimal Pricing for BandwidthSharing[J]. IEEE Communications Magazine, 2007:141.
[31] JI Z, LIU K. Belief-assisted pricing for dynamic spectrum allocation in wirelessnetworks with selfish users[C]//Proc. IEEE Int’l Conference on Sensor, Mesh,and Ad Hoc Communications and Networks (SECON). .[S.l.]: [s.n.] :119–127.
[32] JI Z, LIU K. Dynamic spectrum sharing: a game theoretical overview[J]. IEEECommunications Magazine, 2007, 45(5):88.
[33] WANG B, WU Y, JI Z, et al. Game theoretical mechanism design for cognitiveradio networks with selfish users[J]. IEEE Signal Processing Magazine, 2008,25(6):74–84.
[34] HURWICZ L. The design of mechanisms for resource allocation[J]. The Ameri-can Economic Review, 1973, 63(2):1–30.
[35] FUDENBERG D, TIROLE J. Game theory[M].[S.l.]: MIT Press, 1991.
[36] NASH J. Equilibrium points in n-person games[J]. Proceedings of the NationalAcademy of Sciences of the United States of America, 1950:48–49.
[37] CHEN X, DENG X. Settling the complexity of 2-player Nash-equilibrium[C]//Electronic Colloquium on Computational Complexity. .[S.l.]:[s.n.] , 2005,140.
[38] JOHNSON D, PAPADIMITRIOU C, YANNAKAKIS M. How easy is localsearch?[J]. JCSS, 1988, 37(1):79–100.
[39] DASKALAKIS C, GOLDBERG P, PAPADIMITRIOU C. The complexity of com-puting a Nash equilibrium[J]. 2009.
[40] CHEN X, DENG X. 3-Nash is PPAD-complete[C]//Electronic Colloquium onComputational Complexity. .[S.l.]: [s.n.] , 2005.
[41] ZHAO W, TONG L, SWAMI A, et al. Decentralized cognitive MAC for oppor-tunistic spectrum access in ad hoc networks: A POMDP framework[J]. IEEEJournal on Selected Areas in Communications, 2007, 25(3):589.
[42] JIA J, ZHANG Q, SHEN X. HC-MAC: a hardware-constrained cognitive MACfor efficient spectrum management[J]. IEEE journal on selected areas in com-munications, 2008, 26(1):106–117.
[43] CHANG N, LIU M. Optimal channel probing and transmission scheduling foropportunistic spectrum access[C]//Proceedings of the 13th annual ACM interna-tional conference on Mobile computing and networking. .[S.l.]: [s.n.] , 2007:38.
[44] ZHAO Q, KRISHNAMACHARI B, LIU K. On myopic sensing for multi-channelopportunistic access: Structure, optimality, and performance[J]. IEEE Transac-tions on Wireless Communications, 2008, 7(12):5431–5440.
[45] JAVIDI T, KRISHNAMACHARI B, ZHAO Q, et al. Optimality of myopic sens-ing in multi-channel opportunistic access[C]//IEEE International Conference onCommunications, 2008. ICC’08. .[S.l.]: [s.n.] , 2008:2107–2112.
[46] SU H, ZHANG X. Cross-layer based opportunistic MAC protocols for QoS pro-visionings over cognitive radio wireless networks[J]. IEEE Journal on SelectedAreas in Communications, 2008, 26(1):118–129.
[47] XU D, JUNG E, LIU X. Optimal bandwidth selection in multi-channel cogni-tive radio networks: how much is too much?[C]//3rd IEEE Symposium on NewFrontiers in Dynamic Spectrum Access Networks. DySPAN 2008. .[S.l.]: [s.n.], 2008.
[48] LIU K, ZHAO Q, CHEN Y. Distributed sensing and access in cognitive radionetworks[C]//Proc. of 10th International Symposium on Spread Spectrum Tech-niques and Applications (ISSSTA). .[S.l.]: [s.n.] , 2008.
[49] LIU K, ZHAO Q, CHEN Y. Distributed sensing and access in cognitive radio net-works[C]//10th International Symposium on Spread Spectrum Techniques andApplications (ISSSTA). .[S.l.]: [s.n.] , 2008.
[50] WANG F, KRUNZ M, CUI S. Spectrum sharing in cognitive radio net-works[C]//Proc. of IEEE INFOCOM. .[S.l.]: [s.n.] , 2008:1885–1893.
[51] HUANG J, BERRY R, HONIG M. Distributed interference compensation forwireless networks[J]. IEEE Journal on Selected Areas in Communications, 2006,24(5):1074–1084.
[52] LIU H, HUANG L, KRISHNAMACHARI B, et al. A negotiation game for mul-tichannel access in cognitive radio networks[C]//Proceedings of the 4th AnnualInternational Conference on Wireless Internet. .[S.l.]: [s.n.] , 2008.
[53] CORDEIRO C, CHALLAPALI K, BIRRU D, et al. IEEE 802.22: an introductionto the first wireless standard based on cognitive radios[J]. Journal of communi-cations, 2006, 1(1):38–47.
[54] CORDEIRO C, CHALLAPALI K, BIRRU D, et al. IEEE 802.22: the first world-wide wireless standard based on cognitive radios[C]//New Frontiers in DynamicSpectrum Access Networks, 2005. DySPAN 2005. 2005 First IEEE InternationalSymposium on. .[S.l.]: [s.n.] , 2005:328–337.
[55] FABRIKANT A, PAPADIMITRIOU C, TALWAR K. The complexity of pure Nashequilibria[C]//Proceedings of the thirty-sixth annual ACM symposium on Theoryof computing. .[S.l.]: [s.n.] , 2004:612.
[56] ROSENTHAL R. A class of games possessing pure-strategy Nash equilibria[J].International Journal of Game Theory, 1973, 2(1):65–67.
[57] MONDERER D, SHAPLEY L. Potential games[J]. Games and economic behav-ior, 1996, 14(1):124–143.
[58] VOCKING B. Congestion games: Optimization in competition[C]//Proceedingsof the 2nd Algorithms and Complexity in Durham Workshop. .[S.l.]: [s.n.] ,2006:9–20.
[59] LIU M, WU Y. Spectum sharing as congestion games[C]//Allerton conference..[S.l.]: [s.n.] , 2008:2005–2007.
[60] LIU M, AHMAD S, WU Y. Congestion Games with Resource Reuse and Appli-cations in Spectrum Sharing[J]. Proc. ACM GAMENETS, 2009.
[61] MILCHTAICH I. Congestion games with player-specific payoff functions[J].Games and economic behavior, 1996, 13(1):111–124.
[62] ACKERMANN H, ROGLIN H, VOCKING B. Pure Nash equilibria in player-specific and weighted congestion games[J]. Theoretical Computer Science,2009, 410(17):1552–1563.