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1、1RobustMIMOCognitiveRadioviaGameTheoryJiahengWang,Member,IEEE,GesualdoScutari,Member,IEEE,andDanielP.Palomar,SeniorMember,IEEEAbstract—CognitiveRadio(CR)systemsimprovethespectralthiscontext,alternativeapproacheshavebeenconsideredinefficiencybyallowingthecoexistencei
2、nharmonyofprimarytheliteraturetoallowconcurrentcommunicationsineitherusers(PUs),thelegacyusers,withsecondaryusers(SUs).Thissingle-inputsingle-output(SISO)channels[5]ormultiple-coexistenceisbuiltonthepremisesthatnoSUcangenerateinputmultiple-output(MIMO)channels[6](s
3、eealso[4]forinterferencehigherthansomeprescribedlimitsagainstPUs.Thesystemdesignbasedonperfectchannelstateinformation(CSI)arecenttutorialonthetopic).caneasilyendupviolatingtheinterferencelimitsinarealisticOneclassicalapproachtodeviseCRsystemswouldbesituationwhereCS
4、Imaybeimperfect.Inthispaper,weproposeusingglobaloptimizationtechniques,undertheframeworkarobustdesignofCRsystems,composedofmultiplePUsandofnetworkutilitymaximization(NUM)(see,e.g.,[7],[8])multiplenoncooperativeSUs,ineitherSISOfrequency-selectiveorcooperativegames(N
5、ashbargainingsolutions)[9],[10].channelsormoregeneralMIMOchannels.WeformulatethedesignoftheSUnetworkasanoncooperativegame,wheretheHowever,recentresultsin[11]haveshownthatNUMprob-SUscompetewitheachotherovertheresourcesmadeavailablelemsareNP-hardunderdifferentchoices
6、ofthesystemutilitybythePUs,bymaximizingtheirowninformationratessubjecttofunction.Moreover,the(suboptimal)algorithmsproposedinthetransmitpowerandrobustinterferenceconstraints.Followingtheaforementionedpaperslackanymechanismtocontrolthethephilosophyoftheworst-caserob
7、ustness,wetakeexplicitlyamountofaggregateinterferencegeneratedbythetransmitters,intoaccounttheimperfectnessofSU-to-PUCSIbyadoptingproperinterferenceconstraintsthatarerobustwithrespecttoandtheyarecentralizedandcomputationallyexpensive.Thistheworstchannelerrors.Relyi
8、ngonthevariationalinequalityraisessomepracticalissuesthatareinsurmountableintheCRtheory,westudytheexistenceanduniquenesspropertiesofcontext.Forex