哈工大凸优化报告

年季学期研究生课程考核（读书报告、研究报告）考核科目凸优化理论及应用学生所在院（系）学生所在学科学生姓名学号学生类别考核结果阅卷人第1页（共5页）TheReportofconvexoptimizationcoursePARMinimizationofOFDMSignalsbyConvexOptimization1.Theintroductionoftheproblem:Peak-to-Average-PowerReductionofOFDMSignals1.1ThereasonoftheproblemgeneratedHighbandwidthefficiencyandrobustnessagainstfrequencyfadingarethefeaturesofOFDMsignalsduetomultipathpropagation.However,highpeaktoaverageratio(PAR)ofOFDMsignalslimitsperformanceofpoweramplifier(PA).Becauseofthis,PARshouldbereducedinordertokeepthePAoperatingwithlinearlevel,whichwillresultinlossesofpowerefficiency.Inaword,PAPRofOFDMsignalsshouldbereduced.Namely,tominimizethePAR.1.2TheoverviewofthePARminimizationAnewpowerspectrumdistributionwasdesiredtobedevelopedbyoptimizingthetimedomainpeakpowersubjecttoerrorvectormagnitude(EVM)constraints.Powerthesignaloveritssub-carriersshouldberedistributed,includingthepower-freeones.Itisprocessedbyapowerredistributionofthesignaloveritssub-carriers,includingthepower-freeones..2.PARminimizationinmathematicsAssumethatOFDMsignalhas48data,4pilot,12freesub-carriersand128symbols.The52sub-carriers(data/pilot)weremodulatedusingQAM.Ccn0denotesanidealOFDMconstellation,CcndenotesanOFDMconstellationtransmittedandCxnldenotesthecorrespondingtime-domainsignalobtainedbyIFFTwithl-timesoversampling.ciisasubsetofavailablecarriersofOFDMencodingandidiii,...,2,1(nd),wheren=64,d=52.constantβshouldbeadjustedforanyFFTscaling.p0isistheaveragepowerofthecarrier16-QAMmodulation.nnRSisadiagonalcarrierselectionmatrix.otherswithSii,0data,1(1)AccordingtotheprincipleofOFDMsystem,xcanbeexpressedas][cIFFTxl(2)PARcanbeexpressedasScnxiPARnli222,...,1max(3)EVMcanbeexpressedaspccEVMidiiiid00211(4)With(1)and(4),theEVMconstraintcanbeexpressedoncas0max0)(dpEVMccS(5)Tosumup,theoptimizationproblemisScnxinli222,...,1maxminimizeSubjectto0max0)(dpEVMccS3.ConvexformulationofPARminimizationBecausethepracticalpowershouldbelargerthantheidealone,sothereisanotherpowerconstraint:cSSc022(6)Anditisequivalentto2)(,)(0200ccSccccReAccordingto(5),itcanexpandthelimitsas2)(,200ccscReFinally,accordingtotheknowledgeofconvexoptimizationwehavelearned,itcanbeformulatedasatypeofconvexoptimizationproblemSOCP.Assolving(3)isequivalenttosolvingmaxxi,somakePxi.HenceminimizingmaxxiisequivalenttominimizingPwhilePxi.Thentaketheotherconstraintsmentionedintoconsiderate,theoptimizationcanbetransformedasaconvexoptimizationproblemSOCP.MinimizePSubjecttoPxi,nli,...,2,1][cIFFTxl0max0)(dpEVMccS2)(,200ccscReinvariablesRP,Ccn,Cxnl3.CVXcodeC0=input('Pleaseinputreferenceconstellation:');P0=input('Pleaseinputaveragepowerofthemodulationschemeused:');l=input('Pleaseinputoversamplingtimes:');B=input('PleaseinputrealvaluedFFTscaling:');S=input('Pleaseinputmatrixs');EVMm=input('PleaseinputmaxEVM:');n=64;d=52;e=EVMm*sqrt(d*P0);cvx_beginvariablep;minimizep;subjecttonorm(x(i))=p;x=ifft(c,l);norm(S*(C-C0))=e;real(C0'*S*(C-C0))=-e*e/2;cvx_end参考文献：Peak-to-AveragePowerReductionofOFDMSignalsbyConvexOptimization:ExperimentalValidationandPerformanceOptimization