86IEEECOMMUNICATIONSLETTERS,VOL.4,NO.3,MARCH2000
Peak-to-AveragePowerRatioReductionofanOFDM
SignalUsingPartialTransmitSequences
LeonardJ.Cimini,Jr.,Fellow,IEEE,andNelsonR.Sollenberger,Fellow,IEEE
Abstract—Orthogonalfrequency-divisionmultiplexing(OFDM)isanattractivetechniqueforachievinghigh-bit-ratewirelessdatatransmission.However,thepotentiallylargepeak-to-averagepowerratio(PAP)haslimiteditsapplication.Re-cently,twopromisingtechniquesforimprovingthePAPstatisticsofanOFDMsignalhavebeenproposed:theselectivemappingandpartialtransmitsequenceapproaches.Here,wepresentsuboptimalstrategiesforcombiningpartialtransmitsequencesthatachievesimilarperformancebutwithreducedcomplexity.
IndexTerms—High-speedwireless,OFDM,peak-to-averagepower.
PublisheI.INTRODUCTION
RTHOGONALfrequency-divisionmultiplexing(OFDM)[1]–[3]isaveryattractivetechniqueforhigh-bit-ratetransmissioninaradioenvironment.Bydividingthetotalbandwidthintomanynarrowsubchannels,theeffectsofmultipathdelayspreadcanbeminimized.Onedisadvantageisthepotentiallylargepeak-to-averagepowerratio(PAP)characteristicofamulticarriersignalwithalargenumberofsubchannels.Inparticular,abasebandOFDMsignalwith
;for
O
CIMINIANDSOLLENBERGER:PEAK-TO-AVERAGEPOWERRATIOREDUCTIONOFANOFDMSIGNAL87
Fig.2.Partialtransmitsequenceapproach.
afactoroffour.Notethatsymbol-spacedsamplingwill“miss”someofthesignalpeaksandresultinoptimisticresultsforthePAP.For256subcarriers,theabsolutePAPis24dB.However,withareasonablylargenumberofsubcarriersthesignalampli-tudeisapproximatelyRayleighdistributedandthelargepeaksoccurwithverylowprobability.Inparticular,thePAPexceeds11dBforonly0.1%ofthepossibletransmittedOFDMblocks.IntheSLMapproach,
possibletransmitse-quencesareproducedbymultiplyingtheinformationsequenceby
,then,theCCDFofthebest
ofthe
.Thus,theprobabilityofthePAPexceedingsomethresholdcanbemadeassmallaspossibleattheexpenseofadditionalinversefastFouriertransforms(IFFT’s).In[7],using128subcarriersand
.Then,partition
into
clusters
(3)
where
,iscalledthepartialtransmitse-quence.ThephasefactorsarechosentominimizethePAPof
,andphasefactorslim-itedto
full-length(i.e.,
-pointIFFT’s,ifthetransformscantakeadvan-tageofthefactthatalargefractionoftheinputvaluesarezero,theadditionalcomplexitycanbekepttoaminimum.Nevertheless,inthePTSapproach,anoptimizationisrequiredtobestcombinethepartialtransmitsequences.
III.NEWCOMBININGTECHNIQUE
Inthissection,asuboptimalcombiningalgorithmisintro-ducedthatachievesgoodperformancewithaminimalnumberoftrials.Here,weconsiderbinary(i.e.,
clusters,formthe
and
computethePAPofthecombinedsignal(4).Next,invertthe
firstphasefactor(
)andrecomputetheresultingPAP.IfthenewPAPislowerthaninthepreviousstep,retain
possibilitiesfor“flipping”thesignshavebeenexplored.
InFig.3,resultsareshownforthecaseofasingleOFDMblockand16clusterseachcomposedof16subcarriers.Thetransmittedsignalisoversampledbyafactoroffour.Simula-tionshaveshownthatthisissufficienttocapturethepeaks.Intheresultswhichfollow,100000randomOFDMblocksweregeneratedtoobtaintheCCDF’s.Weassume256subcarriersthroughoutandQPSKdatasymbols.TheunmodifiedOFDMsignalhasaPAPwhichexceeds10.4dBforlessthan1%oftheblocks.ByusingthePTSapproachwiththeoptimumbinaryphasesequenceforcombining,the1%PAPreducesto6.8dB.Inaddition,theslopehasbeenimprovedsothatthereductionwouldbeevenmoresignificantatlowerCCDFvalues.Fortheiterativealgorithm,the1%PAPis7.8dB.Whileadegradation
88IEEECOMMUNICATIONSLETTERS,VOL.4,NO.3,MARCH2000
Fig.4Comparisonoftheiterativeandrandomstrategies.
of1dBisencountered,theoptimizationprocesshasbeenre-ducedto16setsof16additions,aconsiderablesavingsoverdeterminingtheoptimumphasefactors.
Theeffectsofvaryingseveralparameterswerealsostudiedandtheresultswerepresentedin[9].Theseparametersare:1)thenumberofclusters,whichimpactsthecomplexityoftheimple-mentation;2)thenumberofallowedphasesforthevaluesoftheoptimizingsequence,whichagainimpactsthecomplexity;and3)thedataconstellationsize.Asexpected,theimprovementde-creasesasthenumberofclustersdecreases.However,withonly8clusters,andtherefore,only8stepsintheiterativeoptimiza-tion,areductionofmorethan2dBinthe1%PAPisachieved.Whenthephasefactorscanbechosenfromalargerset,specifi-cally,
