On Cyclic Delay Diversity in OFDM Based Transmission …

1 , , F. Schuehleiny, , CyclicDelayDiversity(CDD)isa simpleap-proachtointroducespatialdiversi tytoanOrthogonalFre-quencyDivisionMultip lexing( ofdm )basedtransmissionschemethati tselfhasnobuilt-indiversity. It alsocanbere-gardedasa Space-TimeCode(STC).Butincontrasttothatt here is noadditionaleffortinthereceivernecessary , sincethedifferentcodewordsresultina changedchannelimpulseresponseinthereceiv er. how , weanalyzehowtochoosethecyclicshiftateach transmitantennatoachieve bestpossiblere-sults,andpresenta cyclicdelaydiversity, space-timecodeI. INTRODUCTIONOFDM basedtransmissionschemessufferfromthelac kofbuilt-indiversity. Therefore,it is necessarytoin-troducesomekindofdiversity , ,spatialdiversity, tosucha transmissionsysteminordertoachieve , ,DVB-TorHIPERLAN/2,merelyinterleavingin frequency directionis included,whichonlyinthecaseoffrequency selective channelscanhelptoimprove typicalflatfadingchar-acteristicsonecann ottake advantageoftheinterleavingwhichresultsin significantlossesintermsoftheBitErrorRat e(BER)respective FrameErrorRate(FER).

2 Atthesametime,a widerangeofpublicationsisde-votedto theinvestigationandconstructionofSTCsdur ingDr. HaasisnowwiththeInternationalUniversityB remen(IUB),CampusRing1, 28759 Bremen,Germanythelastfew oftheseanalyzesarecarriedoutforthespecia lcaseofa flatfadingchannelwhichis theAlamoutischeme[1]thatachievesfulldive rsity. Hereby, two con-secutive symbolsareprocessedinsucha [2],a spatialdiversityschemeforOFDM isintro-duced,namelytransmitDelayDiversi ty(DD), verysimplereceiverstructure maximumdelaysarestronglyrestrictedbytheG uardPeriod(GP).Likewise,transmitCyclicDe layDiversity(CDD)[3],[4] , thesignalis nottrulydelayedbutcyclicallyshiftedandth us, domainis PhaseDiversity(PD)[3] considerCDD, ,wefirstintroduceCDD, ,thestructureofa multiplean-tennatransmitter.

3 Then,weshow how theinserteddiver-sitycanbeexploited,anda nalyzehowthecyclicshiftshave tobechosenindependency ofthemodulationalpha-betinSectionIII(wec onsideronlyPhaseShiftKeying(PSK)modulati on).InSectionIV,wepresentsimulationresul tsanda comparisonwiththeAlamoutischemefortwo antennas[1].Finally, TRANSMISSIONSCHEMEPS fragreplacementsPGPGPGPGPOFDMIOFDM cyc;2 cyc; , , ,theInverseFastFourierTransform(IFFT), cyclicallyshiftedbyanantennaspe-cificdel ay cyc;n; n= 1;2; : : : ; N. FromtheequivalentrepresentationofCDD[3]i nthefrequency domaininequation(2)thatcorrespondstotheP Dsignal,wecanseethatit onlymakessensetochoosethecyclicshift cyc;noutoftheinterval0 cyc;n NF 1, ,thenumberofanten-nasis alsorestrictedtothenumberofcarriersNF.

4 Fur-thermore,weassumethedelayofantennaon e(TX1)tobezero, , cyc;1= 0, anddiscardit inthefollowing( ).s(l) =1pNF NF 1Xk=0S(k) ej2 NFkl(1)s((l cyc)modNF)|{z}CDDsignal=(2)1pNF NF 1Xk=0e j2 NFk cyc S(k)|{z}PDsignal ej2 NFkl:Theprefixis addedtofilltheGP. Onthechannelthesesignalssuperimposeandth ereceiverprocessesthesumsignalbysimplyre movingtheGPandperformingtheInverseOFDM(I ofdm ) ,sincethecyclicshiftsappearasmultipathsa t thereceiverandthus,nospecialcombiningand noadditionaleffortisnecessary(exceptfort hechannelestimation).Thesevirtualechosch angethecharacteristicsofthechannelinsuch a waythatit seemstobefrequency selec-tive andthus, and3 show thedistributionofun-codederrorsinthetime -frequency-planefortransmissionovera flatfadingchannelwithoutCDDandwithCDD,re spectively.

5 ThenumberofcarriersisNF= 64andthecyclicdelayonthesecondantennais cyc;2= 2(insam-ples).20040060080010001200140016 0018002000 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 ( Error)2004006008001000120014001600180020 00 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 , cyc;2= 2( Error)ComparedtothecasewithoutCDD( )theerrordistributionchangesif weapplyCDDonthesecondan-tenna( ) , whenweconsidertheBERsofthesetwo ,theuncodedrespec-tive , ,thecodinggainis ,ontheonehandindepen-dency ofthemodulationalphabetandontheotherhand ifweusemorethantwo 410 310 210 1100 ofdm uncodedCDD 0 2 uncodedOFDM codedCDD 0 2, codedPSfragreplacementsSNRindBBitErrorRa te(BER) CYCLICSHIFTANALYSISI nthelastsectionwehave seenthatwecangainfromCDDwhenapplyingForw ardErrorCorrection(FEC) bestresults?

6 Andhowcanthisbeextendedtomorethantwo transmitantennas?Thiscanbeanalyzedusinge quation(2),wherewecanseethattheshiftcorr e-spondstoa phaserotation,whichis ,themean(flatplane)andthevarianceofthech annelseenbythereceiverfora transmissionwithtwoantennasandCDDoverfla tfadingchannelsis depicted,whereonbothantennasthecyclicdel ayisvariedintherangeof0 cyc;n NF; n= 1;2. Themeanofthechanneldoesnotchange, hasa maximum,whenthedifferenceofbothshiftsis maximum, , BP SKopt=j cyc;1 cyc;2j= 32 =NF=2:Thus,theperformanceisonlydependent ontherelativeshiftofantennaonetoantennat wo andit is optimumforNF= antennasthebestcombinationofthecyclicdel aysis shownthatthemeanisconstantforany , ,wherethecyclicdelayofthefirstantennais constantzero, , cyc;1= 0.

7 It seemstobea goodchoiceinthiscasetodividethepossibler angeequidistantly, , cyc;1= 0, cyc;2= 21, and cyc;3= antennasinvestigationshave shownthattheoptimumcyclicdelayonthesecon dantennais cyc;2= 16, whereweuseda shiftof cyc;1= 0 PSfragreplacementsMean/VarianceShiftonAn tenna2 (TX2)ShiftonAntenna1 (TX1) TransmitAntennasPSfragreplacementsMean/V arianceShiftonAntenna3 (TX3)ShiftonAntenna2 (TX2) now QPSKopt=j cyc;1 cyc;2j= 16 =NF=4; , ,theopti-mumcyclicshiftseemstobehave reciprocaltothecardi-nalityofthemodulati onalphabetA, , Aopt=j cyc;1 cyc;2j=NFjAj;(3) ,wherewealsocompareit withthewell-knownAlamouti[1]schemefortwo SIMULATIONRESULTSIn[1],a transmitdiversityschemefortwo callit , everytwo con-secutive symbolsarecombinedandsentin thewayshowninTab.

8 [5]and[6],it is appliedtoanOFDM basedTX1TX2 TimetS1S2 Timet+T S2 S 1 TABLEITRANSMISSIONSCHEME matrix-vector-notation[5] R1R 2 |{z}R= H1H2H 2 H 1 |{z}H S1S2 |{z}S+ N1N2 |{z}N;(4) [5] (bijR) = ln0 BBB@PS2S(0)ie 12 2 NkR HSk2 PS2S(1)ie 12 2 NkR HSk2 1 CCCA;(5)whereS(0)iandS(1)iisthesetoftran smittedsignalsSwithbi= 0andbi= 1, ,theBERsoftheoneantennaandtwo , antennastrans-mitCDD(forinstance6 dBata BERof10 2).Butwithchannelcodingthereremainsonlya ,whereweuseda mem-orytwo convolutionalcodewithgeneratorpolynomial G(D) = (1 +D2;1 +D+D2). Andtheschemecanbeeasilyextendedtomorethe ntwo BERof10 3inthethreeantennascase(herewith cyc;1= 0, cyc;2= 21and cyc;2= 42insamples).

9 Thus,evenwiththebestchoiceofthecyclicshi ft( BP SKopt= 32) wecannotachieve theperformanceoftheAlamoutischemeintheco dedtrans-mission,butontheotherhandtherei s noadditionaleffortinthereceiverforthecom biningrespective forthesoftdemodulationofa vector. 610 510 410 310 210 1100 ofdm uncodedOFDM codedCDD 0 32 uncodedCDD 0 32 codedCDD 0 21 42 uncodedCDD 0 21 42 codedAlamouti uncodedAlamouti codedPSfragreplacementsSNRindBBitErrorRa te(BER) , dBat a BERof10 mustbepointedoutthattheoptimumcyclicshif tis now QPSKcyc= 510 410 310 210 1100 ofdm uncodedOFDM codedCDD 0 16 codedAlamouti uncodedAlamouti codedPSfragreplacementsSNRindBBitErrorRa te(BER) CONCLUSIONSI nthispaperwehave investigatedtheperformanceofa simplemultipleantennatransmissionscheme namelyCyclicDelayDiversity(CDD).

10 Norestrictioninouropinion, have analyzedhowthecyclicshifthastobechosenin dependency ofthenumberofantennasandthemodulationalp habet(forPSKmodulation) shownthatwecannearlyreachtheperformanceo fthewell-knownAlamoutischemethatachieves fullspatialdiversity. Butincontrasttothiswith-outany combiningschemeinthereceiverandthus,with -outadditionalcomplexity. So,it providesa highmea-sureofflexibility, sincewithoutany [1] ,A SimpleTransmitDiversityTechniqueforWire- lessCommunications, IEEEJ ournalonSelectedAreasinCom-munications, ,no8, October1998.[2]I. ,A NewSpaceDiversitySchemeforDVB-T, 5thInternationalOFDM-Workshop(InOWo),Ham burg,2000.[3] ,LowComplex Standard ConformableAntennaDiversityTechniquesfor OFDMS ystemsanditsAppli-cationtotheDVB-TSystem , 4thInternationalITGC onferenceonSourceandChannelCoding,Berlin ,2002.