Our design solves two fundamental chal lenges associated with MIMO full duplex complexity and performance Our design achieves full duplex with a cancellation design whose complexity scales linearly with the number of antennas this complexity is clos ID: 2974
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FullDuplexMIMORadiosDineshBharadiaStanfordUniversitySachinKattiStanfordUniversity ofmilliseconds),letalonemobileenvironmentssuchasLTE.Asecondproblemisperformanceitself.Thekeymet-ricistheresidualinterferenceleftaftercancellationateachreceivechain,theresidualdirectlytranslatestode-creaseinSNRforthedesiredreceivedsignal.AswewillshowinSec.3,evenifonecouldaccommodateaquadraticnumberofcircuitsandDSPcancellationim-plementations,theperformancedegradeslinearlywiththenumberofMIMOchains.Inotherwords,theresid-ualinterferenceaftercancellationateachreceivechainincreaseslinearlywithM.Thisisduetotheaccumu-lationoftheresidualinterferencefromallthecross-talkandselftalkcancellationsystems.Onceagain,asMIMOsystemsscaletosupportmanyantennas,thisessentiallylimitstheperformancegainsoffullduplex.ThispaperpresentsthedesignandimplementationofaMIMOWiFifullduplexradio.OurMantennafullduplexMIMOradiouseseachantennaforsimultaneoustransmitandreceive,i.e.,itusesthesamenumberofan-tennasasastandardhalfduplexM-antennaMIMOra-diounlikepriordesigns.ThedesignusesslightlymorethanMcancellationcircuitsandDSPalgorithmstocan-celalltheselfandcrosstalks.Inotherwords,complex-ityscaleslinearlywiththenumberofchains,whichisthebestperformanceonecouldexpect.Further,theper-formancedoesnotdegradelinearlywiththenumberofMIMOchains,i.e.,theresidualinterferenceisthesameastheSISOdesignanddoesnotincreaselinearlywiththenumberofchains.Weprototypeourdesignandinte-grateitwiththeoff-the-shelfWARPsoftwareradios[4]runningastockWiFibasebandanddemonstrateexperi-mentallythatitachievesclosetothetheoreticaldoublingofthroughput.OurdesignsolvesthekeychallengeofefcientlyandeffectivelyachievingtheMIMOfullduplexusingtwomajorideasasfollows.First,akeyinsightisthatMIMOchainsareco-located,i.e.,“theyshareasimilarenvironment”.Intuitively,thesignalstransmittedbytwoneighboringantennas(sepa-ratedbyafewcm)gothroughasimilarsetofreectorsandattenuationsintheenvironment.Cancellationsys-temsareessentiallytryingtomodelthesedistortions,sowhenwewanttomodelcross-talk,wecanreusetheworkthathasbeendoneformodelingthechain'sownself-talkinterference.Thisresultsinanovel“cas-caded”lterstructureforcancellationthatresultsinanoveralldesignthathasnear-linearcomplexityscalingwiththenumberofMIMOantennas.Second,thereasonperformancedegradeslinearlywiththeSISOreplicationbaseddesignisthateachoftheMindependentcancellationalgorithmsforself-talkandcross-talkatareceivechainproducetheirownestima-tionerrorwhichadduptothelineardegradation.OurkeyinsighthereistoleveragethefactthatwehaveMtransmittersavailablethatcanconcurrentlysendtrain-ingsymbols.Specically,wedesignatrainingpream-bleforWiFithatallowseachreceivechaintoestimateeachoftheself-talkandcross-talkchannelsatanerrorthatisMtimeslowerthantheSISOdesignbycombin-inginformationfromallMtrainingsymbols.Conse-quently,inourdesignwhentheestimationerrorsaddupfortheself-talkandcross-talkcancellations,theoverallerrororresidueisthesameasaSISOsystemwouldhaveachieved,whichisthebestonecanhopefor.Furtherthealgorithmismodularandstructuredinawaythat,ifinthefuturetheSISOfullduplexdesignmanagestoimproveitsperformanceevenfurther,theMIMOdesigninthispaperimmediatelybenets.Weprototypeourdesignusingourowncustomde-signedanalogcancellationcircuits,implementthedigitalcancellationalgorithmsandintegratethemwithoff-the-shelfWARPradios.Ourexperimentsdemonstratethatina33conguration,oursystemachievesaperformancethatleavesanegligible1dBofself-interferenceaftercan-cellation.Wealsoshowthatoursystemachievesa95%throughputgainoverhalfduplexradiosusingastandardWiFicompliantOFDMPHYof20MHzfor802.11nforalldifferentmodulations(BPSK,QPSK,16QAMand64QAM)andcodingratesof(1/2,2/3,3/4,5/6),supportingthreestreamsfor33MIMO.2TheProblemInthissection,wedescribethenatureofinterferenceinaMIMOfullduplexradioandthendiscussthearchitec-turalchallengesindesigningacancellationsystem.Self-talkorcrosstalk(orforthatmatteranytrans-mittedsignal)ismadeupofthreemajorcomponents[5,10,2]:LinearSignal:Thisisthesignalthatthebasebandmo-demwantedtotransmitandisthendistortedbychan-nelreections.Itslinearbecauseitcanberepresentedasalinearcombinationofdelayedandsummedcopiesofthesamesignalthatarisefromenvironmentalmulti-pathreections.Non-linearSignal:Thisisthesignalthatisgeneratedduetonon-lineartransformationsthatthelinearsignalgoesthroughwhenitispassedthroughanalogradiocomponentssuchasmixers,powerampliersinthetransmitchain.TransmitNoise:ThisisthenoisethatisgeneratedbyactiveTXchaincomponentssuchaspowerampliersandlocaloscillators(weclubthingssuchasbroadbandnoiseandphasenoiseintothistermforthesakeofbrevity).Therelativestrengthsofthesecomponentsdependsonthequalityoftheradio.Fig.1atabulatesthestrengthsofthedifferentcomponentsweempiricallymeasuredfora2 (a)Thedifferentcomponentsofthetransmittedsignal(self-talk)foratypicalWiFiradio.Thesecondcolumntabulatestheamountofself-talkcancellationneedstoeliminatethecorrespondingself-talkcom-ponenttothenoiseoor. (b)Interferencecomponentsandcancellationrequirementsfor3an-tennaMIMOfullduplex.Thersttabledescribesthelevelsofdiffer-entinterferencecomponents(linear,non-linearandtransmitnoise)thatmakeupself-talkandcross-talksatonereceiverina3antennaMIMOradio.Cross-talk1isfromtheneighboringantennaandcross-talk2isfromthefartherneighboringantenna.Thesecondtableliststheoverallcancellationneeded,herethevaluesarebumpedupby5dBrelativetothersttabletoensurethatevenwhentheresiduesleftfromtheself-talkandthetwocross-talkcancellationsareaddedup,theoverallnoiseoordoesnotgoup(elseitwouldgoupby5dBifthecancellationrequirementforeachcomponentdidnothavea5dBmargin).Figure1:Requirementtablescommodity20dBmWiFiSISOradio,andtheamountofcancellationneededtoeliminatetheminafullduplexsystem.NotethatthisisacheapradiowidelyusedinmanycommercialWiFidevices[2,4],sowebelievethisisrepresentativeoftheWiFiradiosingeneral.Theaboveanalysisisofcoursetrueevenforasin-gleantennaradiowithoutMIMO,andrecentwork[11]describeshowtodesignacancellationtechniquesthateliminatesallthesesourcesofself-talk.However,whatisuniquewithMIMOiscross-talk.Inotherwords,theinterferencethatresultsatareceivechainduetoatrans-missionfromaneighboringco-locatedMIMOanten-na/chain.Ina3antennafullduplexMIMOradio,eachreceiverchainwouldseetwocross-talksignalsfromtheothertwoantennasasseeninFig.3.Cross-talkisslightlyweakerthantheself-talkgener-atedbythechain'sowntransmission,butisstillquitestrongandhasalltheabovethreeenumeratedcompo-nents.LiketheearlierSISOdesign[11],thetransmitnoisecomponentofthecross-talksignalhastobecan-celedintheanalogdomain,whereasthenon-linearandlinearcomponentscouldbecanceledinbothanalogand Figure2:PriorbestperformingSISOfullduplexdesign.Thegureontherightshowsanequivalentconceptuallterbasedviewofself-talkcancellation.Thelterisparameterizedbyitscomplexity,thenumberoftaps.Theltersubsumesbothanaloganddigitalcancellation.digitaldomains.Fig.1btabulatesthestrengthsofthevariouscomponentsthatmakeupacross-talkandself-talksignalinatypical3-antennaMIMOWiFiradiowith20dBmtransmitpower(notethatthepowerisdividedequallyamongallthreetransmitters,sothepoweroutofeachantennais15dBm).2.1WhycantwereusetheSISOfulldu-plexdesignbyreplicatingit?Atrstglance,theMIMOinterferencecancellationproblemlooksquitesimilartoaSISOfullduplexprob-lem,onlyreplicatedafewtimes.Afterallthecross-talksignalthatneedstobecanceledlookslikeanattenuatedversionofachain'sownself-talksignalthattheSISOdesignmanagestocancelcompletely.Sowhycouldn'twereplicatetheSISOdesignM2�Mtimesforeachofthecross-talksignalsinaMantennaMIMOradioandbedonewithit(showninFig.3)?Tounderstandthereasonthismightnotwork,itwillhelptohaveaconceptualunderstandingofwhataSISOself-talkcancellationsystemaccomplishes.Atitscore,theself-talkcancellationtechniquecanbethoughtofasshowninFig.2.Theinputisthebasebandsignalthatisbeingtransmitted,towhichtransmitnoiseisaddedandthecombinedsignalispassedthroughalinearandnon-linearunknowntransferfunctionthatcapturesthedistor-tionsintroducedbytheanalogcomponentsandthewire-lesschannelandisdenotedbyH.Whatthecancellationcircuitsandalgorithmsaretryingtoaccomplishisesti-mateandrecreatethisunknowntransferfunctionHasaccuratelyaspossible(tothetuneof105dBresolution),andthenpassacopyoftheinputbasebandtransmittedsignalandnoisethroughthisestimatedtransferfunc-tiontorecreatetheself-talkandcancelit.TheestimatedtransferfunctionsaremodeledusingtunableanaloganddigitalFIRlters,forexamplethepriorSISOdesign'sanalogcancellationcircuitrequires12delay-attenuation3 Power level in dBm Cancellation needed in dB Total TX signal 20 105 Linear component 20 105 Non - linear component - 10 75 Transmitter Noise - 20 65 Power and Interference relative to noise floor of - 85 dBm MIMO FD, Receiver 1 Power in dBm Cancellation needed (dB) Self - talk Cross talk 1 Cross talk 2 Self talk Cross talk 1 Cross talk 2 Overall signal at antenna 1 15 - 9 - 15 100 76 70 Linear component 15 - 9 - 15 100 76 70 Non - linear component - 15 - 39 - 45 70 46 40 Transmitter noise - 25 - 49 - 55 60 36 30 Power and Interference relative to noise floor of - 85 dBm MIMO FD, Receiver 1 Self - talk Cross Talk 1 Cross Talk 2 Analog cancellation 65 dB 41 dB 35 dB Digital cancellation 35 dB 35 dB 35 dB Cancellation Requirement Figure3:SISOReplicationBasedDesign:Showsa3antennafullduplexMIMOradio,usingnineSISOcan-cellationcircuits(SISOreplicationdesign).Thisdesignusesintotal9NtapsforM=3assumingeachcircuitre-quiresNltertaps.InthegeneralcasethisdesignwouldrequireM2NforaMantennafullduplexMIMOsystem.tapsthateachrepresentasingleanalogFIRltertap,andwhatisbeingcontrolledistheweightoneachtap(prac-ticallythistranslatestocontrollingtheattenuatoronthatdelay-attenuationanalogline).AsimilarFIRlterstruc-tureisusedfordigitalcancellationandthechallengeiscalculatingtheweightstouseoneachofthetaps.SothekeychallengetheSISOself-talkcancellationsystemissolvingiscalculatingasetofFIRlterweightsthatcanaccuratelymodelthisunknownandtime-varyingtransferfunction.Consequently,therearetwometricsthatcharacterizethisestimationcircuitsandalgorithms.Complexity:canbequantiedbythenumberofltertapsthatareusedintheimplementationsthatrepresenttheestimatedˆH.Themoretapsweneed,themoreanalogcircuitryisneededaswellasDSPresourcesinFPGAtoimplementthem.Keepingthenumberoftapslowisimportantsoastoreducethespaceandpowerconsumedbyanalogcircuits[8]andDSPlogicforFIRimplementations(thebaselineistheSISOde-signthatrequires12analogtapsand132digitalFIRtaps).Togetasenseoftheimpact,12analogtapscon-sumeroughly24sq.cmofboardarea.Asecondcon-sequenceofcomplexityistheamountoftimeittakesustore-tunethecancellationwhentheenvironmentchanges(includingthingssuchastemperature).Thelargerthenumberoftaps,thelongeritwilltaketotunesincetherearemorevariablestoestimated.Whencan-cellationisbeingtuned,theradiocannotbeoperatedinfullduplexmode.Hencetuningtimeispureoverhead,andneedstobeminimized.Estimationerror:Asecondkeymetricisestimationerrorwhichmanifestsasresidualinterferenceleftaf-tercancellationanddirectlyreducestheSNRofthedesiredreceivedsignal.Aperfectlyaccuratecancella-tionsystemwouldleavenoresidue.Thebaselinefor Figure4:CascadedCancellationDesign:Showsa3antennafullduplexMIMOradiodesignwithcascadedlterstructureforcancellation.Thestructureisshownforreceiverchain1only,butthesamestructureisre-peatedfortheotherchains.For,self-talkcancellationwehaveNltertapsoneverychain.FurtherwehaveCandDtapsfeedinginacascadingfashionattheinputoftheNtapself-talkcancellationcircuit.Noticecrosstalk1isstrongersoweneedmoretaps(C�D)ascomparedtocrosstalk2.HoweverbothCandDaresignicantlysmallerthanN.thismetricisthebestperformingpriorSISOself-talkcancellationdesignthatleaves1dBofresidueoverthenoiseoor.Inotherwords,thereceivernoiseoorisincreasedby1dBandthereforetheSNRofthere-ceivedsignalisalsodecreasedby1dB.Toputthisnumberincontext,thisisextremelyaccuratesinceatmostnormalreceivelinkSNRs,a1dBdecreasewillhavenegligibleimpact.Thereasonforthisresidueisestimationandquantizationerrorinthealgorithmsthatcalculatetheweightsfortheltertapsusedinanaloganddigitalcancellation.Estimationerrorisinevitableandcannotbeavoided,butitsimportanttokeepitassmallaspossible.HowwellwouldtheSISOreplicationbaseddesignforMIMOperformonthesetwometrics?Theoptimalsce-nariogiventheSISOdesignisthattheoverallcomplexityofaMantennafullduplexMIMOradiowouldbeMthecomplexityoftheSISOdesign,anditwouldhavethesameestimationerrorastheSISOdesign.Wecan-notdobetterthanalinearincreaseincomplexityandnoincreaseinestimationerror.However,theSISOreplicationbaseddesigndoesn'tcomeclosetoachievingtheseoptimaltargets.Itscom-plexityisM2thecomplexityoftheSISOdesign.ThisisbecauseitrequiresustoreplicatetheSISOdesignforeachcross-talkfactor,andthereforeweneedatotalofM2versionsoftheSISOdesign.Intermsoftapsthisim-plies12M2tapsinanalogcircuitsalone,alongwiththe4 Cross Talk 1 T Σ Circulator TX1 RX1 N taps N taps N taps T Σ Circulator TX2 RX2 N taps N taps N taps T Σ Circulator TX3 RX3 N taps N taps N taps Total 9N Taps, for M=3 General Complexity M 2 .N Cross Talk 2 Self Talk Cascaded Filter Taps: N �� C � D T Σ Circulator TX1 RX1 Σ T Σ Circulator TX2 RX2 Σ T Σ Circulator TX3 RX3 Σ Total Taps: 3N + 4C + 2D, for M=3 General Complexity: ~ M.N M 2 .N C taps C taps C taps Σ D taps Cross Talk 1 Cross Talk 2 Self Talk N taps N taps N taps C taps Σ D taps Σ correspondingincreaseindigitalcancellationFIRtaps.Second,thisdesign'sestimationerrorturnsouttobeevenmoreworse.Ateachreceiverchain,weshowinSec.3.2thattheresidualinterferencescaleslinearlywiththenumberofMIMOchainsM.IntuitivelythereasonisthateachreplicaoftheSISOdesignisrunninganinde-pendentestimationalgorithmfordeterminingthevaluesoftheltertapstouseforcancellation.SinceateachreceiverchainwehaveMversionsoftheSISOdesignrunning,wewillhaveaMincreaseinestimationerrorandconsequentlytheinterferenceresidue.3DesignWepresentanewcrosstalkcancellationtechniqueforfullduplexMIMOwhichisscalableandefcient.ThekeytechniquebehindourMIMOcancellationdesignisacascadedlterstructure.Specically,weexploitthefactthatinMIMO,cross-talkandself-talkarecorre-lated,sincetheyshareasimilarenvironment(orsimilarsetofmulti-pathreectionandattenuationprolesinthechannel).Further,cross-talkacrosschainsisnaturallyreducedcomparedtothechain'sownself-talkbecauseofphysicalantennaseparation.Weexploittheseinsightstodesignalowcomplexityandlowerrorcross-talkcan-cellationsystem.Forcancelingthechain'sownself-talkweusethedesignfrompriorwork[11].3.1ReducingComplexity:TheCascadeOurdesignbuildsonakeyinsight:co-locatedMIMOantennasshareasimilarenvironment.Inotherwordsthetransferfunctionthattransformsthecross-talksignalatareceivechainhasacloserelationshipwiththetransferfunctionthatthechain'sownself-talkundergoes.Intu-itivelythisisbecausethenear-eldenvironmentaroundaradiolooksessentiallythesametoneighboringanten-nassincetheysharethesamereectorsintheenviron-ment,andthedistancetothesereectorsisalmostthesamefromtheclosely-spacedantennas.Theonlydiffer-enceistheadditionaldelayexperiencedbythecross-talksignalcomparedtothechain'sownself-talk.NotethatthisdoesnotmeanthatMIMOself-talkandcross-talkchannelsarecompletelycorrelated,theywillstillhaveindependentphasethatarisesfromtheslightlydifferentdelaysexperiencedbyself-talkandcross-talksignalsatRFfrequencies.Buttheamplitudesofthemulti-pathre-ectionsforselfandcross-talksfromthesamereectortendtobenearlythesamesincethedistancetothere-ectorisalmostequalfromthecloselyspacedMIMOantennas.Theaboveinsightcanbemathematicallymodeledasacascadeoftransferfunctions.LetHi(f)andHct(f)bethetransferfunctionsofthechain'sownself-talkandcross-talkrespectively.Theoverallrelationshipbetweenthesefunctionscanbemodeledasfollows:Hct(f)=Hc(f)Hi(f)(1) (a)Cancellationperformanceinthefrequencydomainforthecas-cadeddesignandthereplicationbaseddesignwiththesamecomplex-ityfora3antennaMIMOfullduplexradiooperatingaWiFiPHYina20MHzbandat0dBmTXpower. (b)Tableshowingthereductionincomplexityandtuningtimewiththecascadeddesigncomparedtothereplicationbaseddesignforbotha3antennafullduplexMIMOradioaswellasthegeneralcaseofaMantennafullduplexMIMOradio.Figure5:CascadeDesignEvaluation.whereHc(f)isthecascadetransferfunction.ThekeyobservationisthatHc(f)whichcascadedwithHi(f)re-sultsinthecross-talktransferfunction,isanextremelysimpletransferfunction.TypicallyHc(f)isasimplede-laythatcorrespondstothefactthatthetwoantennasareseparatedandthecross-talksignalexperiencesslightlyhigherdelaycomparedtotheself-talk.Howmightweexploitthisinsight?TheideaistomimicthecancellationdesigninacascadesimilartotheequationaboveasseeninFig.4.Specically,wecoulddesignsimplelow-complexityanalogcancellationcir-cuitsanddigitalcancellationltersthatmodelthecas-cadefunctionHc(f).Thesecircuitsandlterswouldthenfeedintothecancellationcircuitsanddigitalcan-cellationltersforthechain'sownself-talkcancellationandthusreuseallthatcircuitrytomodelthecross-talkchannel.Rememberthatthecircuitsanddigitalltersforthechain'sownself-talkaremodelingHi(f),hencethecascadedstructureisessentiallyrecreatingtheaboveequation.SotheonlyadditionalcomplexitycomparedtotheoptimalMIMOdesignwouldbefromthecircuitsandltersthatmodelthecascadetransferfunctionHc(f).Thenaturalquestionisofcourse,whatisthecomplex-ityofthecircuitsandltersthatmodelthecascadefunc-tion?Weempiricallymeasureitbyimplementingdiffer-entcomplexitycascadecancellationcircuitsandltersandndingoutwhatcomplexitysufcestomeetthecan-cellationrequirementsdescribedintheprevioussection.WethenprovidetheSISOreplicationbaseddesignthe5 2.44 2.445 2.45 2.455 2.46 -80 -60 -40 -20 0 Transmitted cross t alk Cross talk at RX1 SISO replication cancellation using 4 taps Cascade cancellation u sing 4 taps Power in dBm Frequency in Ghz Spectrum plot 67 dB 18 dB SISO replication design Our design Analog Cancellation taps (3X3) 108 (12*9) 56 ( reduced by 1.92x ) Digital Cancellation taps (3X3) 1188 (132*9) 485 ( reduced by 2.45x ) Tuning time (3X3) 9 ms (1ms*9) .024 ms ( reduced by 375x ) Analog Cancellation taps ( mXm ) O(M 2 N) O(MN) Digital Cancellation taps ( mXm ) O(M 2 R) O(MR) Tuning time ( mXm ) O(M 2 ) O(M ) Resource Comparison between SISO replication and Our design samenumberoftapsandcomparethecancellationper-formance.Weconducttheexperimentbytransmittinga20MHzWiFiOFDM33MIMOsignal,andattempttocancelitusingthetwoapproaches.Fig.5aplotstheresultsfortheimpactofthecas-cadedstructureontheefcacyofanalogcancellation.Aswecanseethecascadedstructureconsistentlyprovides18dBbetterperformancethantheSISOreplicationbaseddesignwiththesamecomplexityandmeetstherequired65dBofanalogcancellation.ThenumberofanalogtapsrequiredtorealizethisperformanceusingthecascadeddesignistabulatedinFig.5b.Foratypical3antennaMIMOWiFiradiowith12cmseparationbetweenanten-nas(typicalofAPs),theantennaseparationitselfpro-videsabout24dBofisolation,soweneedanother41dBofcross-talkcancellationinanalog(seeTable.1bforre-quirements).Aswecanseeweneedonlyfouranalogtapswiththecascadedstructurecomparedtothe12tapsrequiredbythenaivedesignforcancelingcross-talkatanadjacentantennaandonlytwotaps,whencancelingtothefartheroutantennaasshowninFig.4.Thecas-cadeddesignthereforerequires1:92lowernumberoftapscomparedtotheSISOreplicationdesignfora3an-tennafullduplexMIMOradioasseeninFig.5b.Thereductionfactorapproachestheoptimal3numberasthenumberofantennasincreases.Toverifytheimprovementfordigitalcancellation,weconductasimilarexperimentwiththesamesetup(20dBmTXpower).However,weprovidetheSISOrepli-cationdesigntherequirednumberoftapstomeettherequirementonanalogcancellationsowecanspeci-callyevaluatethebenetsfordigitalcancellationwithcascading.AsseeninFig.5b,withacascadedstruc-tureweneedatotalof485tapstocancelself-talkandcross-talktothenoiseoorfora3antennaMIMOra-dio.Further,fortheSISOreplicationbaseddesignusingthesamenumberoftaps(485),theresidualinterferenceisstillanadditional7dB.Toachievethesameperfor-manceasourcascadeddesignwiththeSISOreplicationbaseddesign,wewouldneed1188or2:45moretapsastabulatedinFig.5b.OnceagainthereductionfactorapproachestheoptimalnumberMandthenumberofan-tennas(M)grows.Finallyintermsofcancellationper-formance,a7dBincreaseinnoiseoororreductionindesiredsignal'sSNRisquitehighbyitself,andwhenwetakeintoaccountthereductionincancellationforanalogof18dB,wearelookingata25dBreductioninoverallcancellationfortheSISOreplicationbaseddesignwiththesamecomplexityasourcascadedstructure.Therearetwomainbenetstoreducingcomplexity:Size,CostandTuningtimereduction:Eachadditionalltertapincreasesthesizeofcancellationboardsinana-logandFPGAresourceconsumptionindigitalcancel-lation.Foranalogcancellation,ourcircuitsconsumed110sq.cmofboardareacomparedtonearly216sq.cmfortheSISOreplicationbaseddesignfora3-antennaMIMOfullduplexsystem.Forexample,wefoundex-perimentallythatreducingthenumberofdigitalltertapsfrom1185to485fora3antennaMIMOradiomeansthatalowerclassXilinxKintexseriesFPGAhassufcientDSPresourcestoimplementthecancellation,whereastheSISOreplicationbaseddesignwouldrequirethehigherendVirtexFPGA[6].Thistranslatestoenor-mouspowersavings,aVirtexFPGAconsumesnearly80WofpowerwhereasaKintexconsumesonly40Wontwiceasless[7].PowerreductiontranslatestolessheatandconsequentlysimplerAPdesigns.Finallytoulti-matelyrealizethedesignincompactboardsorinICs,re-ducingthenumberoftapsasmuchaspossibleisamust.Analconsequenceisthetuningtimetocomputetheweightsforeachofthesetapsalsoreduceslinearlywithlessernumberoftaps(tuningtimeispureoverheadsinceduringtuningtheradiocannotbeusedforcommunica-tion).Transmitpowerwaste:Theamountofpowerthatneedstobecoupleofffromthetransmitpathstopoweringcan-cellationcircuitsdependslinearlyonthenumberoftapsinthecancellationcircuits.Thisisbecauseeachtapisofcourseonlyusefulifsomecopyofthetransmittedsignalispassedthroughit,andinadditioneachtaphaslossas-sociatedwithitthataddsup.ThusreducingnumberoftapshelpsreduceTXpowerwaste,whichinturntrans-latestolesserbatteryconsumptionespeciallyformobiledevices.3.2ReducingInterferenceResidue:JointTrainingThegoalofdigitalcancellationistocleanoutanyre-mainingresidualself-interference.Onceagain,anatu-ralquestioniswhynotreusethedigitalcancellational-gorithmsdesignedforSISO?Inotherwords,foreachreceivechaininaMantennafullduplexMIMOradio,runMseparatedigitalcancellationalgorithmsthatesti-matethechain'sownself-talkandtheotherM�1cross-talkinterferencecomponents.Thesealgorithmsworkbyestimatingthedistortionexperiencedbyeachofthein-terference(bothforlinearandnon-linearcomponents).Theythenapplytheestimateddistortionfunctionstotheknownbasebandcopyofthetransmittedsignalandsub-tractitfromthereceivedsignal.Theaboveapproachdoesn'tworkbecauseeveryad-ditionalandindependentdigitalcancellationalgorithmweuseinthereceivechainlinearlyincreasestheresid-ualinterferenceaftercancellation.Inotherwords,per-formanceworsenslinearlywiththenumberofMIMOchains.Toseewhy,westartwithdescribingwhyevenasimpliedSISOdigitalself-interferencecancellational-gorithmwillhavesomeresidualinterferencethatcannot6 Figure6:ThisgureshowsthetransmittedandreceivedpacketsforaSISOfullduplex,2antennaMIMOfulldu-plexwiththetraditionaltrainingtechnique,andourde-signwiththenoveltrainingtechnique.Noticethetrain-ingsymbolstructureinthelastgure,thisallowsustoreducetheestimationerrorbyhalffortheself-talkandcross-talkcomponentsfora2antennaMIMOradio.becanceled.Digitalcancellationworksintwostages,rstthereisatrainingphaseandthencancellationphase.Thetrainingphaseusestrainingsymbols(e.g.theWiFipreamble),andtheassumptionisthatthereisnodesiredreceivedsignalfromtheotherfullduplexnode.Thetrainingsym-bolsareusedtoestimatetheself-interference.Letssaythetrainingself-interferencesymbolissasseeninFig.6.a.Theself-interferencesymbolisbeingreceivedaftertransmissionfromthesameradio(forsimplicityassumethereisnodistortionfromthechannel),andthereceiveraddsitsownnoisen1(variances2)tothereceivedsignal(thisnoisecomesfromeffectssuchasquantizationintheADC).Hencethereceivedsignaly1canbewrittenas,y1=s+n1Thebestestimateoftheself-interferencesinthiscaseissimplyy1Howeverthisestimateˆshassomeestima-tionerror,whichinthiscaseissimplythepowerofthereceivernoiseasshowbelow:ˆs=y1;E((s�ˆs)2)=E(n21)=s2Howcanweusethisestimatetocancelsubsequentself-interference?Forsimplifyingthedescription,letsas-sumethepacketthatisbeingtransmittedandisactingasself-interferenceissimplythesametrainingsymbolrepeatedthroughoutthepacket(realworldpacketsareofcoursenottriviallikethis,butthisassumptiondoesnotchangethebasicinsightbelow).Tocancelthisself-interferencethroughputthepacket,thealgorithmwillsimplysubtracttheaboveestimatefromtheoverallre-ceivedsignal.Letssayxistheactualdesiredreceivedsignal,theoverallsignalreceivedisy,andthesignalaf-tercancellation,aregivenby:y=x+s+n3y�ˆs| {z }cancellation=x+s�ˆs| {z }estimationerror=s2+n3|{z}RXnoiseAswecansee,theestimationerrorshowsupasresidualinterferencewithvarianceofs2.Asthebestknownpriordesignhasshownthisisontheorderof1dBoverthehalf-duplexnoiseoor.SISOReplicationbasedMIMOdesign:ItsnoweasytoseewhyadesignforMIMOthatsimplyusesMreplicasofthedigitalcancellationalgorithmateachreceivechainfortheself-talkandtheM�1cross-talkinterferencesig-nalsincreasestheestimationerrorroughlybyafactorofM.Thetrainingsymbolstructurefora22MIMOtransmissionisshownintheFig.6.b.above,essentiallytherearetwotrainingsymbolss1ands2sentovertwoslotsfromthetwodifferenttransmitchains.Thealgo-rithmsataparticularreceivechainusethesesymbolslikeintheSISOcasetoestimatetheself-talkandthecross-talk,andeachofthemwillhavetheirownestimationer-ror.Whentheseestimatesareusedforcancellation,theestimationerrorsaddup,andtheoverallestimationer-ror(orresidualself-interference)ateachreceivechainistheoreticallytwotimestheSISOcase.Themathbelowshowstheaboveintuitionformally.First,theestimatesfortheself-talkandcross-talksymbolsaregivenby:ˆs1=y1;E((s1�ˆs1)2)=s2ˆs2=y2;E((s2�ˆs2)2)=s2Whencancelingtoattempttorecoverthedesiredre-ceivedsignalx,wecancalculatetheestimationerrorasfollows:y=X+s1+s2+n3y�ˆs1�ˆs2| {z }cancellation=X+s1�ˆs1| {z }s2+s2�ˆs2| {z }s2+n3|{z}RXnoiseAswecansee,theestimationerrorshowsupasresid-ualinterferencewithvarianceof2s2,bothself-talkandcross-talkestimationintroduces2error.WecanrecursivelyshowthatforageneralMantennafulldu-plexMIMOradio,theestimationerrorandconsequentlyresidualinterferenceoneachreceivechaingoestoMs2.OurDesign:Ourkeycontributionisanoveltrainingsymbolstructureandestimationalgorithmthatreducestheestimationerrorforeachinterferencecomponentateachreceiverchain(self-talkorcross-talk)tos2=MforafullduplexMMMIMOradio.Thekeyinsightistore-designthetrainingsymbolstoreducetheestimationerror.Specicallyinsteadofsendingtrainingsymbols7 b ) SISO replication based 2X2 MIMO Full Duplex c) Our Design based 2X2 MIMO Full Duplex TX Transmitted and Received packets a) SISO Full Duplex Data= s s RX y 1 =s + n 1 Training y =x + s + n 2 y 1 = s +n 1 TX2 s 1 Data1= s 1 Data2 = s 2 s 2 TX1 RX1 Training y =x + s + n 3 y 1 = s 1 +n 1 y 2 = s 2 +n 2 TX2 s 1 s 2 TX1 - s 2 s 1 RX1 y 1 =s 1 - s 2 +n 1 y 2 =s 1 +s 2 +n 2 y = x + s 1 + s 2 +n 3 Data1= s 1 Data2 = s 2 Training fromeachofthetransmitchainsseparatelyinconsec-utivetimeslots,wesendacombinationofallofthemfromeachtransmitterinparallel.Theideaistoactuallyleveragethefactthattherearetwotransmittersthatcouldbeleveragedtotransmittraininginformationjointlyandtherebyimproveaccuracy,thereisnoneedtotreateachofthemseparately.Doingsorequiresanintelligentjointtrainingsymboldesignsothateachsymbolcanbeesti-matedasalinearcombinationofthereceivedtransmis-sions.Fig.6.c.showsthemainidea.Weuseasimilarsetofequationsasbeforetoshowfor-mallywhythisworks.AsseeninFig.6.c.,thetrainingsymbolsaretransmittedbychain1andchain2simulta-neously.Intimeslot1,transmitter1and2transmits1ands2,respectively.Andintimeslot2,transmitter1and2transmits1and�s2respectively.Receiver1,receivesthecombinedsymbolsintime-slot1andtime-slot2,y1andy2.Thus:y1=s1+s2+n1;y2=s1�s2+n2Letsassumetherestofthetransmissionsfromthetwochainsarejustrepetitionsofthesamesymbolss1ands2respectively(againthisisfordescriptionsimplicityandsufcestoexplaintheinsight).Weneedtogetestimatesforthedatasymbolss1ands2usingthetwotrainingsym-bolsy1andy2.Thebestestimatesaregivenby:ˆs1=y1+y2 2;E(s1�ˆs1)2=E(�n1+n2 22)=s2 2ˆs2=y1�y2 2;E(s2�ˆs2)2=E(�n1�n2 22)=s2 2Aswecansee,theerrorineachoftheseestimates(self-talkandcross-talk)iss2=2.Nowwhentheseestimatesareusedforcancellation,thefollowingequationresults:y=x+s1+s2+n3y�ˆs1�ˆs2| {z }cancellation=x+s1�ˆs1| {z }s2 2+s2�ˆs2| {z }s2 2+n3|{z}RXnoiseAswecanseetheresidualinterferenceisonlys2,ratherthanthe2s2thatwouldhaveresultedfromtheSISOreplicationbaseddesign.Further,wecanshowbyre-cursionthatthisresidualisthesameastheSISOde-sign,i.e.thereisnolinearincreasewiththenumberofMIMOchainsasthenumberofantennasincreases.ThetrainingsymbolsforthegeneralMantennacasearede-signedsuchthatappropriatelinearcombinationsofthereceivedsymbolsatanychaincanbeusedtoestimatetheself-talkandcross-talksymbolsindividually,theonlyrequirementfordesigningthesetrainingsymbolsisthatthelinearcombinationsinmultipletimeslotsatareceivechainarenotdegenerate.4RobustMIMOInterferenceCancellationInterferencecancellationneedstoberobusttoenableconsistentfullduplexoperationinthefaceoffrequentchannelchanges.Toaccomplishthis,bothanaloganddigitalcancellationneedtocontinuouslytunetheirl-tertapstomaintaincancellation.Themainbottleneckistuninganalogcancellation,sincedigitalcancellationcanbetunedonaper-packetbasisinsoftwareaspriorworkhasshown[23,19,11].Tuninganalogcircuitsre-quiresmeasuringtheresidueindigitalandthensend-ingcontrolsignalstoanalogcomponents,whichisrela-tivelyslow.Minimizingtheamountoftimerequiredtotunehereisthereforecritical,sinceduringthetimespenttuningpacketslikelycannotbereceived.Wefocusonthisprobleminthispaperandre-usethealgorithmsfrompriorworkfortuningdigitalcancellation.ThepriorSISOfullduplexdesigndemonstratedatechniquetotuneasingleanalogcancellationinaroundamillisecond.However,asbeforeifweweretonaivelyreplicatethesamealgorithmforalltheself-interferencecomponents,wewouldneedM2msforaMantennafullduplexMIMOradio(e.g.9msfora3antennafulldu-plex).Suchahighoverheadisuntenableformoderatelymobileenvironmentswherethechannelchangesonav-erageevery60ms(e.g.WiFihotspots).Inthispaperweproposeanoveltechniquethatre-ducestuningtimebythreeordersofmagnitude,i.e.analgorithmthattunesthecircuitin8ms.Notethatthisal-gorithmalsoappliestotheSISOcase,andthereforeim-provesonthebestknownpriorSISOdesigntoo.Ourin-sightistomodelthecancellationcircuitasalterwhoseresponsewearetuningtomatchascloselyaspossiblethefrequencyresponseoftheself-interferencechannel.Likepriorwork,weestimatethefrequencyresponseofthecancellationcircuitfordifferentcombinationsofl-tertapvalues.Thepre-calculatedresponseisrepresentedinamatrixA,whoseeachcolumnisthefrequencyre-sponseoftheanalogcancellationcircuitforaparticularvalueoftheltertapatKdifferentfrequenciesinthebandofinterest(e.g.K=128fora20MHzbandwidthinourcurrentprototypeforWiFi).NowassumingH(f)isthefrequencyresponseoftheself-talkchannelinthefrequencydomain(i.e.thechannelintroducedbytheantenna,circulatorandanystrongenvironmentalreec-tions),theanalogcancellationtuningproblemreducesto:minxjjH�Axjj2Where,HisthecolumnconsistingofH(f)atdifferentfrequencies,andx,representsabinaryindicatorvectorforselectingthecorrespondingltertapvaluesasin[11].TheefcacyofthetuningthatresultsfromtheaboveproblemdependsontheaccuracyinthemeasurementofH(f).WecanmeasureH(f)usingthepreambleofthereceivedinterferencesignaly(t)(e.g.thersttwoOFDMsymbolsofatransmittedWiFipacketwhichareknownpreamblesymbols).Thechallengeismeasuring8 thefrequencyresponseoftheinterferencechannelac-curately.Theaccuracyislimitedbythelinearityofthetransmit-receivechain,whichis30dB,Bythiswemeanthatanyinitialmeasurementcanonlyhaveanaccuracyof30dB.Themainreasonisthatthetransceiverproducesnon-linearitieswhichactasnoisetothechannelestima-tionalgorithm.Inotherwordsthereceivedinterferencesignaly(t)hasnon-linearitiesthatareonly30dBbelowthemainlinearsignalcomponent.Ourkeycontributioninthispaperisatechniquetoaccuratelymeasurethischannelquicklyinthepresenceofnon-linearitiesandtuneanalogcancellation.Sourceoferroranditsmagnitude:Thetransmitterproducesnon-linearities30dBlowerthanthetransmittedsignal.Toshowmathematically,sayx(t)isthebasebandsignalthatisbeingtransmittedafterup-conversionandamplication,wecanwritextx(t)=x(t)+a3x(t)3+a5x(t)5+a7x(t)7+:::+w(t)Thistransmittedsignalxtx(t)issomewhatknowntousbecauseweknowx(t),howeveritsnon-linearcompo-nentsandthetransmitnoisew(t)areunknown.Thissig-nalfurtherundergoesthecirculatorandantennachannelH(f)(whichwewishtoestimate),sowhenitsreceivedatthereceiverthefrequencydomainrepresentationofthereceivedsignalisgivenby:Y(f)=H(f)F(x(t)+a3x(t)3+:::)+transmitnoiseHere,a3isaround10(�30=20),i.e.,its30dBlower.Fur-thertransmitnoisedistortionis40dBlowerthanthesig-nallevelofx(t).Thechallengeisthatourchannelesti-mationalgorithmisonlygoingtouseitsknowledgeofx(t)toestimatethechannelH(f),andtheothertermsinthereceivedinterferencesignallimittheaccuracyoftheestimationto30dB(theestimationnoiseis30dBlower).Accurate,Iterativemethod:Thekeyideaistoruntheestimationalgorithminaniterativefashion.RememberthattheWiFipreamblehastwoOFDMsymbols,eachoflength4ms.AftertherstOFDMsymbol,wesolvetheaboveequationtoproduceaninaccurateestimateoftheinterferencechannelHaandtunethecancellationcircuittoachieve(atbest)30dBofcancellation(wecannotcan-celmorethanourestimationaccuracy).Nowwhenweobtainthesecondpreamblesymbol,weknowthatthenon-linearitiesandthetransmitnoisecomponentsthatwereproducingtheerrorarereducedby30dB.Wecanexploitthisfactbythefollowingtrick:WetransmitoneOFDMsymboltoestimatetheinaccu-rateHa,whichcanbewrittenasafunctionofaccurateHas,Ha=H+e1.Notee1is30dBlowerthenH.Weusethesamealgorithmas[11]tooptimizethefollowing,minxjjHa�Axjj2whichproducesthesolutionasˆx,whichgivesustheval-uestouseintheltertaps.Weprogramthecancellationcircuitusingthesevaluesandachievea30dBcancella-tion.Next,whenwetransmitsecondOFDMsymbolandmeasurethechannelresponseweget:Hb=(H�Aˆx)+e2Noticethate2is30dBlowerthenH�AˆxandH�Aˆxis30dBlowerthanH.Soinessencee2is60dBlowerthanH.Dene,˜H=Hb+Aˆx˜H=H+e2Thus,wecanthisnewestimate˜Hwithanerrorthatis60dBlower.Weusethisestimatetore-tunetheop-timizationalgorithmandndasolution˜xthattellsuswhatvaluestousefortheanalogltertaps.Thisnewsolutionprovides60dBcancellation.Further,weonlyneededtwoOFDMsymbolsof4mseachtogettothiscancellation.ExtensiontoCascadedFilterStructure:Theabovedescriptionisforasinglecancellationcircuit,butourMIMOdesignhasacascadedstructureofmultiplecir-cuits.Thisleadstoacombinatorialexplosioninthepa-rameterspacethatmakestheproblemNPhardtosolveifweusetheaboveapproach.Inthissubsectionwepresentatricktoapproximatetheoverallcombinatorialprob-lemviatworeducedcomplexityproblemswhichcanbesolvedusingthesametechniqueastheSISOonepre-sentedabove.Wedescribethealgorithminthecontextoftuningthecancellationcircuitsatreceiver1forselfandcross-talkina2antennaMIMOradio.LetssayH11istheself-talkchannelresponseandH12isthecross-talkchannelresponse.Thegeneraltuningproblemcanbestatedas:minimizex1;x2t(2)subjecttonorm(H11�A1x1)t(3)norm(H12�(A1x1)(A2x2))t(4)Where,representstheelementwisemultiplicationofthecolumn,andtrepresentstheanalogcancellationachieved,andA1istheresponseoftheself-talkcancel-lationboardwithNtapsinFig.4andA2istheresponseofthecascadecancellationboardwithCtaps.Thesec-ondconstraintEq.4renderstheproblemirreducibletoaconvexsolvableform,andinfactthecolumnwisemultiplicationoftheindicatorvariablevectorsexplodestheproblemspaceandmakesitaNPhardcombinatorialproblem.Weuseanoveltricktoapproximateandhelpsolvethisproblempractically.SincetherstconstraintinEq.3istryingtondA1x1=H11,wecanapproximateA1x1inthenextconstraint,Eq.4withH11whichisknown(sincewemeasuredH11).Thisisofcourseanapproximation,butitsufcestosolveforx2usingthissubstitutionsince9 weareafteralltryingtoemulatethesamecascadedchan-nelresponsestructureusingourcircuitsasdescribedinSec.3.Thusinsteadofacascadeofunknownvariables,thenewproblemtosolveisminimizex1;x2t(5)subjecttonorm(H11�A1x1)t(6)norm(H12�H11(A2x2))t(7)Thisnewproblemisnolongeracombinatorialprob-lem.Thiscanbereducedtoanintegerprogram,whichcanbesolvedusingrandomizedroundinginfractionofmicrosecondspractically[11].Thusineffectthesub-stitutiontrickreducesthenon-tractablecombinatorialproblemintoatractableproblem,whosesolutioncanbefoundusingthetechniquesdescribedabove.ThetuningtimeforeachMIMOchainisstilltwoOFDMsymbols,andtheoveralltuningtimefortheMIMOradiothereforescaleslinearlywithM,thenumberofchains.5EvaluationInthissection,weexperimentallydemonstratethatourMIMOfullduplexdesignalmostcompletelycancelsallself-talkandcross-talkinterferencetothenoiseoorwithalow-complexitydesign.Wealsoshowthatthistranslatestoadoublingofthroughputforthelinkperfor-mance.WeimplementourdesignusingfourWARPv2boardsforbuildinga33MIMOfullduplexlink.Wede-signourownboardsforanalogcancellationandintegratethemwiththeWARPboards.Ateachreceivechain,wehaveanalogcircuitswith12tapsfortheself-talkcancel-lation,4tapsfortherstcrosstalkand2tapsforthefar-thesttransceiver.Intotalwehave56tapsintheanalogcancellationcircuitsfora3antennafullduplexMIMOradio,andtotalof485ltertapsindigitalcancellation.SincetheWARPcannotgenerate20dBmtransmitpower,weuseanexternaloff-the-shelfpoweramplier[3].WecompareagainsttheSISOreplicationbaseddesignprimarily.ThisisthestraightforwardreplicationoftherecentlypublishedSISOfullduplexdesignasdiscussedatthestartofSec.3.Wecompareagainsttwovariantsofthisdesign.Oneisadesignthatfullyreplicatestheana-loganddigitalcancellationimplementationsforallself-talkandcross-talkcancellations.Asdiscussedbeforethecomplexityofthisdesignisafactoroftwohigherforanalogand2:5higherfordigitalcomparedtoourde-sign.WecallthisdesignSISOReplication.HowevertomakeanapplestoapplescomparisonwithourdesignwealsoimplementaSISOreplicationdesignwiththesamecomplexityasourdesign.Thedifferencecomparedtoourdesignisthat,itneitherusethecascadedstructurenorthenovelestimationalgorithm,butsimplyreplicatestheSISOdesignwithlowernumberoftaps.Weex-perimentwiththetapdistributionbetweenself-talkand Figure7:Spectrumplotaftercancellationofvariousself-talkandcross-talkcomponentsforRX1ofa33fullduplexsystemusingourdesign.cross-talktoobtainthebestoverallcancellation.WecallthiscomparedapproachSISOLowComplexityRepli-cation.Unlessstatedotherwise,allexperimentsareconductedbyplacingthetwofullduplexnodesatvariouslocationsinourdepartmentbuilding.Ateachlocation,werepeattheexperimenttentimesandcalculatetheaverageper-formance.5.1Canwecancelalltheinterferencefor3antennafullduplexMIMO?Therstclaimmadeinthispaperiscapabilityofcan-celingalloftheinterferenceforthe33MIMO.Toprovethis,weexperimentallytestifwecanfullycan-celaWiFi802.11n20MHzsignaluptoamaxtransmitpowerof20dBmfora33MIMO.Todemonstratewerstpickoneinstanceofthisexperiment,andshowthespectrumplotofthereceivedself-interferenceaftervar-iousstagesofcancellationinFig.7.Remember,thatinanalogwerstcancelthechain'sownself-talkleakingthroughthecirculator,andthenthecross-talkfromtheothertwoantennas.Finally,weapplyourdigitalcancel-lationsteptocleanuptheresidual.Weseethatoverallinanalogweachieve68-70dBofself-interferencecancella-tionafterallthreestages.ThissatisestherequirementsoutlinedinSec.2.Wenowplacethenodeatseveraldifferentlocationsinthetestbed.AteachlocationwevarytheoverallTXpowerfrom16dBmto20dBmandplottheaveragecan-cellationforeachpoweracrossalllocations.Ateachlo-cationandforeachpower,weconduct40runs.ThegoalistoshowthatwecanconsistentlycanceltothenoiseoorforavarietyoftransmitpowersuptoandincludingthemaxaverageTXpowerof20dBm.Ineachinstanceoftheaboveexperiment,wealsomeasuretheincreaseinnoiseoorduetoanyresidualself-interferencethatisnotcanceled.Notethattheincreaseinnoiseoorrep-resentstheSNRlossthereceivedsignalwillexperiencewhenthenodeisusedinfullduplexmode.Fig.8plots10 !"#$%&!'&()*+$%&,-./&(.%01)+#./0./.+2.&3$+2.%&,-./&3/"44&#$%5&6&3$+2.%&,-./&3/"44&#$%5&7&3$+2.%& Figure8:IncreaseinnoiseoorvsTXpowerontheleftsideandCancellationvsTXpowerontherightside.FordifferentMIMOcancellationdesigns,wepresenttheper-formanceofafullduplex3antennafullduplexMIMOsystem.theaveragecancellationandtheincreaseinnoiseoorasafunctionofTXpower.Fig.8showsthatour3-antennaMIMOfullduplexdesigncancelstheentireselfinterferencealmosttothenoiseoor.Incaseofmaxaveragetransmitpowerof20dBm[11],thenoiseoorisincreasedby1:6dBovereachreceivechain'snoiseoor.TheSISOreplicationdesignincreasesthenoiseoorby4dBperreceivechain,whiletheSISOlowcomplexityreplicationapproachin-creasesthenoiseoorby25dB.Finally,theperformanceofourdesignandtheSISOreplicationdesignscaleswithincreasingTXpower,whiletheotherreplicationbaseddesignislimitedduetoitsinabilitytocanceltheincreas-ingtransmitnoiseandnon-linearitiesduetothereducednumberoftapsavailabletoit.5.2ScalingwiththenumberofMIMOan-tennasAquestionwithMIMOishowdoesfullduplexperfor-mancescalewithincreasingnumberoftransmitchains.TheidealcasewouldbetomaintainthesamelevelofcancellationateachRXchainasthenumberoftransmitantennasincrease,startingfromoneantenna.Inotherwords,evenwithincreasingnumberoftransmitanten-nasandcross-talkcomponentsthatneedtobecanceled,weretainthesameperformanceasiftherewasasin-gletransmitantennaandasingleself-interferencesignaltodealwith.Fig.9plotstheincreaseinthenoiseooratonereceivechainaswegofromonetransmitchaintothreetransmitchainsforaMIMOradioforbothourdesignaswellastheSISOreplicationtechnique.TheoverallTXpowerisxedtobe20dBm(additional10dBofPAPRforWiFi[11],i.e.,total30dBm)toadheretoISMbandEIRPrequirements.Henceifweuseasingletransmitchain,thenallthe20dBmisusedforasinglean-tenna.Ifweusetwochains,theneachantennaproducesa17dBmsignalandsoon.Aswecanseefromthegure,ourdesignmaintainsanear-constantperformanceevenaswegofromonetothreetransmitchains.Inotherwords,theperformanceis Figure9:IncreaseinnoiseoorataRXchainasthenumberofMIMOchainsandconsequentlythenumberofcross-talkcomponentsincreasefrom1to3.Withourdesignweobservea2.5dBimprovementfor33MIMOperRXchaincomparedtotheSISOreplicationdesign.roughlythesameregardlessofthenumberofcross-talkcomponents(Wedowishtonotethatwecouldnotgobe-yondthreetransmitchainsduetohardwarelimitations,verifyingtheaboveclaimforhighernumberoftransmitchainsisfuturework).Ontheotherhand,theSISOrepli-cationdesignshowsthenoiseoorincreasinglinearlywithincreasingnumberoftransmitchains,afactwepro-videdtheoreticalintuitionforinSec.3.2.Thusthisde-signwilllookworseaswescaletohigherMIMOcong-urations.WeomittheSISOlowcomplexityreplicationapproachbecauseitsresultsaresignicantlyworse.5.3DynamicAdaptationAnimportantmetricforanalogcancellationishowquicklycanitbetuned,andhowoftendoweneedtotune?Thebestknowpriortechnique[11]requiredaround1millisecondtotuneasingleSISOanalogcan-cellationcircuit.Sofora33MIMO,applyingthesamealgorithmwilltakeatleast9msfortheSISOrepli-cationbaseddesign.Inthissectionweshowtheef-cacyofournewtuningalgorithmwhichcutsthetuningtimeto8msperreceivechain.Fig.10showsthetuningtimeasafunctionoftheamountofanalogcancellation.Toachievethe70dBanalogcancellation,ouralgorithmtakes8msperchain,foratotalof24msforthefullra-dio.Thepriorworkaswecanseetakeamillisecondperchain.Theinterestingtakeawayisthatbothschemesachieve40dBofanalogcancellationfairlyquickly(withonepreamblesymbol,i.e.4ms),butourschemecov-ersthenal30dBinonemorestepof4ms,whilethepriorschemetakesanexponentialnumberofsymbolstoachievethat.Thereasonforthisimprovementispre-ciselyourabilitytogetaprecisemeasurementoftheself-interferencechannelusingthetrickdescribedinSec.4.Asecondquestionishowoftenoneneedstotune?Thisdependsontheenvironmentandtheamountofana-logcancellationthatneedstobemaintained.Inthispa-per,wetuneforchallengingindoorenvironmentswhich11 16 17 18 19 20 75 80 85 90 95 100 105 16 17 18 19 20 0 5 10 15 20 25 30 TX power Increase in Noise floor in dB Lower is b etter Our Design SISO Replication Higher is b etter SISO Low Complexity Replication Cancellation in dB TX power Figure10:Tuningtimeforanalogcancellation.Therstgureshowsthethreeordersofmagnitudeimprovementintuningtimewithouralgorithmcomparedtothebestknownpriorapproach.Thesecondgureshowshowof-tenthistuningalgorithmneedstoberunforanindoorenvironment. Figure11:CDFofthroughputgainrelativetohalfduplex33WiFiMIMO.Our33MIMOsystemprovidesamediangainof95%relativetohalfduplex,whereastheSISOreplicationdesignonlyprovidesa1.36relativegain.havestrongmulti-path(thisisthemainsourceofanalogcancellationdegradation).Wedeneanear-eldcoher-encetimewhichdependsontheamountofanalogcan-cellationandisessentiallythetimeforwhichthatanalogcancellationcanbemaintainedonaveragebeforethecir-cuitsneedtoberetuned.Fig.10plotsthenear-eldco-herencetimeforthreedifferentanalogcancellationtar-gets.Aswecansee,tomaintainananalogcancellationof70dB,weneedtoretuneroughlyevery60ms.Giventhatourtuningoverheadis24ms,ouroverheadisnegli-gible.5.4DoesFullDuplexDoubleThroughput?Analquestioniswhetherallthiscancellationper-formancetranslatestoathedesireddoublingofover-allthroughput.Weshowexperimentallythethroughputgainsofour33MIMOfullduplexdesigncomparedtotheSISOreplicationbaseddesign.Twofullduplex3-antennaMIMOnodesareplacedatdifferentlocationsandwesend1000packetsinfullduplexmodebetweenthem,andthensend1000packetsforeachdirectionofthehalfduplexmode.WerepeatthisexperimentforeachbitratethatisavailableinWiFi.Wepickthebitratewhichmaximizestheoverallthroughputforallofthecomparedfullduplexdesignsandhalfduplexrespectively.Were-peatthisexperimentfor50differentlocations.Wefoundthereceivedpowerofthelinksvarieduniformlybetween�45to�80dBm,acrosslocationsasfoundintypicalin-doordeployments.Toputthesenumbersinperspective,thisimpliesthattheSNRofthelinksinhalfduplexmoderangesfrom5dBto40dB.Weplotthethroughputforhalfduplexandfulldu-plexdesignsinFig.11.Notethatallofthesethroughputnumbersaccountfortheoverheadintroducedbythepe-riodicanalogcancellationtuning.Aswecansee,ourfullduplexsystemachievesamedianthroughputgainof1:95overthehalfduplexmode,buttheSISOreplica-tionbaseddesignwithfullcomplexityonlyachievesa1:36gain.ThereasonisthehigherincreaseinnoiseoorfromtheSISOreplicationbaseddesign.Forex-ample,ifthelinkSNRinhalfduplexmodeis10dB,a4dBincreaseinnoiseoorwillresultinworseoverallthroughputforfullduplexcomparedtorunningthelinkinhalfduplexmode.Ourabilitytokeepthenoiseoorconstantresultsinaperformanceclosetothetheoreticaloptimum.TheSISOreplicationbaseddesignwithlowercom-plexityisquitepoor,infactin70%ofthescenarios,thethroughputwaszero.Thisisbecauseitincreasesthenoiseoorbyatleast25dBwhichactsasnoiseandiftheSNRisbelow30dBnosignalisdecoded(WiFire-quiresaminimumof4�5dBSNRtodecodethelowestratepacket).Asthehalf-duplexlinkSNRincreases,theperformanceimprovesbutisstillnotsufcienttobeatthesystemthroughputachievedbyhalfduplex.Therea-sonisthatevenifthelinkhalf-duplexSNRis35dB,itimpliesthatweonlyhavetwo10dBlinksforfullduplex.Thethroughputachievedwithasingle35dBhalfduplexlinkisstillhigherthantwo10dBlinks.ConsequentlytheonlyregionwherewecouldndimprovementsforfullduplexoverhalfduplexwiththisdesignwaswhenthelinkSNRwasgreaterthan38dB.6ConclusionThispaperbringstowardscompletionalineofworkonPHYlayeroffullduplexradios,andshowsthatpracticalfullduplexisachievableforthemostcommonwirelessprotocolsandforMIMOwhileusingcommodityradios.Thecancellationtechniquesdevelopedinthispaperarefundamentalandapplytoawidevarietyofproblems[17]whereself-interferencecancellationisneeded.Whilethisworkwrapsupworkonboardlevelrealizationsoffullduplex,muchworkremainsinrealizingthesede-signsinachip.Tacklingtheseproblemsisfuturework.12 0 1 10 100 1,000 10 20 30 40 50 60 70 0 50 100 150 200 0 0.2 0.4 0.6 0.8 1 Sample Run of Algorithms Near field coherence time Time in milli seconds Time in micro - 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