2024 全球6G技術(shù)大會(huì) -10.0O White Paper on Orthogonal Time Frequency Space (OTFS) Scheme0409

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Contents

1.Introduction

2

1.1DocumentStructure

2

1.2KeyApplicationScenarios

3

2.BasicPrinciplesofOTFS

5

2.1PrinciplesofOTFSModulationTransmitter

6

2.2PrinciplesofOTFSModulationReceiver

8

2.3AnalysisofInput-OutputRelationshipinOTFS

1

0

3.AnalysisofDelayDopplerDomainChannelCharacteristics

1

2

3.1CharacteristicsofDelayDopplerDomainChannel

1

2

3.1.1DeterministicDescriptionofChannels

1

2

3.1.2CoherentandStationaryRegionsofChannels

1

4

3.2DelayDopplerDomainChannelCharacteristicsinHigh-SpeedRailwayScenario

1

5

3.2.1ChannelSpreadingFunctionMeasurementSystemBasedonLTE-R

1

5

3.2.2High-SpeedRailwayChannelSpreadingFunctionCharacterizationBasedonLTE-R

1

7

3.3PerformanceEvaluationofOTFSinMeasuredChannels

1

9

4.OTFSChannelEstimationandDataDetection

2

1

4.1PilotDesignforLow-PAPROTFSChannelEstimation

2

1

4.2Off-gridChannelEstimationforOTFS

2

6

4.3Low-ComplexityOTFSDataDetectionSchemeBasedonExpectationPropagation

2

8

5.ExtensionSchemesofOTFS

3

1

5.1Multi-AntennaOTFSScheme

3

1

5.1.1PilotDesignforMIMO-OTFS

3

1

5.1.2Low-ComplexityandLow-OverheadOTFSTransceiverBasedonMulti-AntennaArray

3

6

5.2MultipleAccessTechnologySchemeEmpoweredbyOTFS

4

1

5.2.1OrthogonalTime-FrequencyCodeDomainMultipleAccessScheme

4

1

5.2.2OTFS-SCMASystemBasedonMemoryApproximateMessagePassing(MAMP)

Algorithm

4

5

5.3OTFS-EmpoweredIntegratedSensingandCommunication(OTFS-ISAC)Scheme

5

1

5.3.1AdvantagesofOTFS-ISACScheme

5

1

5.3.2OTFS-ISACWaveformDesign

5

2

6.EvolutionSchemesforOTFS

5

5

6.1NewDelayDopplerDomainMulticarrierModulationScheme

5

5

6.2FusionFrameStructureDesignofOTFSandOFDM

5

7

7.SummaryandOutlook

6

2

References

6

4

ParticipantUnits

6

6

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1.Introduction

Orthogonalfrequencydivisionmultiplexing(OFDM)isawidelyusedmodulationtechniqueinwirelesscommunicationsystemssuchas4G,5G,andWiFi.OFDMbasedoncyclicprefixescaneffectivelydealwithmultipathfadingandonlyrequireslow-complexityfrequencydomainequalizers.Withthedevelopmentofwirelesscommunications,high-speedmobilecommunicationscenariosincomplexscatteringenvironmentsarebecomingincreasinglyabundant,suchasIoV,high-speedrailways,andlow-earthorbitsatellitecommunications.Thesecommunicationscenarioshavealreadyorwillgreatlychangepeople'slifestyles.However,OFDMunderhigh-speedmobilitywilllosesubcarrierorthogonalityduetotheinfluenceofDopplerspread,anditstransmissionreliabilitywilldeteriorate.Therefore,itisimportanttodesignnewmulticarriermodulationschemesforhigh-speedmobile

scenariosinthenextgenerationofmobilecommunicationsystems.

Inrecentyears,researchershaveproposedtheorthogonaltimefrequencyspace(OTFS)multicarriermodulationtechnology.DifferentfromOFDMtechnology,OTFSperformsresourcemappingintheDelayDoppler(DD)domain,andbasedonthesparsityandstabilityoftheDDdomainchannel,itcanachievehigherdatatransmissionreliabilitythanOFDM

underhigh-speedmobileconditions.

Toinvestigatethebasicprinciples,researchandapplicationstatus,andfuturedevelopmentprospectsofOTFS,andtoprovidetechnicalreferencesforindustryandacademia,thiswhitepaperwillintroduceOTFSfromthefollowingsixaspects:(1)BasicprinciplesofOTFS;(2)CharacteristicsofDDdomainchannels;(3)TransmissionwaveformdesignofOTFS;(4)ReceiverschemedesignofOTFS;(5)Multi-antenna,multi-user,andintegratedsensingandcommunicationschemesempoweredbyOTFS;(6)Evolutionschemes

forOTFS.

1.1DocumentStructure

Chapter1istheintroduction,whichintroducesthescopeandstructureofthiswhitepaper,andintroducestheapplicationscenariosofOTFS,pointingouttheneedsandchallengesbroughtbyhigh-speedmobilityinsuchscenarios,thusleadingtothenecessityof

OTFStechnologyresearch.

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Chapter2describesthebasicdesignprinciplesofOTFS,includingtheintroductionoftwoOTFSmodulationimplementationmethods,SFFTandDZT,andabriefdescriptionof

thetransceiverscheme.

Chapter3analyzesthechannelcharacteristicsoftheDelay-Dopplerdomain,andanalyzesthesparsity,compactness,stability,andseparabilityoftheDelay-Dopplerdomain

channelforhigh-speedmobilescenariossuchashigh-speedrailways.

Chapter4introducesthedesignoftheOTFSreceiver,includingthepilotdesignoflow-PAPRchannelestimation,OTFSchannelestimationundernon-integergrids,and

low-complexityOTFSdatadetectionschemebasedonexpectationpropagation.

Chapter5introducesOTFS-empoweredmulti-antenna,multi-user,andintegratedsensingandcommunicationschemes,includingthesystemdesignofMIMO-OTFS,grant-freemultipleaccessschemesforhigh-speedmobilescenariossuchassatellitesandhigh-speedrailwaysformassivemachinetypecommunications,andperformanceanalysisof

integratedsensingandcommunicationsystemdesignbasedonOTFS.

Chapter6introducestheevolutionschemesforOTFS,includingthejointframestructuredesignofOFDMandOTFSthatisforwardcompatiblewithOFDM,andanewtypeof

multicarriermodulationschemeintheDelay-Dopplerdomain.

Chapter7providestheconclusionandoutlook.

1.2KeyApplicationScenarios

High-speedrailwayscenario:Forrailways,continuouslyimprovingtrainspeedsisacommongoalinglobalrailwaydevelopment.Atpresent,theBeijing-Shanghaihigh-speedrailwayhasachievedatestspeedof470kilometersperhour,andtheCR450,a450km/hhigh-speedtrain,willbecompletedin2024.Atthesametime,theCentralJapanRailwayCompanyhasachievedatestspeedof603km/hformaglevtrainsinYamanashi-ken,Japan.Inaddition,thepipelineflyingcar,whichcanreachaspeedofover1,000km/h,isalsounderdevelopment.Basedonthehigh-speeddevelopmentofrailways,countriesworldwidewithdevelopedhigh-speedrailwaysystemsarefocusingontheintelligenceofhigh-speedrailways.

Theintelligencedevelopmentofhigh-speedrailwaysrequiresadvancedcommunication

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systemsandstandardstoprovidesupport,butthehigh-speedmovementoftrainsinhigh-speedrailwayscenarioswillposeagreatchallengetothereliabilityofground-to-train

andtrain-to-traincommunication.

Low-earthorbitsatellitescenario:Low-earthorbit(LEO)satellitecommunicationisatechnologythatusessatellitesinlow-earthorbittoachievecommunication.Unliketraditionalhigh-earthorbitsatellitecommunication,LEOsatellitecommunicationsatellitesaretypicallylocatedbetweenhundredsofkilometersandtwothousandkilometersfromtheground.Comparedwithtraditionalgeosynchronousorbitsatellites,ithastheadvantagesoflowlaunchcost,lowcommunicationdelay,lowtransmissionloss,andseamlessglobalcoverageafternetworking,andhasattractedtheattentionofmanyInternet,communication,andaerospace

companiesaroundtheworld.

Aircoveragescenario:Withtheprogressofaviationcommunication,airplanesaretransformingfromthepast"isolatedislands"ofinformationnetworksintokeycarriersforrealizingglobalinterconnection.Theemergenceofin-flightWi-FiallowspassengerstoaccesstheInternetonairplanes.However,thearrivalofthe5Gerahasbroughtunprecedentedchallengestoaircommunication—thedemandformassivereal-timeInternetdatatransmission.Thischallengerequirescommunicationsystemstobehighlyadaptive,andcapableofimprovingcommunicationqualitybetweenairplanesandgroundstationsorsatellitesinhigh-speedmobileenvironments,ensuringlow-latencyandhigh-reliability

transmissionofinternetdata.

InternetofVehicles:BasedontheOTFS-ISACmechanism,thefollowingInternetofVehiclesfunctionsorapplicationscanbesupported:Accuratelysensingthesurroundingdrivingenvironment,includingvehicles,obstacles,roadconditions,etc.,toenhancedrivingsafetyandachieveintelligentdriving;accuratelysensingthepositionsandmotionstatesofbothreceiversandtransmitters,providingpriorinformationforchannelestimation,beamforming,etc.,toimprovecommunicationperformance;distributednodecollaborativesensing,expandingtherangeofnodesensing,andenhancingtheaccuracyandprecisionof

sensing.

UnderwaterAcousticCommunication:The"SmartOcean"projectisamajorproject

relatedtothenationalstrategyofbuildingamaritimepower,andwiththeadvancementofthe

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maritimepowerandtheconstructionofthe"SmartOcean"project,rapiddevelopmenthasbeenachievedinvariousfieldssuchasmodernfisheries,marineobservationandmonitoring,offshoreoilandgasexplorationanddevelopment,andmarinetransportation.Underwateracousticcommunicationisanimportantpartofthemarinecommunicationnetwork.Acousticwavesarecurrentlytheonlyeffectivelong-distanceinformationtransmissioncarrierunderwater.Theunderwateracoustic(UWA)channelisachannelwithfasttime-varyingcharacteristics,largedelayspread,seriousDopplereffect,andlimitedavailablebandwidth.Incommonmarineenvironments,multipatheffects,Dopplereffects,andenvironmentalnoiseexistduringthepropagationofunderwateracousticsignals,whichmakesitimpossibleforthereceivingendofthecommunicationsystemtoobtaincorrectchannelinformationwhendetectingsignals.Thisbringsgreatobstaclestothedesignofthecommunicationsystem.Atthesametime,thephasefluctuationsinthechannelmakeitverydifficultforthereceivingendtorecoverthecarrierandperformcoherentdemodulation.TheOFDMmodulationtechnologywidelyusedinUWAcommunicationnetworksiseasilyaffectedbyDopplerspread,leadingtoseveredegradationinsystemperformance.HowtoachieveefficientdatatransmissionincomplexandvariablemobileUWAcommunicationscenariosiscurrentlya

keyissuethatneedstobeaddressed.

2.BasicPrinciplesofOTFS

OTFSwasproposedbyR.Hadanietal.in2017[2.1],anditwaspointedoutthatcomparedwithOFDMmodulation,itcouldusethefulldiversitygainofthetime-frequencydomaintoachievebetterdatatransmissionperformanceunderhighmobility[2.2].Accordingtothecontentofthischapter,itcanbefoundthatOTFScanberegardedasaprecodedOFDMsystem,whichhasthepotentialtobecompatiblewithOFDMsystems.However,comparedwiththeOFDMschemethathasbeenmaturelyappliedin5GNR,LTE,Wi-Fi,andotherprotocols,OTFSfacesmanynewchallenges,suchasDDdomainchannelmodeling,reliableDDdomainchannelestimation,low-complexityequalization,multi-antennaOTFSsystemdesign,multi-userOTFSsystemdesign,OTFS-enabledcommunication-sensingsystemdesign,etc.ThissectionwillbrieflyintroducethebasicprinciplesofOTFSmodulation,with

theremainingcontentbeingelaboratedinsubsequentsections.Thissectionmainlyrefersto

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theliterature[2.3].

2.1PrinciplesofOTFSModulationTransmitter

Figure2.1BlockDiagramoftheISFFT-basedOTFSTransmitter

Figure2.1showstheblockdiagramoftheISFFT-basedOTFStransmitter.Considerthe

systembandwidthMΔfandtimedurationNT,whereMisthenumberofsubcarriers,Δfisthesubcarrierspacing,Nisthenumberofslots,andTistheslotduration

.1

Let{XDD[k,l],k=0,…,N-1,l=0,…,M-1}representtheQAMmodulatedsymbol

mappedontheDDgrid,OTFSmodulationfirstusestheInverseSymplecticFiniteFourier

Transform(ISFFT)tomaptheDDdomainsymbolsXDD[k,l]totheTFgridtoobtain

XTF[n,m]:

XTF[n,m]=ΣΣ1XDD[k,l]ej2π-

(2-1)wheren=0,…,N-1,m=0,…,M-1.Thediscreteresourcegridrelationshipbetweenthe

DDdomainandtheTFdomainintheequation(2-1)isshowninFigure2.2.

1NotethatunlikeOFDM,whichonlyconsidersmulticarrierdataforonesymboltimeτ,OTFSconsidersmulticarriernetworkpacketswithaperiodofτ.

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Figure2.2ResourceGridRelationshipbetweenDDDomainandTFDomain

Figure2.3IDZT-basedOTFSTransmitter

Subsequently,thetime-frequencydomainsignalXTF[n,m]isembeddedwithaCPand

transformedintothetimedomainsignals(t)throughwirelesschanneltransmissionusing

theHeisenbergtransformationasfollows:

s(t)=XTF[n,m]gtx(t-nT)ej2πmΔf(t-nT)

(2-2)wheregtx(t)isthetransmitpulseshapingfilter.Basedontheabovecontent,itcanbefound

thattheISFFT-basedOTFSsystemcanbecompatiblewiththeOFDMsystemandthe

correspondingtime-frequencydomainsignalprocessingmethods.Additionally,theOTFS

transmittercanalsobedesignedbasedontheInverseDiscreteZakTransform(IDZT),and

thetransmitterblockdiagramisshowninFigure2.3.

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2.2PrinciplesofOTFSModulationReceiver

Figure2.4OTFSWaveformReceiverBlockDiagram

Figure2.4showstheblockdiagramoftheSFFT-basedOTFSreceiver(Theblock

diagramoftheOTFSreceiverbasedonDZTisanalogoustoFigures2.3and2.4andis

thereforenotelaboratedhere).TheDelay-Dopplerdomainchannelspreadingfunctionis

representedash(τ,v),where‘a(chǎn)ndvrepresentthedelayandDoppler,respectively.Then

thereceivedsignalr(t)canberepresentedas(ignoringnoiseforsimplicity):

r(t)=τ,v)s(t一τ)ej2πv(t一τ)dτdv

Notethatthereareusuallyonlyafewreflectorsinthechannel,so

sparsityandcanberepresentedas2

:

h(τ,v)=

(2-3)

h(τ,v)exhibits

(2-4)

wherePisthenumberofpropagationpaths,hi,τi,andvirepresentthepathgain,delay,

andDopplershiftofthei-thpath,respectively,andδ(.)representstheDiracdeltafunction.

ThedelayandDopplertapsofthei-thpathareexpressedasfollows:

lτikvi+Kvi

τi=MΔf,vi=NT

(2-5)

Sincethedelayresolutionisusuallysmallenough,lτicouldberegardedasaninteger;theDopplerresolutionisusuallylimited,sokviisusedtorepresentitsinteger

partandKvie(一0.5,0.5)isusedtorepresentitsfractionalpart.Atthereceiver,the

time-frequencydomainsignalobtainedthroughtheWignertransformisrepresentedas:

2Channelcharacterizationunderhigh-speedmovementconditionswillbeintroducedindetailinChapter3.

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YTF[n,m]=Y(t,f)t=nT,f=mΔf

(2-6)

wheren=0,…,N一1,m=0,…,M一1,

Y(t,f)=Agrx,r(t,f)蘭∫gx(t,一t)r(t,)e一j2πf(t,一t)dt,

(2-7)

Agrx,r(t,f)representsthetime-frequencydomainsignal(cross-ambiguityfunction)

obtainedbymatchedfiltering.SubstitutingEquations(2-1)to(2-3)intoEquation(2-6)yields

theinput-outputrelationshipofOTFSinthetime-frequencydomainasfollows:

YTF[n,m]=ΣΣHn,m[n,,m,]XTF[n,,m,]

(2-8)

whereHn,m[n,,m,]representstheequivalentchannelconsideringinter-subcarrier

interferenceandinter-symbolinterference(ISI):

Hn,m[n,,m,]=

根ej2π(v+m,Δf)((n一n,)T一τ)ej2πvn,Tdτdv

(2-9)

ItcanbefoundthatHn,m[n,,m,]isaffectedbythetransmittingpulse,channelresponse,andreceivingpulse.Finally,YTF[n,m]isconvertedtotheDDdomainthrough

theSFFToperationtoobtainthereceivedsignalYDD[k,l]:

(nkml)

YDD[k,l]=ΣΣ1YTF[n,m]ej2π|（一N+M)|

(2-10)

Foridealtransmittingandreceivingpulses,thefollowinginput-output

relationshipholds:

YDD[k,l]=Σ

(2-11)

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where

hΦ[.,.]isthesampledversionoftheimpulseresponsefunction:

NTMΔf

hΦ[k-k,,l-l,]=hΦ(v,τ)v=k-k,,τ=l-l,

(2-12)

ForhΦ(v,τ)isthecircularconvolutionofthechannelresponseandthe

windowfunctionSFFTinthetime-frequencydomain:

hΦ(v,τ)=τ,,v,)Φ(v-v,,τ-τ,)e-j2πvτdτ,dv,

Φ[v,τ]=e-j2π(vnT-τmΔf)

2.3AnalysisofInput-OutputRelationshipinOTFS

Accordingtoequation(2-11),itcanbefoundthatthereceivedsignal

(2-13)

(2-14)

YDD[k,l]isa

linearcombinationofalltransmittedsignalsXDD[k,,l,].Consideringthesparsityof

h(τ,v)inequation(2-4),equation(2-13)canbefurtherexpressedas:

hΦ(τ,v)=

=hie-j2πviτiG(v,vi)F(τ,τi)

(2-15)

where

Whenτ=

l-l,

MΔf,

F(τ,τi)Σej2π(τ-τi)m,Δf

(2-16)

G(v,vi)Σej2π(v-vi)n,T

(2-17)

F(τ,τi)willbefurtherexpressedas:

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F,τi=Σejl_l,_lτi)m,=

ej2π(l_l,_lτi)_1

ejl_l,_lτi)_1

Sinceτi=,andlτiisusuallyaninteger,then:

F,τi=〈l__l,_lτiM

where[x]MrepresentsthemodulooperationontheintegerM,thatis

addition,G,vicanbeexpressedas:

(k__k,)e_j2π(k_k,_kvi_Kvi)_1G|（NT,vi)|=e_jk_k,_kvi_Kvi)_1

(2-18)

(2-19)

mod(x,M).In

(2-20)ItcanbefoundthatwhenKvi+0,G,vi+0.Thisphenomenonintroduces

interferenceknownasDopplerInterference.Accordingtoequation(2-20),

()

sinNθ

Nsinθ

G,vi=canbeobtained.Whenθ_k__k,_kvi_Kvi),

(())(())

sinN_1θcosθ+sinθcosN_1θ

Nsinθ

sinNθ

Nsinθ

NN

()=<N_1cosθ+1

(2-21)

WhenNislarge,G,viwilldecreaserapidly,indicatingthatDoppler

interferencemainlycomesfromadjacentDDdomainresourcegrids.Therefore,weconsiderthatDopplerinterferencemainlycomesfromtheneighboringNigridpoints.WhenNi<N,[k__,kvi_Ni]M<k,<[k__kvi+Ni]N,consideringthederivationprocessabove,

YDD[k,l]inequation(2-21)canbesimplifiedas:

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(

)

e-j2π(-q-Kvi)-1

|||

|

|

|

YDD[k,l]~

（Ne-jk-q-Kvi)-N)

hie-j2πviτiXDDk-kvi+qN,l-lτiM

i=1q=-Ni

(2-22)

Equation(2-22)indicatesthatthereceivedsignalYDD[k,l]intheDDdomainis

significantlyaffectedbyinter-symbolinterference,andtheequivalentchannelintheDDdomainisdifficulttobeunitarilydiagonalized.Therefore,comparedtoOFDM,OTFSwillrequirehigherequalizationcomplexity.Additionally,accordingtothereference[2.4],OTFSchannelestimationwillintroducesignificantpilotoverheadandresultinalargerpeak-to-averagepowerratio(PAPR).Ontheotherhand,comparedtoOFDM,OTFSusesfewerCPs(onlyonesegmentperframe),therebyimprovingspectralefficiency.Furthermore,OTFShasstrongerresistancetoDopplerfrequencyoffsetandmultipathinterference.PotentialsolutionstothechallengesinOTFSchannelestimationandequalizationwillbe

providedinChapter4.

3.AnalysisofDelayDopplerDomainChannelCharacteristics

3.1CharacteristicsofDelayDopplerDomainChannel

ThemostsignificantfeaturethatdistinguishesOTFSfromtraditionalmulticarriermodulationschemessuchasOFDMisthatitperformsresourcereuse,channelestimation,anddatadetectionintheDelayDopplerdomain.Therefore,thechannelcharacteristicsintheDelayDopplerdomainplayacrucialroleintheresearchofOTFSschemes.Thissectionwillexplainthedifferentrepresentationforms,physicalconnections,andcharacteristicsoftheDelayDopplerdomainchannel.Themainreferenceforthissectionis[3.1],anditonlyfocusesonthesmall-scalefadingcausedbymultipathpropagationofthechannel,anddoes

notconsiderlarge-scalefadingcharacteristicssuchasshadowfading.

3.1.1DeterministicDescriptionofChannels

IntheTime-delay(TD)domain,wirelesschannelsaretypicallycharacterizedusing

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ChannelImpulseResponse(CIR).DenotingtheCIRash(t,τ),consistingofPtaps

whereeachtapiscomposedofseveralindivisiblemultipaths,h(t,τ)canbeexpressedas

follows:

h(t,τ)=1hi(t)δ(τ一τi),

(3-1)wherehi(t)andτirepresentthetime-varyingchannelfadinganddelayoftheitap,respectively,andi=1,2,…,P,δ(.)representsthedeltafunction.Underhigh-speedmobilityconditions,hi(t)mayvaryovertimeduetofactorssuchasmultipathfading,

Dopplershift,etc.IfconsideringonlytheeffectofDopplershift,hi(t)canbeexpressedas:

hi(t)=hiej2πvit,

(3-2)

wherehiandvirepresentthefadingandDopplershiftofthetap,respectively.Notethateachtapiscomposedofseveralindivisiblemultipaths,andinrichscatteringenvironments,hiistypicallymodeledascomplexGaussianrandomvariableswithamplitudefollowing

Rayleighdistribution.

IntheDelay-Doppler(TD)domain,wirelesschannelscanbecharacterizedasChannel

spreadingfunctions(CSF).DenotingtheCSFash(τ,v),andassumingthatthetime-varyingcharacteristicsofthetapsaresolelycausedbyDopplershift,theCSFcanbe

expressedintermsofCIRasfollows:

h(τ,v)=∫h(t,τ)e一j2πvtdt=1hiδ(τ一τi)δ(v一vi).

(3-3)

wherevirepresentstheDopplershiftofthetap.

IntheTimefrequency(TF)domain,wirelesschannelsarecharacterizedasChannel

TransferFunctions(CTF)h(t,f),assumingthatthetime-varyingcharacteristicsofthetaps

aresolelycausedbyDopplershift.TherelationshipbetweenCTFandCIRisgivenby:

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h(t,f)=∫h(t,τ)e-j2πτfdτ=1hiej2πvite-j2πτif.

(3-4)

ItcanbeseenthattheCIRintheTDdomain,theCSFintheDDdomain,andtheCTFintheTFdomainaremutuallyFouriertransformpairs.Particularly,ifthenumberoftapsPisregardedasthenumberofscatterers,andassumingthatthesystem'sdelayandDopplerresolutionsaresufficientlysmall(networkpacketbandwidthanddurationaresufficientlylarge),thenunderfinitedelayspreadandDopplerspread,theCSFexhibitsclearsparsity,

separability,andcompactnessintheDDdomain.

3.1.2CoherentandStationaryRegionsofChannels

Thetime-varyingnatureofthechannelunderhigh-speedmobilityposeschallengesforaccuratechannelestimation.ForCIRandCTF,thechannelcoherencetimeandcoherencebandwidtharecommonlyusedtoapproximatelyconsiderthechannelasinvariant.TheycanbeapproximatedbytheinverseofthechannelDopplerspreadanddelayspread,respectively.ForDDdomainchannelCSF,thechannelsmoothnesstimeandsmoothnessbandwidthcanbeusedtoapproximatelyconsiderthechannelasstatisticallyinvariant,i.e.,satisfyingthe

Wide-sensestationaryuncorrelatedscattering(WSSUS)assumption:

Eh(τ,v)h*(τ,v)=C(τ,v)δ(τ-τ,)δ(v-v,),

(3-5)

whereC(τ,v)representsthechannelscatteringfunction,whichdenotestheaveragedensity

ofthetwo-dimensionalscatteringfunctionrandomprocess.Accordingtoreference[3.1],the

channel'sstationarytimeandstationarybandwidthareusuallymuchlargerthanthechannel's

coherencetimeandcoherencebandwidth.Therefore,resourcereusebasedonCSF

characteristicscanpotentiallysavetheoverheadofchannelestimationunderhigh-speed

mobilityconditions.

However,itshouldbenotedthatthefadinghiobservedforeachtapatanygivenmomentisarandomvariableratherthanadeterministicconstant,soitcannotbesimply

assumedthathiisconstantwithinthestationarytimeandbandwidthofthechannel,as

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statedin(3-5).Nevertheless,mostcurrentresearchstillassumesthehypothesisthat"hi

remainsconstantwithinthestationarytimeandbandwidthofthechannel."Toinvestigatethe

validityofthishypothesis,weconductedmeasurementsandcharacterizationofCSFin

high-speedrailwayscenarios.

3.2DelayDopplerDomainChannelCharacteristicsinHigh-SpeedRailway

Scenario

Asapreliminarywork,wecharacterizedthechannelspreadingfunctionofHigh-speedrailway(HSR)channelsbasedonchannelmeasurements,andevaluatedtheperformanceof

OTFSinHSR[3.2].

3.2.1ChannelSpreadingFunctionMeasurementSystemBasedonLTE-R

Firstly,wecharacterizedtheChannelspreadingfunction(CSF)oftheHSRchannelbasedonmeasuredchanneldatafromtheLTE-RnetworkontheBeijing-Shenyangline.ThechannelmeasurementscenarioisshowninFigure3.1.SinceitischallengingtotransmitOTFS-modulatedsignalsfromHSRbasestations,h(τ,v)isdifficulttoobtainthrough

directmeasurement.Accordingtotherelationshipbetweenh(τ,v)withCTFdescribedin

3.1,wefirstobtainthechanneltransferfunctionCTFandthentransformitintotheChannelspreadingfunctionCSF.Inthemeasurementsystem,thecarrierfrequencyisfc=465MHz,thesubcarrierspacingisΔf=15kHz,theOFDMsymboltimelengthisT=66.7μs,thenumberofsubcarriersisM=300,andthenumberofOFDMsymbolsNisdeterminedbythemeasurementduration.Thetrainmovesataspeedof371.1km/h.AsshowninFigure3.1,theLTE-RbasestationcontinuouslytransmitsLTEsignalsduringthemeasurement.TwoomnidirectionalantennasareconnectedtotheUniversalsoftwareradioperipheral(USRP)andplacedoutsidetherooftocollectdownlinksignals.Additionally,theUSRPdeviceswere

connectedtotheGlobalPositioningSystem(GPS)torecordthetrain'sspeedandposition.

Figure3.2showstheprocessingflowforobtainingthechannelspreadingfunction.Upon

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receivingthesignal,synchronizationandchannelestimationareperformedfor4datastreams,and1datastreamisrandomlyselectedtocharacterizethechannelspreadingfunction.Specifically,cellsearchandframeoffsetestimationareconductedbasedonthePrimarysynchronizationsignal(PSS)andSecondarysynchronizationsignal(SSS)forframesynchronization.FrequencysynchronizationisachievedbasedontheCyclicPrefix(CP).Inchannelestimation,inter-subcarrierinterferenceandinter-symbolinterference(ISI)aretreatedasnoise.Finally,atwo-dimensionalFouriertransformisappliedtotheobtained

channeltransferfunction(CTF)toderivethemeasuredchannelspreadingfunction(CSF).

Figure3.1:High-speedRailway