Adaptive OFDM Radar for Target Detection in

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Adaptive OFDM Radar for Target Detection in

最前沿的ofdm国外研究成果

78IEEETRANSACTIONSONSIGNALPROCESSING,VOL.59,NO.1,JANUARY2011

AdaptiveOFDMRadarforTargetDetectionin

MultipathScenarios

SatyabrataSen,StudentMember,IEEE,andAryeNehorai,Fellow,IEEE

Abstract—Wedevelopmethodsfordetectingamovingtargetinthepresenceofmultipathre?ections,whichexist,forexample,inurbanenvironments.Wetakeadvantageofthemultipathprop-agationthatincreasesthespatialdiversityoftheradarsystemandprovidesdifferentDopplershiftsoverdifferentpaths.Weemployabroadbandorthogonalfrequencydivisionmultiplexing(OFDM)signaltoincreasethefrequencydiversityofthesystemasdifferentscatteringcentersofatargetresonatevariablyatdifferentfrequencies.Toovercomethepeak-to-averagepowerratio(PAPR)problemoftheconventionalOFDM,wealsouseconstant-envelopeOFDM(CE-OFDM)signalingscheme.First,weconsiderasimplescenarioinwhichtheradarreceivesonlya?nitenumberofspecularlyre?ectedmultipathsignals.Wedevelopparametricmeasurementmodels,forboththeOFDMandCE-OFDMsignalingmethods,underthegeneralizedmulti-variateanalysisofvariance(GMANOVA)frameworkandemploythegeneralizedlikelihoodratio(GLR)teststodecideaboutthepresenceofatargetinaparticularrangecell.Then,weproposeanalgorithmtooptimallydesigntheparametersoftheOFDMtransmittingwaveformforthenextcoherentprocessinginterval.Inaddition,weextendourmodelstostudytheaspectsoftemporalcorrelationsinthemeasurementnoise.Weprovideafewnumer-icalexamplestoillustratetheperformancecharacteristicsoftheproposeddetectorsanddemonstratetheachievedperformanceimprovementduetoadaptiveOFDMwaveformdesign.

IndexTerms—Adaptivewaveformdesign,asymptoticperfor-manceanalysis,multipath,OFDMradar,targetdetection,urbanscenarios.

I.INTRODUCTION

HEproblemofdetectionandtrackingtargetsinthepres-enceofmultipath,particularlyinurbanenvironments,arebecomingincreasinglyrelevantandchallengingtoradartechnologies.In[1],wehaveshownthatthetargetdetectioncapabilitycanbesigni?cantlyimprovedbyexploitingmultipleDopplershiftscorrespondingtotheprojectionsofthetargetvelocityoneachofthemultipathcomponents.Furthermore,themultipathpropagationsincreasethespatialdiversityoftheradarsystembyprovidingextra“looks”atthetargetandthusenablingtargetdetectionandtrackingevenbeyondtheline-of-sight(LOS)

ManuscriptreceivedJanuary04,2010;acceptedOctober04,2010.DateofpublicationOctober11,2010;dateofcurrentversionDecember17,2010.ThisworkwassupportedbytheDepartmentofDefenseundertheAirForceOf-?ceofScienti?cResearchMURIGrantFA9550-05-1-0443andONRGrantN000140810849.Theassociateeditorcoordinatingthereviewofthismanu-scriptandapprovingitforpublicationwasDr.DenizErdogmus.

TheauthorsarewiththeDepartmentofElectricalandSystemsEngineering,WashingtonUniversityinSt.Louis,St.Louis,MO63130USA(e-mail:ssen3@ese.wustl.edu;nehorai@ese.wustl.edu).

Colorversionsofoneormoreofthe?guresinthispaperareavailableonlineathttp://wendang.chazidian.com.

DigitalObjectIdenti?er10.1109/TSP.2010.2086448

[2],[3].Otherareasofapplicationinwhichmultipatheffectsareofprimaryinterestareinlow-angletracking(sea-skimmers)[4]–[7],height?nding[8],[9],andradar-aidednavigationandlandingsystems[10].Similarproblemshavebeenaddressedinsonarliteratureduetobottombounceinshallowwaters[11],[12].Notethatin[13]wehavedemonstratedthatthedirection-?ndingcapabilityofaradarsystemcanbeimprovedalsobyexploitingmultipathre?ectionsclosetothesensors.

Toresolveandexploitthemultipathcomponentsitisgener-allycommontouseshortpulse,multi-carrierwidebandradarsignals.Weconsidertheorthogonalfrequencydivisionmulti-plexing(OFDM)signalingscheme[14],[15],whichisoneofthewaystoaccomplishsimultaneoususeofseveralsubcarriers.TheuseofOFDMsignalmitigatesthepossiblefading,resolvesthemultipathre?ections,andprovidesadditionalfrequencydi-versityasdifferentscatteringcentersofatargetresonateatdif-ferentfrequencies.

AlthoughOFDMhasbeenelaboratelystudiedandcom-mercializedinthedigitalcommunication?eld[16],ithasnotsowidelybeenstudiedbytheradarcommunityapartfromafewrecentefforts[17]–[19].OneofmajorreasonsofsuchunpopularityisthatOFDMhasatime-varyingenvelopeandthatoriginatesapotentiallyhighpeak-to-averagepowerratio(PAPR)[20],[21].AhighvalueofPAPRdemandsforsystemcomponents(e.g.,transmitter’spowerampli?er)withalargelinearregionofoperation.However,practicalpowerampli?ersoperateoverlimitedlinearregion,beyondwhichtheysaturatecausingnonlineardistortiontothesignal[22].

Overtheyears,anumberofapproacheshavebeenproposedtodealwiththePAPRproblem.AcomprehensivesurveyofPAPRreductiontechniquescanbefoundin[20]and[23,Ch.6].OneofsuchmethodsistoapplythephasemodulationtransformthatachievesthelowestpossiblePAPR(0dB).Inthiswork,besidesconsideringconventionalOFDM,wealsoincludetheconstant-envelopeOFDM(CE-OFDM)signalingscheme[21],[24]–[27],whichisbasedonusingareal-valuedbasebandOFDMsignaltophasemodulatethecarrier.

First,wediscussadetectionprobleminwhichtheradarhasthecompleteknowledgeofthe?rst-order(orsinglebounce)specularlyre?ectedmultipathsignals.Wealsoassumethattheclutterandmeasurementnoisearetemporallywhite.InSectionII,wedevelopthemeasurementmodels,forboththeOFDMandCE-OFDMsignalingschemes,underthegeneralizedmultivariateanalysisofvariance(GMANOVA)framework[28],[29].Basedonthesemodels,inSectionIII,weformulatethedetectionproblemasahypothesistesttodecideaboutthepresenceofatargetinaparticularrangecell.Duetothelackofknowledgeofalltheparametersinourmodels,

最前沿的ofdm国外研究成果

SENANDNEHORAI:ADAPTIVEOFDMRADARFORTARGETDETECTIONINMULTIPATHSCENARIOS79

weemploythegeneralizedlikelihoodratio(GLR)test[30,Ch.6].Wepresentnumericalresultstoevaluatetheperformanceoftheseproposeddetectors,aswedonothaveanyanalyticalexpressionstoevaluatetheirperformances.

Then,inSectionIV,weproposeacriteriontoadaptivelycomputetheparametersofthenexttransmittingwaveform.Toconstructsuchacriterionwe?rstlookintotheperformancecharacteristicsoftheGLRteststatisticsforbothOFDMandCE-OFDMmodelsassumingthatthetargetvelocityisknown.However,thisanalysisdoesnotcharacterizethedetectionper-formanceofourdetectors,inwhichthetargetvelocityisun-known.TheanalysiswithknowntargetvelocityshowsthattheGLRtestresultsinconstantfalsealarmrate(CFAR)detectorsforbothOFDM(withlargenumberoftemporalsamples)andCE-OFDM(with?nitenumberoftemporalsample)models,andthedetectionperformancesdependonthesystemparametersthroughthecorrespondingnoncentralityparametersofthedis-tributionsunderalternatehypothesis.Thisimpliesthatitispos-sibletoimprovethedetectionperformancebymaximizingthesenoncentralityparameters.Weapplythisideatoourproblemandformulatetheoptimizationproblemtoselecttheparametersofthenexttransmittingwaveformthatmaximizesthesameex-pressionofthenoncentralityparametersubjecttoa?xedtrans-mission-energyconstraint.FortheOFDMmodel,weshowthatthesolutionofthisoptimizationproblemresultsinaneigen-vectorcorrespondingtothelargesteigenvalueofamatrixthatdependsonthetarget,clutter,andnoiseparameters.However,fortheCE-OFDMmodelwecannotimprovethedetectionper-formanceinthiswaybecausethenoncentralityparameterdoesnotdependonthetransmittingwaveform.

Laterinthepaper,inSectionV,werelaxtheassumptionoftemporalwhitenesstostudytheeffectsoftemporallycor-relatedmeasurementnoiseprocessonourmodels.Temporalcorrelationsexistincertainradarapplications,inparticularathighpulserepetitionfrequencies(PRF)[31],[32].Tomodelthetemporalcorrelationmatrix,welookintoabranchofstatisticsknownasthenearestneighboranalysis[33],[34],andpresenttheconsequentdetectiontests.

Toillustratethepotentialofourproposeddetectors,wepresentnumericalexamplesinSectionVI.We?ndthatthewidebandOFDMmodelperformsbetterthanthenarrowbandCE-OFDMmodelinexploitingthemultipathre?ections.Inaddition,weachievesigni?cantperformanceimprovementduetoadaptiveOFDMwaveformdesign.However,theCE-OFDMsignallackssuchanadaptivedesignasthedetectionper-formancedoesnotdependonthetransmittingcoef?cients.Finally,wegiveconcludingremarksandsomethoughtsonafewunaddressedissuesinSectionVII.

Notations:Welistheresomenotationalconventionthatwillbeusedthroughoutthispaper.Weusemathitalicforscalers,lowercaseboldforvectors,anduppercaseboldformatrices.Fora

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matrix

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and

denotethetranspose,conjugate-transpose,deter-

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minant,

thentry,generalizedinverse(such

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that),trace,vec-operation,andblock-diagonalvec-operation(de-?nedin[35,eq.(7)])

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of,

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respectively.representsaniden-titymatrixof

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dimension

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formsasquarematrixwithnonzeroentriesonlyonthemaindiagonal.Additionally,

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,Fig.1.Schematicrepresentationofthemultipath

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scenario.

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andaretheinner-product,Kroneckerproduct,andele-ment-wiseHadamardproductoperators,respectively.

II.PROBLEMDESCRIPTIONANDMODELING

Weconsiderafar-?eldpointtargetmovingwithaconstantrelative

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velocity,withrespecttotheradar,inamultipath-richenvironment,asshowninFig.1.Attheoperatingfrequency,weassumethatthere?ectingsurfacesproduceonlyspecularre-?ectionsoftheradarsignal.Weassumethattheradarhasthecompleteknowledgeoftheenvironmentthatisundersurveil-lance.Hence,foreveryrangecelltheradarknowsthenumber

ofpossible

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multipath

betweentheradarandtargetandthedirection-of-arrival(DOA)unit-vectors

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(

)alongeachsuchpath.Underthisscenario,we?rstintro-ducetheparametricmeasurementmodelsforbothOFDMandCE-OFDMsignalingtechniques.Then,wediscussourstatis-ticalassumptionsontheclutterandnoise.A.OFDMMeasurementModel

WeconsideranOFDMsignalingsystem[15]

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with

ac-tivesubcarriers,abandwidth

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Hz,andpulseduration

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ofseconds.

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Letrepresentsthecomplexweightstransmittedover

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thesubcarriers,

satisfying

.Then,thecomplexenvelopeofthetransmitted

signalcanberepresented

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(1)

wheredenotesthesubcarrierspacing.

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Letbethecarrierfrequencyofoperation,thenthetransmittedsignalisgiven

(2)

whererepresentsthethsubcarrierfrequency.Interchangingtherealandsummationoperators,wecanalsorewrite(2)

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(3)

最前沿的ofdm国外研究成果

etection problem as a hypothesis test to decide about the presence of a target in a particular range cell. Due to the lack of knowledge of all the parameters in our models, 1053-587X/$26.00 © 2010 IEEE SEN AND NEHORAI: ADAPTIVE OFDM RADAR FOR TARGET DETECTION IN MULTIPATH SCENARIOS 79 we employ the generalized likelihood ratio (GLR) test [30, Ch. 6]. We present numerical results to evaluate the performance of these proposed detectors, as we do not have any analytical expressions to evaluate their performances. Then, in Section IV, we propose a criterion to adaptively compute the parameters of the next transmitting waveform. To construct such a criterion we ?rst look into the performance characteristics of the GLR test statistics for both OFDM and CE-OFDM models assuming that the target velocity is known. However, this analysis does not characterize the detection performance of our detectors, in which the target velocity is unknown. The analysis with known target velocity shows that the GLR test results in constant false alarm rate (CFAR) detectors for both OFDM (with large number of temporal samples) and CE-OFDM (with ?nite number of temporal sample) models, and the detection performances depend on the system parameters through the corresponding noncentrality parameters of the distributions under alternate hypothesis. This implies that it is possible to improve the detection performance by maximizing these noncentrality parameters. We apply this idea to our problem and formulate the optimization problem to select the parameters of the next transmitting waveform that maximizes the same expression of the noncentrality parameter subject to a ?xed transmission-energy constraint. For the OFDM model, we show that the solution of this optimization problem results in an eigenvector corresponding to the largest eigenvalue of a matrix that depends on the target, clutter, and noise parameters. However, for the CE-OFDM model we cannot improve the detection performance in this way because the noncentrality parameter does not depend on the transmitting waveform. Later in the paper, in Section V, we relax the assumption of temporal whiteness to study the effects of temporally correlated measurement noise process on our models. Temporal correlations exist in certain radar applications, in particular at high pulse repetition frequencies (PRF) [31], [32]. To model the temporal correlation matrix, we look into a branch of statistics known as the nearest neighbor analysis [33], [34], and present the consequent detection tests. To illustrate the potential of our proposed detectors, we present numerical examples in Section VI. We ?nd that the wideband OFDM model performs better than the narrowband CE-OFDM model in exploiting the multipath re?ections. In addition, we achieve signi?cant performance improvement due to adaptive OFDM waveform design. However, the CE-OFDM signal lacks such an adaptive design as the detection performance does not depend on

最前沿的ofdm国外研究成果

the transmitting coef?cients. Finally, we give concluding remarks and some thoughts on a few unaddressed issues in Section VII. Notations: We list here some notational convention that will be used throughout this paper. We use math italic for scalers, lowercase bold for vectors, and uppercase bold for matrices. For a matrix , , , , , , , , denote the transpose, conjugate-transpose, deterand th entry, generalized inverse (such that minant, ), trace, vec-operation, and block-diagonal vec-operation (de?ned in [35, eq. (7)]) of , respectively. represents an idenforms a square matrix with tity matrix of dimension . , nonzero entries only on the main diagonal. Additionally, Fig. 1. Schematic representation of the multipath scenario. , and are the inner-product, Kronecker product, and element-wise Hadamard product operators, respectively. II. PROBLEM DESCRIPTION AND MODELING We consider a far-?eld point target moving with a constant relative velocity , with respect to the radar, in a multipath-rich environment, as shown in Fig. 1. At the operating frequency, we assume that the re?ecting surfaces produce only specular re?ections of the radar signal. We assume that the radar has the complete knowledge of the environment that is under surveillance. Hence, for every range cell the radar knows the number between the radar and target and the of possible multipath direction-of-arrival (DOA) unit-vectors ( , ) along each such path. Under this scenario, we ?rst introduce the parametric measurement models for both OFDM and CE-OFDM signaling techniques. Then, we discuss our statistical assumptions on the clutter and noise. A. OFDM Measurement Model acWe consider an OFDM signaling system [15] with Hz, and pulse duration tive subcarriers, a bandwidth of of seconds. Let represents the complex weights transmitted over the subcarriers, satisfying . Then, the complex envelope of the transmitted signal can be represented as (1) where denotes the subcarrier spacing. Let be the carrier frequency of operation, then the transmitted signal is given by (2) where represents the th subcarrier frequency. Interchanging the real and summation operators, we can also rewrite (2) as (3) 80 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 59, NO. 1, JANUARY 2011 where (4) represents the transmitted signal due to the th subcarrier only. Then, the received signal along the th path (represented by the DOA vector ) due to only the th subcarrier can be written as (5) is a complex quantity representing the scattering coefwhere ?cient of the target along the th subchannel and th path; where is the relative Doppler shift along the th path and is the speed of propagation; is the roundtrip delay between the radar and target along the th path; represents the clutter and measurement noise along the th subchannel and th path. Therefore, the received signal over all available paths due to an -carrier OFDM signal is given by where (9) Stacking the measurements of all subchannels into

最前沿的ofdm国外研究成果

one , we get column vector of dimension (10) where ? ? is an complex diagonal matrix that contains the transmitted weights ; is an complex ? rectangular block-diagonal matrix where each nonzero , , block represents the scattering coef?cients of the target at the th subchannel over all multipath; ? is an complex vector where , , contains the Doppler information of the target at the th subchannel over all multipath; ? is a column vector containing the unknown target-velocity components; is an vector ? of clutter returns, measurement noise, and co-channel interference. Then, concatenating all the temporal data columnwise into an matrix we obtain the OFDM measurement model as follows: (11) where ? ; is an ? matrix containing the Doppler information of the target through the parameter ; is an matrix com? prising clutter returns, noise, and interference. B. CE-OFDM Measurement Model A CE-OFDM signal is realized by using a real-valued baseband OFDM signal to phase modulate the carrier. The complex envelope of a CE-OFDM transmitted signal is represented as [21] (12) where signal is the modulation index in radians and message bears an OFDM signal structure (13) are real-valued weights at difwhere ferent subcarriers. Assuming a narrowband signal model (which can be achieved with small modulation index [21]), the complex envelope of the (6) and hence the corresponding complex envelope is given as (7) Let us assume at this point that the relative time gaps between any two multipath signals are very small in comparison to the for . actual roundtrip delays, i.e., These assumptions can be justi?ed in systems where the path lengths of multipath arrivals differ little (e.g., narrow urban canyon where the range is much greater than the width). Furas the roundtrip delay corresponding to ther, let us denote the range cell under consideration. Then, the information of the roundtrip delays can be automatically incorporated into the , , model by choosing where is the pulse repetition interval (PRI) and is the number of temporal measurements within a given coherent processing interval (CPI). Hence, corresponding to a speci?c range cell containing the target, the complex envelope of the received signal at the output of the th subchannel is (8) SEN AND NEHORAI: ADAPTIVE OFDM RADAR FOR TARGET DETECTION IN MULTIPATH SCENARIOS 81 received signal corresponding to a speci?c range cell containing the target can be written as (14) is the target scattering coef?cient at the operating frewhere are roundtrip delay quency along the th path, and and and relative Doppler shift, respectively, along the th path. Then, as before assuming that all the multipath delays are for , and approximately equal, i.e., , , we can representing simplify (14) into irregularities on the re?ecting surface (e.g., windows and balconies of the buildings in an urban scenario), that cannot be modeled as specular components. Therefore, for both OFDM and CE-OFDM measureme