Radio frequency interference suppression for landmine detection by quadrupole resonance

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Radio frequency interference suppression for landmine detection by quadrupole resonance
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EURASIP Journal on Applied Signal Processing
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English
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Liu, Guoqing
Jiang, Yi
Xiong, Hong
Li, Jian
Barrall, Geoffrey A.
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BioMed Central
Hindawi Publishing Corporation
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The quadrupole resonance (QR) technology can be used as a confirming sensor for buried plastic landmine detection by detecting the explosives within the mine. We focus herein on the detection of TNT mines via the QR sensor. Since the frequency of the QR signal is located within the AM radio frequency band, the QR signal can be corrupted by strong radio frequency interferences (RFIs). Hence to detect the very weak QR signal, RFI mitigation is essential. Reference antennas, which receive RFIs only, can be used together with the main antenna, which receives both the QR signal and the RFIs, for RFI mitigation. The RFIs are usually colored both spatially and temporally, and hence exploiting only the spatial diversity of the antenna array may not give the best performance.We exploit herein both the spatial and temporal correlations of the RFIs to improve the TNT detection performance.

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University of Florida
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HindawiPublishingCorporation EURASIPJournalonAppliedSignalProcessing Volume2006,ArticleID29890,Pages 1 – 14 DOI10.1155/ASP/2006/29890RadioFrequencyInterferenceSuppressionforLandmine DetectionbyQuadrupoleResonanceGuoqingLiu,YiJiang,HongXiong,JianLi,andGeoffreyA.BarrallDepartmentofElectricalandComputerEngineering,UniversityofFlorida,P.O.Box116130,Gainesville,FL32611-6130,USA Received24August2004;Revised26June2005;Accepted30June2005 Thequadrupoleresonance(QR)technologycanbeusedasaconrm ingsensorforburiedplasticlandminedetectionbydetecting theexplosiveswithinthemine.WefocushereinonthedetectionofTNTminesviatheQRsensor.SincethefrequencyoftheQR signalislocatedwithintheAMradiofrequencyband,theQRsignalcanbecorruptedbystrongradiofrequencyinterferences (RFIs).HencetodetecttheveryweakQRsignal,RFImitigationisessential.Referenceantennas,whichreceiveRFIsonly,canbe usedtogetherwiththemainantenna,whichreceivesboththeQRsignalandtheRFIs,forRFImitigation.TheRFIsareusually coloredbothspatiallyandtemporally,andhenceexploitingonlythespatialdiversityoftheantennaarraymaynotgivethebest performance.Weexploithereinboththespatialandtemporalcorr elationsoftheRFIstoimprovetheTNTdetectionperformance. Copyright2006HindawiPublishingCorporation.Allrightsreserved.1.INTRODUCTION Thequadrupoleresonance(QR)technologyhasbeenreceivingincreasingattentionforexplosivedetectioninapplicationsincludinglandminedetection[ 1 – 4 ].Itcanbeusedas aconrmingsensorforburiedplasticlandminedetection bydetectingtheexplosives(e.g.,trinitrotoluene(TNT)and RoyalDemolitioneXplosive(RDX))withinthemine.Inthis paper,wefocusonthedetectionofTNTviatheQRsensor. Whenthe14NintheTNTisexcitedbyasequenceof pulses,itwillemitasignalconsistingofasequenceofechoes [ 1 5 ].Thissignalhasauniquefrequencysignaturespecicto theTNTandisreferredtoastheTNTQRsignal.ThewaveformoftheQRsignalisknown apriori towithinamultiplicativeconstant[ 5 ]. SincetheTNTQRsignalfrequency(around842KHz [ 1 ])islocatedwithintheamplitudemodulation(AM)radiofrequencybandandcannotbechangedbyothermeans, theAMradiosignalscanappearasstrongradiofrequency interferences(RFIs)thatcanseriouslydegradetheQRsignal detectionperformanceinamineeld.Hencetodetectthe veryweakQRsignal,theRFImitigationisessential. Referenceantennas,whichreceiveRFIsonly,canbeused togetherwiththemainantenna,whichreceivesboththeQR signalandtheRFIs,forRFImitigation.Bytakingadvantage ofthespatialcorrelationoftheRFIsreceivedbytheantenna array,theRFIscanbereducedsignicantly.However,the RFIsareusuallycoloredbothspatiallyandtemporally,and henceexploitingonlythespatialdiversityoftheantennaarraymaynotgivethebestperformance. WeexploithereinboththespatialandtemporalcorrelationsoftheRFIstoimprovetheTNTdetectionperformance. First,weconsiderexploitingthespatialcorrelationofthe RFIsonlyanddeployamaximum-likelihood(ML)estimator[ 5 ]forparameterestimation;wealsodesignaconstant falsealarmrate(CFAR)detectorforTNTdetection.Second, weadoptamultichannelautoregressive(MAR)model[ 6 ]to takeintoaccountthetemporalcorrelationoftheRFIsand deviseadetectorbasedonthemodel.Third,wetakeadvantageofthetemporalcorrelationbyusingarobustCapon beamformer(RCB)[ 7 ]inatwo-dimensional(2D)fashion (referredtoas2DRCB)withtheMLestimator[ 5 ]forimprovedRFImitigation.Finally,wecombinethemeritsof allofthethreeaforementionedmethodsforTNTdetection.Thee ectivenessoftheproposedRFImitigationmethodsandthecombinedapproachisdemonstratedusingthe experimentaldatacollectedbyQuantumMagnetics(QM), Inc. Therestofthispaperisorganizedasfollows.In Section2 weintroducetheQRdataacquisitionandsignalmodeland formulatetheproblemofinterest. Section3 presentsourRFI mitigationapproaches,whichincludeaspatialMLscheme, atemporalMARlter,ajointfast-andslow-time2DRCB method,andacombinationofthesethreeapproachesfor improvedTNTdetection.Alsogivenin Section3 isaCFAR detectorforTNTdetection.Experimentalexamplesarepresentedin Section4 toillustratetheperformanceoftheproposedapproaches.Finally, Section5 containsourconclusions.

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2EURASIPJournalonAppliedSignalProcessing 2.PROBLEMFORMULATION ConsideraQRsystemconsistingofamainantennaand Ncreferenceantennas.Eachoftheseantennasprovidesaspatial dataacquisitionchannelandthedataacquisitionisdonesimultaneouslyonthesechannels.Themainantennareceives bothRFIsandtheQRsignalandthereferenceantennasreceiveonlytheRFIs.TheQRsignalisdemodulatedtothedirectcurrent(DC)(i.e.,zerofrequency)upondigitalization inthereceiver. Todetectthe14NQRresponseofTNT,asequenceof pulsesisusedintheQRsystembuiltbyQM[ 1 ].Onepulse sequenceconsistsofapositiveandanegativesubsequence, eachofwhichcontainsasequenceof Nsechoescalledan echotrain.Eachechoissampledtoobtain Nffast-timesamplesduringtheacquisitionwindowandthecorresponding samplinginterval Tfisreferredtoasthefast-timesampling interval(inanalogytotheradarterminology[ 8 ]).Thecorrespondingsamplesfromoneechotoanotherformthe Nsslow-timesamples.Thefast-andslow-timesamplesforman NfNsmatrix.Theamplitude ( ns)ofthe nsthechodecays exponentiallywithatimeconstant T2[ 5 ]: ns =eŠ( nsŠ1) Ts/T2, ns=1, ... Ns,(1) where Tsisthetimeintervalbetweentwoadjacentechoes ortheslow-timesamplinginterval.Equation( 1 )alsoindicatesthechangeoftheQRsignalfromoneechotoanother (orfromoneacquisitionwindowtoanother).Forthedata sets,wehave Nf=50, Ns=54,andthefast-andslow-time samplingintervalsare Tf=10Š5sand Ts=1 1510Š3s, respectively. Apairofadjacentpositiveandnegativepulsesisreferred toasapulseloop.Thepulseloopisthenrepeatedmultiple times(say Nptimes),thatis,thedataacquisitionprocessis repeated Nptimes,witheachprocessobtainingthesameQR signal.Theentiredatacollectionprocessintheserepeated pulseloopsiscalledascan.Hence,eachscanobtains Npdatamatricesofdimension NfNs.Thedatacollectedfrom thenegativepulsesubsequenceissubtractedfromthatinthe positivepulsesubsequence.Thisprocessisreferredtoasderinging,whichcancelsoutanyringingfromtheconstantphaserefocusingpulsesandaddsuptheQRsignals. Hence,wehavea2Dcomplex-valueddatamatrix Xnc, npofdimension NfNsforthe ncthantennaatthe npth pulseloop.Therefore,theQRsystemacquires Npthreedimensional(3D)( Nc+1spatialchannels, Nffast-time,and Nsslow-timesamples,asshownin Figure1 )datavolumeat eachscanlocation. SincethespecicQRsignalfrequencyisdown-converted tozerofrequencyupondigitalizationinthereceiver,itis convenienttocomeupwithadatamodelinthefrequency domainbyperformingtheone-dimensional(1D)Fourier transform(FT)alongthefast-timedimensionforthedata setsfromeachantennaandthenpickinguptheproperfrequencybinscorrespondingtothedown-convertedQRsignalfrequency.Todoso,awindowedFT(WFT)isusually usedtoreducethesidelobes(wewilluseaHanningwindow inourexperiments),andthezero-frequencybinispicked upfromthemainantennawhilemultiplefrequencybins (say Nb)aroundthezerofrequencyarecollectedfromthe referenceantennaoutputs.Foreachechoofapulseloop, (1+ NcNb),spatialsamplesareobtainedfromonemain and Ncreferenceantennas.Hence,afterpickingfrequency bins,wehavea2Dcomplex-valueddatamatrixofdimension(1+ NcNb)NpNs.Consequently,thecorresponding fast-frequency-domaindatamodelcanbeexpressedas xl= a sl+ el, l=1, ... L ,(2) where 0istheunknownsignalamplitude, a isavectoroflength(1+ NcNb)withtherstelementbeing1and theremainingonesbeingzeros,duetothefactthatthemain antennareceivesboththeQRsignalandRFIswhilethereferenceantennasreceiveonlyRFIs; slisthesignalwaveform givenby sl= (mod[ lŠ1, Ns]+1)(withmod[ lŠ1, Ns]denotingthemoduleof lŠ1over Ns);wereferto a asthesteeringvectorand L=NpNsasthenumberofsnapshots; elis avectorcontainingtheRFIsandnoise.Inthedatamodelin ( 2 ),wemodelthesequence{el}L l=1asazero-meanspatially orbothtemporally(slow-time)andspatiallycoloredcircularlysymmetriccomplexGaussianrandomprocesswithan unknownandarbitrary,butxed,spatialcovariancematrix. 3.RFIMITIGATIONAPPROACHES 3.1.SpatialMLestimatorandCFARdetector In[ 5 ],anMLapproachhasbeenproposedforageneralproblemofestimatingthecomplex-valuedamplitude withknownwaveformandknownsteeringvectorcase. Basedonthedatamodelin( 2 )andwithanassumption thattheinterference-plus-noisetermisazero-meantemporallywhitebutspatiallycoloredGaussianprocesswithan unknownspatialcovariancematrix Q ,thespatialMLapproach[ 5 ]estimatesthesignalamplitudebymaximizingthe likelihoodfunctionoftherandomvectors{xl}L l=1.Thenormalizedlog-likelihoodfunctionof{xl}L l=1is C=Šln|Q|ŠtrQŠ11 LLl=1xlŠ a slxlŠ a slH,(3) where||andtr()denotethedeterminantandthetraceof amatrix,respectively,and()Hdenotestheconjugatetranspose.TheMLestimateof canbereadilyobtainedsimilarly asin[ 5 ]ML= ReaHTŠ1xs+ PsaHTŠ1a ,(4) where Ps=1 LLl=1 sl 2,(5) xs=1 LLl=1xlsl,(6) T= RŠxsxH s Ps,(7)

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GuoqingLiuetal. 3 SpatialchannelFasttimeSlowtime01. .Ncxl1 Ns2 NsNpNsl1stpulse loop Ncthref.ch. 1stref.ch. Mainch. 2ndpulse loop Ncthref.ch. 1stref.ch. Mainch.Npthpulse loop Ncthref.ch. 1stref.ch. Mainch. 1NsNs+12 Ns( NpŠ1) Ns+1NpNs1NfFFTalong fasttime thenstack collected freq.bins Figure 1:DatacubefromQRdatacollection.withR=1 LLl=1xlxH l. (8) Here()denotesthecomplexconjugate,Re()denotesthe realpartofacomplexvalue,and[ ]+=max(0, ). Notethattheprocessin( 4 )containsthreestepsthathave clearphysicalinterpretationsasexplainedbelow. (1)Constructingaspatiallter:w=TŠ1a aHTŠ1a (9) (2)Filteringinthespatialdomain: fl= wHxl, l=1, ... L. (10) (3)Filteringinthetemporaldomain:ML=1 LPsReLl=1flsl+. (11) TheestimateofthesignalamplitudeMLisnotasound statisticforCFARdetectionbecausetheestimatedsignalamplitudeishighlysusceptibletotheenvironmentalperturbationssuchasthechangeoftheinterferenceandnoiselevel. Forthisreason,itisdesiredtodesignadetectorwiththe CFARbehaviorsuchthatthefalsealarmrateisindependent oftheinterferenceandnoisepowerlevel.Inthefollowing,we proposeanintuitivemethodwhichhastheCFARproperty. Afterlteringthemultichanneldatainthespatialdomain,wegetascalarsequence{fl}L l=1asshownin( 10 ).The residueofthesequence{fl}L l=1afterremovingtheestimated signalcomponent{ MLsl}L l=1is{flŠ MLsl}L l=1.Thepowerof theresidueis Pe=1 LLl=1 flŠ MLsl 2=wHRwŠPs2 ML= wHRw ,ML=0, 1 aHTŠ1a + 1 PsIm2aHTŠ1xs aHTŠ1a2,ML> 0, (12) whereIm()denotestheimaginarypartofacomplexvalue. Wethencalculatethesignal-to-noiseratio(SNR)of{fl}L l=1as SNR=LPs2 ML Pe=LReaHTŠ1xs2 + PsaHTŠ1a +Im2aHTŠ1xs) (13) Intheappendix,weshowthattheteststatisticdenedin( 13 ) isindependentofthenoiseandinterferencescenario,and thusitisaCFARtest. WerefertotheRFImitigationviathespatialMLapproachintroducedinthissubsectionasMethod1,whichincludesthefollowingsteps. Step1. Performing1DWFTalongfast-timedimensionfor thedatasamplesfromeachantenna. Step2. UsingthespatialMLestimatortoobtaintheMLestimateMLoftheQRsignalamplitude(see( 4 )). Step3. CalculatingtheoutputSNR(see( 13 )). 3.2.TemporalmultichannelautoregressiveModeling TheabovespatialMLapproachassumesthattheinterferenceandnoisetermisspatiallycoloredbuttemporallywhite.

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4EURASIPJournalonAppliedSignalProcessing However,theinterferenceandnoise(especiallytheRFIs)are usuallyspatiallyandtemporallycolored[ 6 ].Thetemporal correlationcanbeduetothecarrierofanAMradiostation operatingaroundtheTNTfrequency.Inthiscase,theML approachmayperformpoorly.Thismotivatesustoconsider takingintoaccountthetemporallycoloredinterferenceand noiseinourQRsignaldetectionproblem.Inthissubsection, weadoptanMARmodel[ 6 ]todealwiththetemporalcorrelationoftheRFIs. TheMARlterhasthefollowingstructure[ 6 ]: HzŠ1 =I +Kk=1HkzŠk,(14) where zŠ1denotestheunit-delayoperator, I isanidentity matrix,and K istheorderoftheMARmodel.TheMARlter isobtainedsothattheoutputoftheMARlterin( 14 ) HzŠ1el= el(15) istemporallywhite. Weassumethattheorder K oftheMARprocessisknown (weuse K=1inourexperiments).If K isunknown,itcan beestimated,forinstance,byusingthegeneralizedAkaike informationcriterion(GAIC)[ 9 ].The K MARcoe cient matrices H=[ H1, ... HK]areestimatedbasedonthefollowingleast-squarescriterion:H1, ... ,HK=argminH1, ... HKNpnp=1 Nsns=K +1 enp, ns+Kk=1Hkenp,( nsŠk ) 2, (16) where enp, nsdenotestheinterferenceandnoisetermofthe datamodelduetothe nsthslow-timesampleatthe npthpulse loop(afterderinging),anddenotestheEuclideannorm. Thesolutionto( 16 )isgivenbyH=E HHŠ1,(17) where = 1npNp, np= np, K +1np, nsnp, Ns, np, ns=Š eT np,( nsŠ1)eT np,( nsŠK )T, E= E1EnpENp, Enp= enp, K +1enp, nsenp, Ns. (18) Here()Tdenotesthetranspose. OncetheMARltercoe cientsaredetermined,weapplytheltertotheacquireddataonaperpulse–loopbasis. TheoutputoftheMARlterforthe nsthslow-timesample atthe npthpulseloophastheform xl= HzŠ1xl= a sl+ el, l=npNs+ ns, np=1, ... Np, ns=K +1, ... Ns, (19) whereH ( zŠ1)hasthesameformas H ( zŠ1)in( 14 )except that{Hk}K k=1arereplacedby{ Hk}K k=1, a= I +Kk=1HkekTs/T2a el= HzŠ1el, l=npNs+ ns, np=1, ... Np, ns=K +1, ... Ns. (20) NotethataftertheMARltering,thenumberofthe slow-timesampleswithinonepulseloopisreducedtobe NsŠK .SincetheMARlteringwhitenstheinterferenceplus-noiseinthetemporal(slow-time)domain,theMAR lteredinterference-plus-noiseisstillspatiallycolored.Also notethatduetothenatureoftheexponentiallydampedQR signalwaveform(see( 2 )),theMARlteringdoesnotdisturbthesignalwaveform,andthedatamodelin( 2 )isstill validfortheMARltereddata.Therefore,thespatialMLapproachdescribedintheprevioussectioncanbedirectlyused todealwiththespatiallycoloredMARlteredinterferenceplus-noiseandtoestimatethesignalamplitude. WerefertotheRFImitigationviathetemporalMARand spatialMLapproachintroducedinthissubsectionasMethod 2,whichincludesthefollowingsteps. Step1. Performing1DWFTalongthefast-timedimension forthedatasamplesfromeachantenna. Step2. UsingthetemporalMARltertodealwiththetemporalcorrelationoftheRFIsandnoise. Step3. ApplyingthespatialMLestimatortotheMARltereddataandobtainingtheMLestimateoftheQRsignal amplitude. Step4. CalculatingtheoutputSNR. 3.3.Jointfast-andslow-time2DRCB Inthissubsection,weconsiderusing2DadaptivebeamformingapproachandtheMLestimatorfortheRFImitigation. Thedata-adaptivestandardCaponbeamformer(SCB)[ 10 ] isknowntohavebetterresolutionandmuchbetterinterferencerejectioncapabilitythanthedata-independentdelayand-sum(DAS)beamformer[ 11 ].SCBshouldperformwell sincetheTNTQRsignalisveryweak.However,theperformanceofSCBmaystilldegradewhenthenumberofsnapshotsissmalland/ornonstationaryinterferenceandnoise exist.Thesetwofactorscanbeviewedasequivalenttosteeringvectorerrorsevenwhenthearraysteeringvectorhasno error[ 12 ].HenceinsteadofSCB,weusetherobustCapon beamformer(RCB)[ 7 13 ],whichisanaturalextensionof SCBtothecaseofuncertainsteeringvectors,inourQR applicationfortheRFImitigation.Particularly,werstuse 2DRCBtomitigatetheRFIsjointlyinthefast-andslowtimedimensionsandthenapplytheMLapproachtowhiten theresidualinterference-and-noiseinthejointtemporaland spatialdomainandestimatethesignalamplitude. Detailedderivationsofthe1DRCBapproachcanbe foundin[ 7 ].Theextensionofthe1DRCBtothe2Dcase isgivenasfollows(seealso Figure2 ).

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GuoqingLiuetal. 5 Moving M1M2X0 1Moving M1M2X0 ,NpMoving M1M2XNc, 1Moving M1M2XNc,NpStackeach M1M2chip andput sidebyside Matrix B (size M1M2( Nc+1) NpL1L2) Apply 1DRCB and reshape Output2Dmatrix ( Nc+1) L1NpL2Input2Dmatrices Xnc,npofsize NfNs. Figure 2:Flowchartof2DRCB.Let M1and M2bethenumbersoftapsinthefast-and slow-timedimensions,respectively.Wechoosea2Dwindow ofsize M1M2andslideitdownwardandforwardovereach 2D NfNsmatrix Xnc, np.Atthe( m n )thwindowlocation within Xnc, np, m=1, ... L1with L1=NfŠM1+1and n=1, ... L2with L2=NsŠM2+1,weobtainavector bnc, np( m n ) bystackingthecolumnsofthesubmatrixof Xnc, np,covered bythemovingwindow,ontopofeachother.Wethenput allso-obtainedvectorssidebysideandobtainanew2Ddata matrix B= B0BncBNc,(21) where Bnc= Bnc,1Bnc, npBnc, Np, nc=0, ... Nc,(22) with Bnc, np= bnc, np(1,1)bnc, np( m n )bnc, npL1, L2, nc=0, ... Nc; np=1, ... Np. (23) Withthispreparation,the1DRCBisthenappliedtothe newdatamatrix B whosecolumnsareconsideredassnapshots.Inthiscase,theestimatedsamplecovariancematrixRfsisgivenbyRfs=1 Nc+1NpL1L2BBH,(24) andthedesiredsteeringvectorisgivenby a0= s11T M1sM21T M1T,(25) with 1M1beinganall-onevectoroflength M1.Notethatusing 1M1in( 25 )isanapproximationsincetheQRsignalisnot aconstantstrictlyoverthefasttime. Figure3 showstheTNT QRsignalasafunctionofthefast-timesamplenumberobtainedbyscanningaTNTmineinahighSNRandRFI-free experiment.RCBisrobustagainstthisapproximationofthe QRsignal. GiventheestimatedsamplecovariancematrixRfsandthe desiredsteeringvector a0,RCBestimatestheactualsteering 50 40 30 20 10 0 Fast-timesampleindex 0 0 2 0 4 0 6 0 8 1Signalamplitude Figure 3:QRsignalversusfast-timesamplenumber(obtainedby scanningaTNTmineinahigh-SNRandRFI-freeexperiment).vector a andthesignalpower 2bysolvingthefollowingoptimizationproblem[ 7 ]: max2, a2subjecttoRfsŠ2 a aH0, aŠa0 (26) whereisauserparameterwhichisusedtodescribethe steeringvectoruncertainty.Notethattherstlineof( 26 )can beinterpretedasacovariancettingproblem:givenRfsand a ,wewishtodeterminethelargestpossiblesignalofinterest 2 a aHthatcanbeapartofRfsunderthenaturalconstraint thattheresidualcovariancematrixispositivesemidenite. Itisshownin[ 7 ]thattheaboveoptimizationproblemis equivalenttothefollowingquadraticoptimizationundera sphericalconstraint: min a aHRŠ1 fs a subjectto aŠa0 2= (27)

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6EURASIPJournalonAppliedSignalProcessing ThisoptimizationproblemcanbesolvedbyusingtheLagrangemultipliermethodology,whichisbasedonthefunction f= aHRŠ1 fs a + aŠa0 2Š ,(28) where 0istheLagrangemultiplier.Theestimaeof a is obtainedas[ 7 ] a=a0ŠU ( I + )Š1UHa0,(29) whereRfs=U UH,(30) withthecolumnsin U denotingtheeigenvectorsofRfsand thediagonalelementsofthediagonalmatrix thecorrespondingeigenvaluesofRfs. Oncetheestimateof a isobtained,adata-dependent weightvectorg canbedeterminedby[ 7 ]g= RŠ1 fs a aHRŠ1 fs a= Rfs+(1 / ) IŠ1a0 aH 0 Rfs+(1 / ) IŠ1Rfs Rfs+(1 / ) IŠ1a0. (31) Notethatg isavectoroflength M1M2.LetG bea2D M1M2matrixobtainedbyreshapingg byusingtherst M1elementsofg astherstcolumnofG andsoforth.ThenG istheimpulseresponseofa2Dniteimpulseresponse (FIR)lterwithtaps M1and M2inthefast-andslow-time dimensions,respectively.The2DFIRlterisappliedtoeach 2Ddatamatrix Xnc, np.The2DFIRlteroutputmatrix Ync, np, correspondingto Xnc, np,hasdimension L1L2. Bystackingthe2DFIRlteroutputmatrices{Ync, np}Ncnc=0fromeachantennaontopofeachotherandincludingall Npdatasets,ateachscanlocation,weobtaina2Dcomplexvalueddatamatrixofdimension( Nc+1) L1NpL2.Thedata vector ylconsistingofthe2DFIRlteroutputsamplesofall antennasatthe l thechohastheform yl= a sl+ el, l=1, ... NpL2,(32) where hasthesamemeaningasin( 2 ), a actsasasteering vectorsimilarto a in( 2 )butwithalongerlength( Nc+1) L1(since L1canbemuchlargerthan Nb), slisthesignalwaveformgivenby sl= (mod[ lŠ1, L2]+1), l=1, ... NpL2, elisavectorcontainingthe2DFIRlteroutputduetothe RFIsandnoiseassociatedwiththe l thecho,whichweassume tobespatiallycoloredbuttemporallywhite(duetothe2D FIRlteringinthefast-andslow-timedimensions)Gaussianwithunknownandarbitrary,butxed,spatialcovariancematrix.Thetotalnumberofsnapshotsassociatedwith thedatamodelin( 32 )is NpL2. Thedatamodelin( 32 )accountsforthejointfast-time andspatialdatainformation.Thesteeringvector a contains thefast-timeresponsesoftheQRsignalatallantennas(spatialchannels).Therst L1elementsof a correspondtothe mainantennaandareones(similarto( 25 ),thisisanapproximationsincetheQRsignalisnotaconstantstrictlyoverthe fasttime)andtheremaining NcL1elementsof a correspond tothereferenceantennasandarezeros. Duetothesimilaritybetweenthetwodatamodelsin( 2 ) and( 32 ),thespatialMLapproachdevisedin Section3.1 and basedonthedatamodelin( 2 )canbedirectlyappliedtothe 2DFIRlteroutputdata(modeledin( 32 ))toobtaintheML estimateoftheQRsignalamplitude. However,becausethedatamodelin( 32 )accountsfor bothfast-timeandspatialdatainformation,thesizeofthe jointfast-timeandspatialdimensioncanbeverylarge.To reducethedimensionbyhalf,let Ync, np,1and Ync, np,2betwo submatricesof Ync, npcontainingtherstandlast(1 / 2) L1( L1needstobeanevennumber)rowsof Ync, np,respectively.Let Znc, np=[ Ync, np,1Ync, np,2].Westackthecolumnsofthematrices{Znc, np}Ncnc=0ontopofeachotherandincludeallsuch Npdatamatrices.Thenweobtaina2Ddatamatrixofdimension(1 / 2)( Nc+1) L12 NpL2ateachscanlocation.With thisrearrangement,thesizeofthejointfast-timeandspatial dimensionisreducedbyhalfwhilethenumberofthesnapshotsisdoubled. Notethatthestructureofthejointfast-timeandspatialdatamodelin( 32 )isstillvalidfortherearrangedmatrixabove.Therefore,wecandirectlyapplytheMLapproach totherearrangeddatatoestimatetheQRsignalamplitude. Fornotationalconvenience,wecontinuetousethesame notationsasin( 32 )fortherearrangedmatrix.Thesteeringvector a neededtoapplytheMLestimatornowconsistsof(1 / 2)( Nc+1) L1elementswiththerst(1 / 2) L1elementscorrespondingtothemainantennaandbeingones andwithalltheremaining(1 / 2) NcL1elementscorrespondingtothereferenceantennasandbeingzeros.TheQRsignalwaveformfortherearranged2DFIRlteroutputdatais sl= (mod[ lŠ1, L2]+1), l=1, ... ,2 NpL2. WerefertotheRFImitigationviathejointfast-andslowtime2DRCBandjointfast-timeandspatialMLapproach introducedinthissubsectionasMethod3,whichincludes thefollowingsteps. Step1. Estimatingthe2DFIRlterbyusing2DRCBjointly inthefast-andslow-timedimensions. Step2. Usingthe2DFIRltertomitigatetheRFIsjointly inthefast-andslow-timedimensionsandrearrangingthe outputdata. Step3. Applyingthejointfast-timeandspatialMLestimator totherearranged2DFIRlteroutputdatatoobtaintheML estimateoftheQRsignalamplitude. Step4. CalculatingtheoutputSNR. 3.4.CombinedapproachforRFImitigation WemaycombinethemeritsofallthreeaforementionedapproachesforTNTdetection.Thecombinedapproachisa three-stagedetectorasshownin Figure4 WerstuseMethod1asabaselineandthenprogressively employMethods2and3.Atascanlocation,iftheestimated

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GuoqingLiuetal. 7 Collecteddata Fast-timeWFT+spatialML SNR >1Fast-timeWFT+temporalMAR&spatialML SNR >2Jointfast-&slow-time2DRCB+jointfast-time&spatialML SNR >3Background Mine Mine Mine Yes Yes Yes No No No Figure 4:CombineddetectorforTNTdetectionbyQR. Table 1:Descriptionofthethreeexperimentaldatasets. Dataset NumberofNumberofNumberofantennasNumberofTNTles minescansbackgroundscansused( Nc+1)afterderinging( Np) 1909045 2100160413 317816045 SNRviaMethod1isgreaterthanaprespeciedthreshold (say 1),weclaimthatthereisamineatthisscanlocation. Otherwise,thedetectorgoesonandusesMethod2formakingadecision.IftheestimatedSNRviaMethod2isgreater thanthesecondprespeciedthreshold(say 2),weclaimthe presenceofthemine.Ifnot,Method3isthenapplied.Again, theestimatedSNRiscomparedwithadetectionthreshold (say 3)andanaldecisionismade. 4.EXPERIMENTALRESULTS Wepresentexperimentalresultstoillustratetheperformance oftheproposedapproachesforlandminedetectionbyQR. Threedatasets(referredtoasDatasets1,2,and3,resp.)collectedbytheQRsensorbuiltbyQMareusedinourexperimentalexamples.Descriptionsofthedatasetsarelistedin Table1 Dataset1contains90scansfromaTNTsimulantand90 scansfrombackground.Dataset2contains100and160scans fromminesandbackground,respectively.Ofthe100mine scansinDataset2,40TNTminesareburiedat5depth, and60TNTminesat3depth.Bothtypesofminesare plastic-cased.Thereare178minescans(foraplastic-cased TNTmine)and160backgroundscansinDataset3.When thedatawerecollected,theQRsequencewasautomatically optimizedbasedontheestimatedminetemperatureentered bythesystemoperator.Forallthedatasets, Nf=50, Ns=54, Tf=10Š5seconds,and Ts=1 1510Š3seconds.Afterderinging,thereare Np=5,13,and5TNTlesleftforeach scaninDatasets1,2,and3,respectively.EachTNTlecorrespondstoapulseloop.Foreachscan,weexploitdatasamples from4antennas(1mainand3referenceantennas). ItisobservedthatstrongRFIsappearjustaroundtheQR signalfrequencyforDataset3. Figure5 showsanexampleof a2Dfast-andslow-timedatamatrix(size5054)collected bythemainantennaoveramineinDataset3. Figure5(a) isthetime-domainimage(realpart)ofthe2Ddatamatrix wherethehorizontalandverticalaxesarefortheslow-and fast-timesampleindices,respectively,Figures 5(b) and 5(c) arethemagnitudesofthe1DFTimagesobtainedbyperforming1DFTalongtheslow-andfast-timedimensionsof the2Ddatamatrix,respectively,and Figure5(d) isthemagnitudeimageofthe2DFTofthe2Ddatamatrix.ThehorizontalaxisofFigures 5(b) and 5(d) isfortheslowfrequency normalizedwiththeslow-timesamplingfrequency1 /Ts.The verticalaxisofFigures 5(c) and 5(d) isforthefastfrequency normalizedwiththefast-timesamplingfrequency1 /Tf.The centeroftheimagein Figure5(d) (markedwithacircle)is thefrequencylocationoftheQRsignal.From Figure5(c) ,it isclearthatoneofthestrongRFIcarrierfrequenciesisvery

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8EURASIPJournalonAppliedSignalProcessing 50 40 30 20 10 Slow-timesampleindex 50 40 30 20 10Fast-timesampleindexŠ2Š1 0 1 2103 (a) 0 4 0 2 0Š0 2Š0 4 Normalizedslow-frequency 50 40 30 20 10Fast-timesampleindex1 2 3 4 5 6104 (b) 50 40 30 20 10 Slow-timesampleindex 0 4 0 2 0Š0 2Š0 4Normalizedfastfrequency1 2 3 4 5 6 7104 (c) 0 4 0 2 0Š0 2Š0 4 Normalizedslowfrequency 0 4 0 2 0Š0 2Š0 4Normalizedfastfrequency0 5 1 1 5 2 2 5 3106 (d)Figure 5:Timeandfrequencyimagesofdatasamplesreceivedbythemainantennaoveramine;(a)2Dtime-domainimage(realpart),(b) magnitudeofFFTimagealongslow-timedimension,(c)magnitudeofFFTimagealongfast-timedimension,and(d)magnitudeof2DFFT image(thecenterofthecircleisthezero-frequencylocationoftheQRsignal,whichistooweaktobeseen).closetotheQRsignalfrequency(inthemiddleoraround zero)inthefast-frequencydimension.ThisshowsthechallengeoftheQRsignaldetectioninthepresenceofstrong RFIs.From Figure5(b) ,wenotethattheRFIsarenotwhite intheslow-timedimensionandtheircarrierfrequenciesare farfromtheQRsignalfrequency(inthemiddleoraround zero)intheslow-frequencydimension.Thisgureveries themotivationtomitigatetheRFIsbyexploitingthetemporal(slow-time)correlationoftheRFIs. ForMethods1and2,weuseaHanningwindowinthe fast-timedimensionpriortoperformingFTand Nb=3 frequencybinsarepickedupfromeachreferencechannel. Wechoose K=1(i.e.,rstorder)fortheMARltering forMethod2.Regardingtheimplementationof2DRCBfor Method3,wechoosethenumbersoftaps M1=19and M2=2inthefast-andslow-timedimensions,respectively, and =0 1isadoptedforRCBtoallowuncertaintyforthe steeringvector.Asforthecombinedapproach,wechoose 1=2 2and 2=1 7asthethresholdstoactivateMethods2 and3,respectively.Wethenchangethethirdthreshold 3to obtainaseriesofvaluesofprobabilityofdetection(Pd)versusfalsealarmrate(FAR),whichformthereceiveroperating characteristic(ROC)curveasaperformanceindicator.Fora giventhreshold,Pdisgivenbytheratioofthenumberofdetectedminescansoverthenumberoftotalminescans,and FARistheratioofthenumberofbackgroundscanswhose estimatedSNRvaluesexceedthethresholdoverthenumber oftotalbackgroundscans. First,wepresentanexampletodemonstratehowour proposedmethodsareusedtomitigatetheRFIsbyexploitingboththespatialandtemporalcorrelationsoftheRFIs. Inthisexample,weapplythe2DRCBapproachinvolvedin

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GuoqingLiuetal. 9 50 40 30 20 10 Slow-timesampleindex 30 25 20 15 10 5Fast-timesampleindexŠ4Š2 0 2 4102 (a) 0 4 0 2 0Š0 2Š0 4 Normalizedslowfrequency 30 25 20 15 10 5Fast-timesampleindex1 2 3 4 5 6103 (b) 50 40 30 20 10 Slow-timesampleindex 0 4 0 2 0Š0 2Š0 4Normalizedfastfrequency2 4 6 8 10 12 14103 (c) 0 4 0 2 0Š0 2Š0 4 Normalizedslowfrequency 0 4 0 2 0Š0 2Š0 4Normalizedfastfrequency2 4 6 8 10 12 14104 (d)Figure 6:TimeandfrequencyimagesafterRFImitigationvia2DRCBforthedatasamplesconsideredin Figure5 ;(a)2Dtime-domain image(realpart),(b)magnitudeofFFTimagealongslow-timedimension,(c)magnitudeofFFTimagealongfast-timedimension,and(d) magnitudeof2DFFTimage(thecenterofthecircleisthezero-frequencylocationoftheQRsignal,whichcanbeclearlyseenaftertheRFI mitigation).Method3totheQRdatacollectedfromthemineconsideredin Figure5 .Forthe2DRCBltereddata,Figures 6(a) through 6(d) showthetimeandfrequencyimagesthatcorrespondtoFigures 5(a) through 5(d) ,respectively.Weseefrom Figures 6(b) and 6(c) thatthestrongRFIshavebeenmitigatedbythe2DRCBltering,andasaresultinthecenterof theimagein Figure6(d) ,theQRsignalclearlyshowsup.Also notefrom Figure6(d) thattherearestillsomeresidualinterferencecomponentsremainingaroundthezero-frequency component.Theseresiduesaretobereducedbyexploiting thespatialinformationintheMLprocessingstepofMethod 3. Inthisexample,weapplybothMethods1and2tothe sameminescanconsideredinFigures 5 and 6 Figure7(a) plotsthemiddlerow(correspondingtothezerofastfrequencybin)of Figure5(d) ,whichisthespectralpattern ofthezero-frequencysamplesfromallthe Nsacquisition windowsintherstTNTleforthemainantenna.Once again,thedominatingRFIindicatesthattheRFIistemporallycolored. Figure7(b) presentstheoutputoftheltering inthespatialdomainbyMethod1accordingto( 10 ),while Figure7(c) givesthecorrespondingresultbyusingMethod 2.ItisclearthattheonlyspatialMLapproachitselfdoes notproduceasatisfactoryRFImitigationresult.NotethesignicantimprovementintheRFImitigationachievedbyusingMethod2. Figure7(d) presentstheresultoftheltering inthespatialdomainproducedbyMethod3.Wenotethat Method3outperformsMethod2inthattheformerproduces

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10EURASIPJournalonAppliedSignalProcessing 0 5 0Š0 5 Normalizedslowfrequency 0 2 4 6 8 10 12Magnitude105 (a) 0 5 0Š0 5 Normalizedslowfrequency 0 1 2 3 4 5 6 7 8Magnitude103 (b) 0 5 0Š0 5 Normalizedslowfrequency 0 5 10 15 20 25 30Magnitude102 (c) 0 5 0Š0 5 Normalizedslowfrequency 0 10 20 30 40 50 60Magnitude (d)Figure 7:RFImitigationexampleforthemineconsideredin Figure5 ;(a)magnitudeofthespectrumofthezero-frequencysampling sequencefromthemainantenna,(b)lteringoutputinthespatialdomainbyMethod1,(c)lteringoutputinthespatialdomainby Method2,and(d)lteringoutputinthespatialdomainbyMethod3.narrowermainbeamwidthandlowerresidualinterference andnoisespectrathanthelatter. Next,weexaminethee ectsofthesnapshotdoubling manipulationdiscussedin Section3.3 onthedetectionperformance.WeapplyMethod3toDataset3intwocases,with andwithoutsnapshotdoubling.TheattainedROCcurves areplottedin Figure8 ,fromwhichweseethatthesnapshot doublingdoeshelpimprovingthedetectionperformance. Theperformanceofusing Np=4TNTleswithsnapshot doublingiscomparabletothatofusing Np=5TNTles withoutsnapshotdoubling.Thisdemonstratestheusefulnessofthesnapshotdoublingmanipulation. WenowcomparetheRFImitigationperformancevia variousprocessingschemes.Particularly,wecompareour proposeddata-adaptiveapproaches,Methods1,2,and3, withthedata-independentDASapproachandtheadaptive SCBapproach.TheimplementationoftheDASapproachis similartothatofMethod1withthematrix T in( 9 )being replacedbyanidentitymatrix.Thestepsof2DSCBfollow thoseof2DRCBasintroducedin Section3.3 and Figure2 exceptthatSCBreplacesRCB.SimilartoMethod3,the2D SCBapproachisfollowedbythespatialMLapproachbased onthedatamodelin( 32 ).Weshowin Figure9 theROC curvesofapplyingtheveapproachestoDataset3.Asexpected,alltheadaptiveapproachessignicantlyoutperform thenonadaptiveDASapproach.Wenotefrom Figure9 that 2DRCBperformsbetterthan2DSCB. Finally,weapplyourproposedmethodstoallthreedata sets.Figures 10(a) through 10(c) presenttheROCcurvesfor Method1(dashedanddottedline),Method2(dottedline), Method3(dashedline),andthecombinedapproach(solid line)whenusingDatasets1,2,and3,respectively.TheRFIs

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GuoqingLiuetal. 11 0 45 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 0 FAR 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1Pd5les,w/snapshotdoubling 4les,w/snapshotdoubling 5les,w/osnapshotdoubling Figure 8:Detectionperformancecomparisonbetweenwithand withoutthesnapshotdoublingmanipulationforMethod3when appliedtoDataset3. 0 45 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 0 FAR 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1PdDAS Method1(ML) Method2(MAR+ML) Method3(2DRCB+ML) 2DSCB+ML Figure 9:DetectionperformancecomparisonofDAS(solidline with),Method1(dashedanddottedline),Method2(dotted), Method3(dashedline),and2DSCBfollowedbythespatialML approach(solidline).inDataset1arenotclosetotheQRsignalfrequencyand Method1worksbetterthanMethods2and3forDataset1. Method3performsconsistentlyandperformsmuchbetter thanMethods1and2forDatasets2and3,whereanRFIis veryclosetotheQRsignalfrequency(thisisespeciallysofor Dataset3). Figure10(d) presentstheROCcurvesforthecase ofusingallthreedatasets.Overall,theseresultsin Figure10 verifythenecessityoftakingintoaccountthetemporal correlationofRFIswhenperformingRFImitigationand demonstratethee ectivenessofourRFImitigationapproachesthatexploitboththespatialandtemporalcorrelationsofRFIs.Therobustnessofourcombinedapproachis demonstratedaswellduetousingdatasetscollectedatdifferenttimesandconditions. 5.CONCLUSIONS WehaveinvestigatedtheRFImitigationforlandminedetectionbyQR.WehaveexploitedboththespatialandtemporalcorrelationsoftheRFIstoimprovetheTNTdetection performance.Wehaverstconsideredexploitingthespatial correlationsoftheRFIsonlyandproposedanMLestimatorforsignalamplitudeestimationandaCFARdetectorfor TNTdetection.WehavethenadoptedanMARmodelto takeintoaccountthetemporalcorrelationoftheRFIsfor RFImitigation.Wehavealsoconsideredusingjointfast-and slow-time2DRCBandjointfast-timeandspatialMLestimatorforRFImitigation.Finally,wehavecombinedthemerits ofallthreemethodsforTNTdetection.Theexperimental resultswiththreedatasetscollectedbyQuantumMagnetics (QM),Inc.,havebeenusedtoverifythenecessityoftaking intoaccountthetemporalcorrelationofRFIswhenperformingRFImitigationanddemonstratedthee ectivenessofour RFImitigationapproachesthatexploitboththespatialand temporalcorrelationsofRFIs.Thecombinedapproachhas alsobeenshowntooutperformallthethreeproposedmethods,anditsrobustnesshasbeendemonstratedaswelldueto usingdatasetscollectedatdi erenttimesandconditions. APPENDIX CFARPROPERTYOF ( 13 ) Wenowshowthatthestatisticdenedin( 13 )isindependent ofthenoiseandinterferencescenario,andthusitisaCFAR test.Tofacilitateourdiscussion,werecall( 6 ), xs=1 LLl=1xlsl. (.33) Astraightforwardcalculationshowsthat xsN ( Ps a ( Ps/L ) Q ).Denotingthat = ( L/Ps) xs,wehave SNR= ReaHTŠ12 + aHTŠ1a +(1 /L )Im2aHTŠ1,(.34) where N ( LPs a Q ).Furthermore,letting C=QŠ1 / 2TQŠ1 / 2, d=QŠ1 / 2a =QŠ1 / 2 (.35) wehave CCW ( M LŠ1; I )with M denotingthelengthof a and I beinganidentitymatrix,whichisacomplexWishart distribution,and N (0, I )whennotargetispresent.It followsfromthetransformationdenedin( .35 )that SNR= RedHCŠ12 + dHCŠ1d +(1 /L )Im2dHCŠ1. (.36)

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12EURASIPJournalonAppliedSignalProcessing 0 45 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 0 FAR 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1PdMethod1 Method2 Method3 Combinedapproach (a) 0 45 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 0 FAR 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1PdMethod1 Method2 Method3 Combinedapproach (b) 0 45 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 0 FAR 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1PdMethod1 Method2 Method3 Combinedapproach (c) 0 45 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 0 FAR 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1PdMethod1 Method2 Method3 Combinedapproach (d)Figure 10:DetectionperformanceofMethod1(dashedanddottedline),Method2(dottedline),Method3(dashedline),andthecombined approach(solidline)for(a)Dataset1,(b)Dataset2,(c)Dataset3,and(d)allthreedatasetstogether.Notethattherandomvariables C and arebothinvariantto aunitarytransformation.Wecandesignaunitarymatrix V suchthat VHd=d 1 0T MŠ1T, d (.37) where 0MŠ1isanall-zerovectoroflength MŠ1,denotes theEuclideannorm,and()Hand()Tdenotetheconjugate transposeandthetranspose,respectively.Thus( .36 )canbe simpliedas SNR= ReHDŠ12 + HDŠ1 +(1 /L )Im2HDŠ1,(.38) where D=VHCV ,and =VH .Itisclearfrom( .38 )that theSNRisindependentoftheinterference-and-noisescenario.ThustheproposedstatisticisaCFARtest. ACKNOWLEDGMENTS ThisworkwassupportedinpartbytheUSArmyunderContractDAAB15-01D-0004andtheNationalScienceFoundationGrantCCR-0104887. REFERENCES[1]A.N.Garroway,M.L.Buess,J.B.Miller,etal.,“Remotesensingbynuclearquadrupoleresonance,” IEEETransactionson GeoscienceandRemoteSensing ,vol.39,no.6,pp.1108–1118, 2001.

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GuoqingLiuetal. 13 [2]A.D.Hibbs,G.A.Barrall,P.V.Czipott,etal.,“Landmine detectionbynuclearquadrupoleresonance,”in Detectionand RemediationTechnologiesforMinesandMinelikeTargetsIII vol.3392of ProceedingsofSPIE ,pp.522–532,Orlando,Fla, USA,April1998. [3]A.D.Hibbs,G.A.Barrall,P.V.Czipott,etal.,“Detectionof TNTandRDXlandminesbystando nuclearquadrupoleresonance,”in DetectionandRemediationTechnologiesforMines andMinelikeTargetsIV ,vol.3710of ProceedingsofSPIE ,pp. 454–463,Orlando,Fla,USA,April1999. [4]R.M.Deas,I.A.Burch,andD.M.Port,“DetectionofRDX andTNTmine-liketargetsbynuclearquadrupoleresonance,” in DetectionandRemediationTechnologiesforMinesandMinelikeTargetsVII ,vol.4742of ProceedingsofSPIE ,pp.482–489, Orlando,Fla,USA,April2002. [5]Y.Jiang,P.Stoica,andJ.Li,“Arraysignalprocessinginthe knownwaveformandsteeringvectorcase,” IEEETransactions onSignalProcessing ,vol.52,no.1,pp.23–35,2004. [6]A.L.SwindlehurstandP.Stoica,“Maximumlikelihoodmethodsinradararraysignalprocessing,” ProceedingsoftheIEEE vol.86,no.2,pp.421–441,1998. [7]J.Li,P.Stoica,andZ.Wang,“OnrobustCaponbeamforming anddiagonalloading,” IEEETransactionsonSignalProcessing vol.51,no.7,pp.1702–1715,2003. [8]J.Ward,“Space-timeadaptiveprocessingforairborneradar,” Tech.Rep.1015,MITLincolnLaboratory,Lexington,Mass, USA,December1994. [9]T.S ¨ oderstr ¨ omandP.Stoica, SystemIdentication ,PrenticeHall,London,UK,1989. [10]J.Capon,“High-resolutionfrequency-wavenumberspectrum analysis,” ProceedingsoftheIEEE ,vol.57,no.8,pp.1408–1418, 1969. [11]H.L.VanTrees, OptimumArrayProcessing:PartIVofDetection,Estimation,andModulationTheory ,JohnWiley&Sons, NewYork,NY,USA,2002. [12]D.D.FeldmanandL.J.Gri ths,“Aprojectionapproachfor robustadaptivebeamforming,” IEEETransactionsonSignal Processing ,vol.42,no.4,pp.867–876,1994. [13]P.Stoica,Z.Wang,andJ.Li,“RobustCaponbeamforming,” IEEESignalProcessingLetters ,vol.10,no.6,pp.172–175,2003. GuoqingLiu receivedtheB.S.,M.S.,and Ph.D.degreesinelectricalengineeringfrom UniversityofElectronicScienceandTechnologyofChina,Chengdu,China,in1988, 1991,and1996,respectively.FromAugust 1993toDecember1995,hewasaVisiting ScholarattheDepartmentofRemoteSensingApplications,AleniaSpazioSPA,Rome, Italy.InApril1996,hejoinedthefacultyat theDepartmentofElectronicEngineering, UniversityofElectronicScienceandTechnologyofChina,where hehasbeenanAssociateProfessorsinceJuly1996.Hewaswiththe DepartmentofElectricalandComputerEngineering,Universityof Florida,Gainesville,Fla,USA,asaPostdoctoralResearchAssociate fromNovember1998toAugust2000andfromSeptember2001to March2005.FromAugust2000toAugust2001,hewasaSenior ResearchAssociateattheDepartmentofElectronicandComputer Engineering,IllinoisInstituteofTechnology,Chicago,Ill,USA,as wellasaContractorattheGlobalSoftwareGroup,MotorolaInc., ElkGroveVillage,Ill,USA.HehasbeenaprincipalSystemsEngineerwithBAESystems,LosAngeles,Calif,USA,sinceMarch2005. HeisaSeniorMemberofIEEE.HisexpertiseandresearchinterestincludeLFM-CWradarsystemanalysisanddesign,SAR/ISAR signalprocessingandimageformation,polarimetricSAR,spectralanalysis,arraysignalprocessing,andautomatictargetrecognition. YiJiang receivehisB.S.degreeinelectricalengineeringandinformationscience fromtheUniversityofScienceandTechnologyofChina(USTC),Hefei,China,in 2001.HereceivedtheM.S.andPh.D.degreesinelectricalengineeringfromtheUniversityofFlorida,Gainesville,Fla,USA,in 2003and2005,respectively.Inthesummerof2005,heworkedasaResearchConsultantintheInformationSystemTechnologyInc.(ISTI),FortCollins,Colo,USA.Heisnowa PostdoctoralResearcherattheUniversityofColorado,Boulder,Colo,USA.Hisresearchinterestsareintheareasofsignalprocessing,wirelesscommunications,andinformationtheory. HongXiong receivedtheB.S.degreein electricalengineeringfromNanjingUniversifyofAeronauticsandAstronautics,Nanjing,China,in1988,andtheM.S.degreeinelectricalengineeringfromUniversityofElectronicScienceandTechnologyofChina(UESTC),Chengdu,China, in1991.ShealsoreceivedtheM.S.degreeinelectricalengineeringfromUniversityofFlorida,Gainesville,Fla,in2003. FromApril1991toAugust1999,shewasaLecturerwiththe DepartmentofElectricalEngineeringatUESTC.Sheisnow workingtowardsthePh.Ddegreeinelectricalengineeringat theUniversityofFlorida.Herresearchinterestsincludespectralanalysis,adaptiveandrobustbeamforming,andsignaldetection. JianLi receivedtheM.S.andPh.D.degrees inelectricalengineeringfromTheOhio StateUniversity,Columbus,in1987and 1991,respectively.FromJuly1991toJune 1993,shewasanAssistantProfessorwith theDepartmentofElectricalEngineering, UniversityofKentucky,Lexington.Since August1993,shehasbeenwiththeDepartmentofElectricalandComputerEngineering,UniversityofFlorida,Gainesville, wheresheiscurrentlyaProfessor.Hercurrentresearchinterests includespectralestimation,statisticalandarraysignalprocessing, sensornetworks,machinelearning,andtheirapplications.Sheisa FellowofIEEEandaFellowofIEE.Shereceivedthe1994National ScienceFoundationYoungInvestigatorAwardandthe1996O ce ofNavalResearchYoungInvestigatorAward.ShewasanAssociate EditoroftheIEEETransactionsonSignalProcessingfrom1999 to2005.ShehasbeenanAssociateEditoroftheIEEESignalProcessingMagazinesince2003.SheispresentlyaMemberoftwoof theIEEESignalProcessingSocietyTechnicalCommittees:theSignalProcessingTheoryandMethods(SPTM)TechnicalCommittee andtheSensorArrayandMultichannel(SAM)TechnicalCommittee.

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14EURASIPJournalonAppliedSignalProcessing Geo reyA.Barrall receivedtheB.S.degreeinchemistryandmathematicsfrom theUniversityofCaliforniaDavisin1990 andthePh.D.degreeinphysicalchemistry fromtheUniversityofCaliforniaBerkeleyin1995.HeiscurrentlytheTechnologyLeaderforGESecurityinSanDiego. Inthisrole,heisresponsibleforleadingthe developmentofquadrupoleresonanceand low-frequencymagneticsensingtechnologiesandproductsforGESecurity.Hehasbeenexploringtheuse ofquadrupoleresonanceforthedetectionofexplosivesinboth landmineandsecurityapplicationsforthepast9years.Hiscontributionshavespannedthetheoretical,experimental,andsignal processingaspectsofQRdetection.