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ThisisarepositorycopyofPassiveInterferingMethodforInSARBasedonCircularlyMovingStrongScatterers.
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uk/85480/Version:AcceptedVersionArticle:Wu,Z-F.
,Xu,H-P.
,Li,J-W.
etal.
(1moreauthor)(2015)PassiveInterferingMethodforInSARBasedonCircularlyMovingStrongScatterers.
IEEETransactionsonAerospaceandElectronicSystems,51(3).
pp.
1877-1890.
ISSN0018-9251https://doi.
org/10.
1109/TAES.
2015.
1304372015IEEE.
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APassiveInterferingMethodforInSARBasedonCircularlyMovingStrongScatterersZhe-fengWu,Hua-pingXu,Jing-wenLi,WeiLiuSchoolofElectronicandInformationEngineering,BeihangUniversity,Beijing,100191,Chinae-mail:wuzheming001@126.
comAbstract—Anoveljammingmethodbasedoncircularlymovingstrongscatterersisproposed.
ThejammingsignalmodelisfirstlypresentedandthecorrespondingimagingresultsarederivedthroughaRange-Doppleralgorithm.
Detailedanalysisshowsthattheproposedmethodcandecreasethecorrelation,produceinterferometricphasebias,resultinfailureofphaseunwrappingandreducetheaccuracyofdigitalelevationmodel(DEM).
Simulationresultsareprovidedtoverifytheeffectivenessoftheproposedmethod.
IndexTerms—jamming,interferometry,syntheticapertureradar(SAR),strongscatterer,passiveinterference.
I.
INTRODUCTIONSyntheticApertureRadar,asanall-weatherall-timeremotesensingtechnique,hasbeenwidelyusedinbothmilitaryandcivilianapplications,suchasmonitoring,geologicalinvestigationandgroundmovingtargetrecognition[1]-[3].
InSAR,afurtherdevelopmentofthetraditionalSARtechnology,employstwoormoreSARantennastoobtaintheelevationinformationofthegroundsurfacebymeasuringthephasedifferencebetweenthedualimages[2].
Forthedual-passInSAR,themasterantennaandtheslaveantennatransmitandreceiveSARsignalsbythemselves.
WhenInSARworksinthesingle-passmode,themasterantennaservesasatransmitterandbothantennasrecordtheechosignalssimultaneously[2],[3].
Inthepast,severalworkingInSARsystemshavebeendeployed.
ThesatelliteTanDEM-X,launchedin2010,canachieveaDEMprecisionassmallas2m[4].
TheShuttleRadarTopographyMission(SRTM),withtwoantennasusingsingle-passInSARandoperatingatawavelengthof5.
6cm,producedthemostaccuratenear-globalDEMcoveringmostlandandadjacentnear-shoreoceanareasbetweenlatitudes56°southand60°north[5].
RADARSAT-1andRADARSAT-2,theCanadianSARremotesensingsatellites,arestillfullyoperationalandcontinuetoprovideInSARdatatoworldwideusers[6].
Allthesesystemshavehighmeasuringaccuracyandcandetectavarietyofimportanttargetseffectivelyfordifferentpurposes.
Meanwhile,inordertoprotectimportantfacilitiesagainstmilitaryreconnaissance,thedevelopmentofeffectivejammingmethodsforInSARhasbecomemoreandmoreimportant.
Ontheotherhand,researchonjammingmethodscanhelpidentifytheweaknessofcurrentInSARsystems,sothatmoreeffectiveandrobustsystemswithfurtherimprovedperformancecanbedevelopedinthefuturetoworkincomplicatedreal-worldscenarios.
Withtheneedandrapiddevelopmentofelectroniccountermeasures(ECM),alargeamountofworkhasbeenfocusedonthejammingofairborneorspaceborneSARsystems.
In[7],[8],differenttypesofECMjammingsignalswereintroducedandtheyarenowusedwidely.
DigitalRadioFrequencyMemory(DRFM),alow-costandyetveryeffectiveECMjammingmethod,wasintroducedin[9],byretransmittingareplicaofthereceivedsignals.
Adetailedstudyforlargescenedeceptivejammingwasprovidedin[10],basedonwhichafastalgorithmwasthenproposed.
Althoughthesetraditionalbarragejamming[7],DRFManddeceptiveinterferencecanjamtheamplitudeoftheSARimagetodifferentdegrees,thephasepartiscancelledthroughinterferometry.
Asaresult,theirinterferingeffectsoninterferometryarelimited.
Cross-eyejamming,withtwojammerantennassimultaneouslytransmittingtheinterference,generatesanglejammingforthethreatradar,whichisusuallyappliedtoagainstamonopulseradar[11]-[14].
However,theideaofmulti-antennajammingprovidesapossiblemethodforjammingInSAR.
Inthecross-eyejamming,theinterferencetransmittedbythetwoantennasofjammerwillproducethephasenoiseintheresultantinterferogram.
Sincetheresultantphasenoiseissimultaneouslyaffectedbyboththemagnitudeandthephaseoftheintererence,thewholesituationwillbemorecomplicated.
Therefore,anin-depthstudyoftheeffectofmulti-antennainterferenceisneededforitsapplicationinInSARjamming.
Inthispaper,weproposeanovelmethodbasedoncircularlymovingstrongscatterers,suitableforjammingbothairborneandspaceborneInSARsystems.
DifferentfromconventionalSARjammingmethods,thenewmethodisaimedtochangetheinterferometricphaseinformationoftherealscenetosignificantlyreducetheaccuracyofDEMorresultinlossofsometerrainfeatures.
CornerreectorsareoriginallyusedforexternalcalibrationofSARsystems[15].
CircularmotionofthecornerreflectorwithacertainangularspeedinthehorizontalplanewillresultinvaryingtimedelaysandleadtochangesinDopplerfrequency[16]-[18].
ThedifferenceinDopplerfrequencyhasadefocusingeffectonthejammingsignalalongtheazimuthdirection,whichcanproducephaseperturbationsdifferentfromeachotheratbothantennas.
Theresultantphasenoisedistributedalongtheazimuthdirectionwillcausesignificanterrorstotheinterferometricphaseoftherealscene.
Asaresult,comparedtothetraditionalSARjammingmethod,thenewmethodcanreducetheaccuracyofelevationestimationoftheInSARsystemsignificantly.
Therearetwomajoradvantageswiththeproposedmethod.
Firstly,asapassiveinterferingtechnique,itisenergysavingbyreflectingthetransmittedsignalofthethreatradareffectively.
Althoughthereflectedenergyislimited,thejammingeffectcanbeimprovedasthedensityandthecoverageofstrongscatterersincrease.
Secondly,sincesignaldetectionandanalysisequipmentisnotused,thecostismuchlowerthantraditionalelectronicjammingsystems.
Moreover,studyoftargetmicromotioncharacteristicshasattractedmoreandmoreinterestrecentlyandtheresearchresultforcircularlymovingstrongscatterersobtainedherecanbeappliedtostudytheinfluenceoftargetmicromotiononSARandInSARinthefuture.
Theremainderofthispaperisorganizedasfollows.
SignalmodelsandtheimagingoutputsatthetwoantennasduetocircularlymovingstrongscatterersaregiveninSectionII.
InSectionIII,theinterferometricphasemodelfortheproposedmethodisderivedandtheeffectofjammingoncorrelationandelevationestimationaccuracyisanalyzed.
SimulationresultsareprovidedinSectionIVandconclusionsaredrawninSectionV.
II.
CIRCULARLYMOVINGSTRONGSCATTERERJAMMINGFORSARIMAGINGForcircularlymovingstrongscattererjamming,wefirstestablishthejamminggeometryand,then,theimagingresultsintwoantennasmodelsarederived.
Generally,manytargetsbelongtostrongscatterers.
Withoutlossofgenerality,weusecornerreflectorsforanalysisbelow.
A.
PrincipleofCircularlyMovingStrongScattererJammingTheECMscenarioisshowninFig.
1(a).
Points1Aand2Arepresentthemasterantennaandtheslaveantenna,respectively.
TheSARplatformfliesalongthex-axisinafixedaltitudeandimagesanareaonthegroundplane.
θdenotesthelookangle,Histheflightaltitudeofthemasterantenna,andXOY(groundplane)isthetargetfocusplane.
InFig.
1(b),0θistheinitialanglevalue.
Thecornerreflectormovesinacircularpatharoundthecenter000(,,)xyzonthehorizontalplanewitharadiusrandanangularspeedω,asshowninFig.
1(b).
Asthereflectormovesaroundafixeddatum,bothantennasreceiveechoesfromtherealsceneandthereflectorsimultaneously.
ThecircularlymovingcornerreflectorechoeswillfurtheraffecttheimagingresultsandinterferometricprocessingofInSAR.
Inwhatfollows,wewillgiveananalysisofboththesignalmodelandtheimagingoutputforthecircularlymovingcornerreflector.
B.
EchoSignalModelforCircularlyMovingStrongScattererJammingInpractice,toachieveahighrangeresolution,thesensorusuallytransmitsLFMsignals.
Assumethatthesignaltransmittedbythemasterantenna1Ais21()rectexp22rmrcrrrPtStjftKtTπ=+(1)wherertisthefast(range)time,PTisthepulseduration,cfandrKdenotethecarrierfrequencyandthechirprate,respectively,and[]rectistherectangularwindowfunction[1]-[3].
ThecornerreflectorreflectsechosignalsastheSARplatformpassesby.
Assumethatthesystemworksintheside-lookingmode.
Afterdown-converting,thepulsebackscatteredfromthecornerreflectorforjammingthemasterimagecanbeexpressedas22()/2()4()(,)rectrectexpexprmjamjamjaamrarrPLtRtcRtRttJttjKtjTTcππλ=(2)wherecisthespeedoflight,LTdenotesthesyntheticaperturetime,λisthewavelength,and()mjaRtistheinstantaneousslantrangebetweenthephasecenterofInSARmasterantennaandthepositionofcornerreflectorwithrespecttoslowtimeat.
Theinstantaneouspositionofthecornerreflectorcanbedefinedas(0cos()caxrtωθ++,0sin()cayrtωθ++,cz).
UsingTaylorseriesexpansion,()mjaRtisapproximatedas2220000022220000()cossin2sin()2mjaaaaaaamaMMRtxrtvtyrtzHrxvtryxvtttRRωθωθωθθ′≈+(3)wherevisthevelocityoftheSARplatform,MRistheminimumslantrangebetweenthemasterantennaandtherotationcenterofcircularlymovingcornerreflector,and()atθ′isgivenby00()arctanamaxvttyθ′=(4)Similarly,theinterferencereceivedbytheslaveantennacanbeexpressedas22()/2()4()(,)rectrectexpexprsjasjasjaasrarrPLtRtcRtRttJttjKtjTTcππλ=(5)where()sjaRtistheinstantaneousslantrangebetweentheslaveantennaandthecornerreflector,givenby22200000()cossincos()sin()sjaaaaRtxrtvtyrtBzHBωθωθαα(6)whereBisthelengthofthebaseline,αdenotestheinclinationofthebaseline.
C.
SARImagingModelforJammingWenowderivetheimagingsignalmodelduetojamminginthedual-passmode.
Therearedifferentimagingalgorithmsavailableandtheyallachievethesameimagingresult.
Withoutlossofgeneralityandforsimplicity,weadopttheRange-Doppleralgorithmhere[19].
First,rangematchedfilteringisperformedto(2)usingthefilter{}2_()exprrrefrrrPtHtrectjKtTπ=(7)Therange-compressedsignaloftheinterferenceinthemasterimageisgivenby__2()4()sincexpmrcramarrefrmjamjaaPrrLJttJtHtdRtRttTrectBtjTcτττπλ==∫(8)whererBrepresentstherangebandwidthoftheecho.
Fordifferentrotationalangularvelocity,theinterferenceafterRangeCompression(RC)andbeforeRangeCellMigrationCorrection(RCMC)isgiveninFig.
2.
SinceMRr>>,thetermsrelatedtorin(3)areignored.
ThesignalformulationafterRCMCisgivenby_4()2(,)rectsincexpmjaaMmrcraPrrLRttRJttTBtjTcπλ≈(9)Substituting(3)into(9),wehave()[]22_000242(,)rectsincexpexp4exp()sin()aMMmrcraPrrLMaamaavtrtRRJttTBtjjTcRrtttxjππλλπωθθλ+′++(10)where0()artisdefinedas(AsshowninAppendixA)222200000aaMaSrtryvtxRryvtxR11)Forazimuthcompression,Besselfunctionofthefirstkindisused[20],whichisgivenby{}{}expsin()()expnnjxJxjn+∞=∞=∑(12)where()nJrepresentsthethnBesselfunctionofthefirstkind.
Substituting(12)into(10),_(,)mrcraJttchangesto()[]{}22_000242(,)rectsincexpexp4()exp()aMMmrcraPrrLMnnaaamavtxrtRRJttTBtjjTcRJrtjnttππλλπωθθλ+∞=∞+′++∑(13)Let1aKbetheDopplerchirprateofthemasterimage[18],[20].
Thenazimuthmatchedfilteringisperformedto(13)usingthefilter{}2_1()rectexpaarefaaaLtHtjKtTπ=(14)Theimagingoutputoftheinterferencedisplayedinthemasterimageisexpressedas[]{}2_000124(,)sincexp24()sincexp()2MmoutraPLrrMMnaaamanaRrJttTTBtjRcRnJrtBtjnvtKxπλπωθθλπ+∞=∞′+∑(15)Similarto(15),theimagingoutputoftheslaveantennaisgivenby[]{}2_000224(,)sincexp24()sincexp()2SsoutraPLrrSSnaaasanaRrJttTTBtjRcRnJrtBtjnKxtvπλπωθθλπ+∞=∞′+∑(16)whereSRistheminimumslantrangebetweenthephasecenteroftheInSARslaveantennaandthecircularlymovingcornerreflector,and00()arctancos()asaxvttyBθα′=(17)Clearly,accordingtoCarson'srule[20],theexponenttermsof(12)willintroducemultiplesymmetricDopplershiftsandpairedechoesoftheoriginalsignal.
Thevalueofthethnpairedechoesisdeterminedby[]04()/naJrtπλ.
InFig.
3,theimagingoutputforthecornerreflectorinterferenceisshown,withparametersofthereflectorlistedinTableIandparametersoftheInSARsysteminTableII.
III.
CIRCULARLYMOVINGSTRONGSCATTERERJAMMINGFORINSARInsectionII,itisshownthatthepairedechoes,duetocircularlymovingstrongscattererjamming,aredistributedalongtheazimuthdirectionintwoSLCimages.
Ontheonehand,thejammingwilldecreasecorrelationofthetwoSLCimagesandreducetheestimationaccuracyoftheinterferometricphase,whichwillleadtodiscontinuitiesoftheunwrappedphase.
Ontheotherhand,thephasesofpairedechoesinthesamelocationoftwoSLCimagesaredifferentfromeachother.
Thephasebias,definedasthebiasofinterferometricphaseduetocircularlymovingstrongscattererjamming,willresultinmoreerrorstotherealphase.
Therefore,thecircularlymovingstrongscatterercanincreasephaseerrorsthroughtwodifferentways:thecorrelationoftwoSLCimagesandthephasebiasofjamming.
Inthissection,thephasebiascausedbythepairedechoeswillbederived,withananalysisofthejammingeffectoncorrelationconsideredsubsequently.
Furthermore,theevaluationofDEMerrorsbasedonphasenoiseoftheinterferenceisprovided.
A.
InterferomtricPhaseAnalysisforJammingInterferometricphase,asthebasisofelevationmeasurement,candirectlyaffecttheaccuracyofDEM[21].
IfthetwoSLCimagesareaccuratelyco-registered,thephasedifferenceduetojammingcanbederivedthroughconjugatemultiplicationofthetwoco-registeredSARimages.
Inthedual-passmode,thediscrepancybetween2/rMtRcand2/rStRcinboth(15)and(16)willcauseanenvelopeshiftbetween_(,)moutraJttand_(,)soutraJtt.
Thisdifferencecanbecompensatedbyhighprecisionimageco-registrationprocessing.
Byassumingthattheslaveimage(16)isadjustedinthelightofthemasterimage,soutraJttisrearrangedas[]{}2_000224(,)sincexp24()sincexp()2MsoutraPLrrSSnaaasanaRrJttTTBtjRcRnJrtBtjnKxtvπλπωθθλπ+∞=∞′+∑(18)IgnoringtheinfluenceofdifferentDopplerchirpratesonthelocationofpointseriesandcomparingthephasesinboth(15)and(18),wecanderivethephasedifferenceofthepairedechoesas[]24()211MSIFmasanMSRRrnttRRππθθλλ+∞=∞′′∑(19)wherethefirsttermrepresentsthepositionoftherotationcenter,andtheremainingtermsconstitutethephaseinterference.
Phasenoisecausedbythepairedechoesisgeneratedintheimagingprocessandthejammingresultcanbeconsideredasaseriesofinterferencesignalswithphasenoises(asshowninFig.
4.
).
TheinterferenceswillnotonlyaffectthetwoSLCimages,butalsojamtheinterferometricphaseorevenleadtofailureofthephaseunwrappingprocess.
B.
JammingEffectonCorrelationCorrelation,ameasureofsimilaritybetweentwoSLCimages,isdeterminedbypropertiesofreceivedsignalsandseveralsystemparameters[22].
Inwhatfollows,wewillgiveananalysisofthejammingeffectoncorrelation.
ThecorrelationγoftwoSLCimages1Sand2Sisdefinedas*12**1122SSSSSSγ=(20)where()*denotescomplexconjugate,andrepresentstheensembleaverage[22].
Theaveragepowerofthecrossmultiplicationofthecorrespondingpixelpairsofthetwoco-registeredSARimagesisgivenby()()*12realmmoutrealssoutrealmrealsmoutsoutSSSJSJSSJJ21)where_realmSand_realsSrepresentthecorrespondingpixelsintwoSARimageswithoutjamming,respectively.
Then,theindividualsignalpowersofthejammedpixelsaregivenby*11____realmrealmmoutmoutSSSSJJ=+(22)*22____realsrealssoutsoutSSSSJJ=+(23)Substituting(21),(22)and(23)into(20),weobtainthecorrelationofthejammedpixelsas()()____realmrealsmoutsoutrealmrealmmoutmoutrealsrealssoutsoutSSJJSSJJSSJJγ+=++(24)Tosimplifytheanalysis,wehavethefollowingconsiderations{}{}2____2____2__002__expexprealmrealmrealsrealsmoutmoutsoutsoutJrealmrealsmoutsoutJJJSSSSAJJJJASSAjJJAjγφγφ======(25)where0γandJγrepresentthecorrelationsoftheoriginalpixelpairsandthejammingpart,respectively,and0φandJφdenotethecorrespondingphases.
Substituting(25)into(24),thecorrelationofthejammedpixelsbecomes{}{}220022expexpJJJJAjAjAAγφγφγ+=+(26)Clearly,theidealcorrelationwithoutinterferenceisgivenby0γanditsatisfies01γ<.
For0JγγConsideringthephaseofthejammingpartisdifferentfromthatofSARimages,γinequation(26)willbesmaller.
Ineffect,theinputjammingtosignalratio(JSR)inarealscenarioismuchlargerthan0dB,andwehave0Jγγ≈.
Thus,thecorrelationofthejammedpixelpairsismainlydeterminedbycorrelationofthejammingparts,andtheeffectofjammingonthecorrelationwillbemoreprominent,leadingtoevensmallervalues.
Thecorrelationmap,asthemapofcorrelationcoefcientsextractedfromtheInSARdata,isthebestindicatorofthequalityoftheresultantphasedata.
AccordingtotheparameterslistedinTablesIandII,agroundareaisestablishedinoursimulation.
AsshowninFig.
5(a),thecorrelationcoefficientsofthegroundimagewithoutjammingaregreaterthan0.
9.
Forthecasewithjamming,asinglecircularlymovingcornerreflectorisplacedatthecenterofthescene,andtheinputJSRis35dB.
AsshowninFig.
5(b),thecorrelationvalueswithinthejammedareaisfarlessthanthosewithoutjamming.
Inthiscase,afailureoftheunwrappingprocessisinevitable,andwewillnotbeabletoobtainthecorrectelevationinformationoftheterrain.
C.
JammingEffectonElevationEstimationDEM,asadigitalmodelor3Drepresentationofaterrain'ssurface,iscreatedbyphaseunwrappingandinversion[23].
TheaccuracyofDEMandDEM-derivedproductsmainlydependsonphaseerrorscausedbyphaseinterferences.
ThemathematicalformulationforDEMerrorsisderivedinthissubsectionbyexploitingthegeneralrelationshipbetweenDEMandtheinterferometricphase.
Aftertopographicphaseunwrapping,thesensitivityofDEMdeflection(h0)ontopographicphase(φ0)canbedescribedas:04sinBhRφπλθ⊥0=0(27)whereB⊥denotesthebaselinecomponentperpendiculartotheviewline,0RistherangebetweenthetargetandtheSARmasterantenna,andθrepresentstheviewingangleofthetarget[23].
FortheheightofthetopographyisapproximatedbyDEM,theelevationerrorforeachpixelcausedbyphasejammingisexpressedas0sin4RhBεελθφπ⊥=(28)Accordingtothepositionofjamming,therealphaseofthejammedpixelisgivenby()4MSrealRRπλ=(29)Therefore,thephaseerrorforthejammedpixelisexpressedas[]2211()()IFrealmasanMSrnttRRεπφθθλ+∞=∞′′∑(30)AstheorderoftheBesselfunction,nalsorepresentsadifferentazimuthposition,anditisrelatedtotheslowtimeatby12aaKtnπω=(31)Substituting(30)and(31)into(28),wehave[]21sin2112()()4cos()MaamasaMSRrKthttBRRελθππθθπθαλω′′=(32)where0MRR=(32a)cos()BBθα⊥=(32b)From(32),weseethattheDEMerrordependsonnotonlysomesystemparameters,suchasthebaselineB,wavelengthλ,thelookangleθandtheinclinationofthebaselineα,butalsotherotationradius,locationofthereflector,andtherotationalangularvelocityω.
Thederivedelevationerrorsvarywiththechangeofazimuthpositions,asshowninFig.
6.
Theelevationerrorwithdifferentrotationalangularvelocitiesisalsopresentedthere.
ThemaximumelevationerrorisrelatedtotherelativepositionofthestrongscattererandtheInSARantennas,whiletheminimumelevationerrordependsontheslowtimeat.
Withco-registrationerrorduetolowcorrelationconsidered,theDEMerrorwillbelargerthanthecurrentresult.
Throughourtheoreticalanalysis,wecanseethatthecircularlymovingstrongscattererswillproducevaryingphasenoisealongtheazimuthdirectionandreducethecorrelationoftwoSLCimages,bothofwhichwillincreasetheerrorsoftheunwrappedphase.
TheunwrappedphasewiththepropagatedphaseerrorshasadirectimpactontheprecisionofDEM.
AlltheseshowthatthecircularlymovingstrongscattererisaverypromisingjammingmethodinthefieldofInSARelectronicwarfare.
IV.
SIMULATIONANDANALYSISTheaforementionedsectionshaveanalyzedthejammingeffectsoninterferometricphase,correlation,andelevationestimation.
Inwhatfollows,todemonstratetheperformanceoftheproposedmethod,simulationresultsareprovidedbasedontheTerra-SARsystem.
Thecornerreflector,asatypeofstrongscatterer,isusedinoursimulation.
Thecoverageanddensityofcircularlymovingstrongscatterersarealsodiscussedindetail.
A.
JammingEffectsonImagingandInterferometryInthispart,weanalyzethejammingeffectscausedbythecircularlymovingcornerreflector.
Withoutlossofgenerality,acircularlymovingcornerreflectorisplacedatthecenterofthescene,asshowninFig.
1(a)and(b).
Assumethatthesizeofthecornerreectorislargeenoughtoreach35dBoftheinputJSR[15].
Toremovetheeffectoftopographyoninterferometricprocessing,aflatterrainwithanareaof1424m*892m(groundrangeandazimuthdirection)isconsidered.
ParametersofthecircularlymovingcornerreflectorarelistedinTableIandthoseforthesystemandthescenearelistedinTablesIIandIII,respectively.
Toacquirethenalterrainelevationwithjamming,theprocessingprocedureofInSARinvolvesechosimulation[24],RDimaging[19],relevantregistration[22],[25],interferometry[2],[3],phasefiltering[26],phaseunwrapping[26],[27]andelevationinversion[2],[4].
Sinceechosignalsfromtheoriginalsceneandthecornerreflectorarereceivedbytheantennassimultaneously,simulationoftheSARechosignalswithinterferenceisfirstperformed.
ThetwoSLCimagesareproducedthroughtheRange-Doppleralgorithm.
Withoutlossofgenerality,onlythemasterimageisshowninFig.
7(a).
Clearly,thejammingoutputinthemasterimage,shownaspointseriesalongazimuth,agreeswithequation(15).
Throughco-registrationandcomparingbothcompleximages,theinterferometricphasewithjammingisobtainedanddepictedinFig.
7(b).
Themultiplediscretelinesalongtheazimuthdirectionarecausedbythepointpairs.
Ontheonehand,thephasenoiseispartlyinducedbyphaseerrors,asshownin(30).
Ontheotherhand,thelowcorrelationofthepointpairsproducesmorephasenoise,whichisdepictedin(26).
Astheinterferometricphaseiswrappedintotheinterval[],ππ,itmustbeunwrappedbeforeconvertingittoelevationresult.
Afterphasefiltering,theunwrappedphaseincludingthejammingeffectisobtainedbyusingthebranch-cutphaseunwrappingmethod[23],[24],asshowninFig.
7(c).
Thejamminglineisdistributedalongtheazimuthdirection.
Furthermore,thefailureofphaseunwrappingcanbeobservedintherightpartofthefigure.
Finally,DEMisproducedaccordingtothegeometricrelationshipofthescene.
Toshowthejammingeffectsmoreclearly,theDEMbeforeandafterjammingarerespectivelyshowninFig.
8(a)and(b).
TheDEMwithoutjammingisdisplayedasaflatterrain,whilethejammedoneshowsseriouselevationerrors.
InFig.
8(b),theelevationerrorsarecomposedofthreeparts.
Thefirstpart,describedin(32),isderivedfromphaseerrorsduetothepointseries.
Thesecondpartisduetothelowcorrelationofthepointpairs.
Moreover,thefailureofunwrappingcanresultinerrorsintherightpartofthefigure.
Itagaindemonstratestheeffectivenessoftheproposedjammingmethod.
B.
CoverageAnalysis1)InAzimuth:Theimagingoutputduetojammingisshownaspointseriesorghostpointssincetheechoesspreadoveranumberofazimuthcells.
Theexpression(15)appearstoshowthatthenumberofpairedechoesisinfiniteintheory.
However,[]04()/naJrtπλwillapproachtozerowhennincreases.
ThepointseriesbeyondtheDopplerbandwidthwillbefoldedover.
AccordingtoCarson'srule[28],thenumberofthepairedechoesis088()5sin5aNrtrππθλλ33)Accordingto(15),thespacingx0betweenthoseazimuthpointscanbederivedas[20]124MavRxKvωωλππ0==(34)Fig.
9showstheinfluenceofangularvelocityonazimuthspacing,withcorrespondingparameterslistedinTableIandTableII.
Clearly,thespacingx0willbelargerasangularvelocityincreases.
Then,theazimuthcoverageofjammingcanbeobtainedbycombining(33)and(34)52sin4MaRLxNrvλωθπ=0=+(35)Equation(35)tellsusthattheazimuthcoverageofthejammingdependsonmanyparameters,includingr,ω,λ,MR,v,andθ.
Largerradiusrandangularvelocityωresultinalargerazimuthjammingcoverage,asshowninFig.
10(a)and(b).
InFig.
10(c),thejammingcoveragealongazimuthdoesn'tvaryoverazimuthtimefordifferentradiiandangularvelocities.
Itprovesthevalidityoftheapproximationin(33).
2)Inrange:Accordingto(15),therangecoverageofjammingisdeterminedbythesincfunctionrelatedtothefasttime.
ConsideringtheRCM(RangeCellMigration)causedbythecircularlymovingcornerreflector,(15)changesto[][]{}222000_200012()sin()2(,)sinc()244exp()sincexp()22aamamoutraPLrrMMMnaaamanMarryvtxttJttTTBtRcRrnxjRJrtBtjntRKvωθθππωθθλλπ+∞=∞′≈+′∑(36)Clearly,in(36),thejammingisspreadoverseveralrangecellsintherangedirectionandtherangecoverageofjammingcanbeapproximatedas2sinrrLrρθ≈+(37)whererρisrangeresolutionoftheInSARsystem.
Sotherangecoverageofjammingisdeterminedbyrρ,randθ.
Fortypicalparameters(1mr=,30θ=°,0.
03125mλ=,15πrad/sω=,545.
1kmMR=,7604m/sv=,130MHzrB=),wehave2.
2660kmaL=and2.
1538mrL=,i.
e.
,acircularlymovingcornerreflectorwitharadius1mandanangularvelocity15πrad/swillcreateajammingareaof2.
2660km2.
1538m*,asshowninFig.
7(a).
Toincreasethesizeofthejammingarea,thecircularlymovingcornerreflectorsshouldbespacedwiththeazimuthgridofaLandtherangeintervalofrL.
Sothesizeofsuchajammingarraywilldependontherequiredjammingcoverageandthesizeoftheprotectedscenes.
Indesigningsuchasystem,weshouldalsobearinmindthatthejammingintensityisrelatedtothebackscatteringcoefficientsofthecornerreflectorandthespacingx0.
V.
CONCLUSIONSInthispaper,anInSARjammingmethodusingcircularlymovingstrongscatterershasbeenproposed.
ThesescatterersareplacedinthecenterofthesceneandcancauseseriouserrorsintheelevationmeasurementresultsofanInSARsystem.
1)Withtheproposedjammingmethod,theimagingresultswillincludepairedechoesalongtheazimuthdirectionandtheresultantphaseinterferenceofthepairedechoescannotbeoffsetcompletelybycomparingthetwoSLCimages.
2)TheproposedmethodwillreducethecorrelationofthetwoSLCimages.
Afterinterferometry,thegeneratedphasenoisevariesalongtheazimuthdirectionandcancauseseriouserrorstotheinterferometricphaseoftherealscene.
3)Sincethephasebiasoftheinterferencecannotbefilteredoutbythephasefilter,itfurtherincreasesthephaseerrorsintheprocessofphaseunwrappingandevenleadstofailureofthephaseunwrappingoperation.
4)TheDEMproducedwiththeproposedjammingmethodcontainsseveralerrors:phasebiasduetojamming,reducedcorrelationduetojamminganderrorpropagationinphaseunwrapping.
AsalsoshownbyoursimulationresultsbasedontheTerra-SARsystem,theproposedmethodcaneffectivelyjamtheInSARsystemandshowsgreatpromiseinthefieldofelectronicwarfare.
Furthermore,thisjammingmethodalsorevealsaweakpointofcurrentInSARsystems,whichprovidesastartingpointforfurtherimprovingtheperformanceandrobustnessofInSARsystemsinthefuture.
APPENDIXAInthispart,theeffectofapproximationontheaccuracyof0()artisanalyzed.
Accordingto(11),0()artcanberewrittenas22220000()()sinaaaMMryvtxvtxrtrRRθ+==+(A.
1)Considering0aMvtxR,wehave0()sinartrθ≈.
Theapproximationerrorof0()artcanbederivedas2200011sin()sin()()aaMSMrBrtryvtxRRRθαθ0(A.
2)Forsin()sinMrBrBRθαθ≤,theapproximationerrorof0()artisverysmallandcanbeignored.
FortypicalparameterslistedinTableII,theapproximationerrorof0()artisshowninFig.
11.
APPENDIXBThisappendixdiscussesthecorrelationofthejammingpartsinthetwoSARimages.
Accordingto(15)and(16),thepositionsofghostpointsaredeterminedbysincfunctions.
Intheazimuthdirection,thepositionofcorrespondingpointseriesintwoSARimagesdependon()1/2anKωπand()2/2anKωπ.
Then,thetimebiasforthecorrespondingghostpointsisgivenby1211()2aaanTKKωπ0=(B.
1)where212aMvKRλ=,222aSvKRλ=(B.
2)Substituting(B.
1)into(B.
2),wehave()22sin()44aMSnnBTRRvvωλωλθαππ0=≈(B.
3)ThecorrespondingdistancebiasintheSARimagecanbeexpressedassin()4biasanBXvTvωλθαπ=0=(B.
4)Equation(B.
4)showsthattheincreasingωwillresultinlargerdistancebiasalongazimuth.
UsingtheparameterslistedinTableII,theazimuthdistancebiasforthecorrespondingpointseriesatdifferentangularvelocitiesiscalculatedandshowninFig.
12(a).
Suchdistancebiaswilleffectivelyreducecorrelationofthejammingparts.
Intherangedirection,thedistancebiasforthecorrespondingghostpointsalongrangeisdeterminedby()[][]220000sin()sin()2amaasabiasaMSttttYryvtxRRωθθωθθ′′++++≈+(B.
5)Fig.
12(b)showstherangedistancebiasat15rad/sωπ=.
Itwillbelargerwithincreaseoftheradius.
Althoughthedistancebiasalongrangeissmall,consideringtheazimuthdistancebias,thecorrespondingghostpointsintwoSARimagescannotbeco-registeredwitheachother.
Therefore,wehave0Jγγ<.
Moreover,thelowcorrelationofthejammingpartswillreducethecorrelationoforiginalSARimagesandgeneratemorephasenoise.
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r0θXYω000(,,)xyzJ(a)(b)Fig.
1.
Thejammingscenario.
(a)InSARandjammergeometry.
(b)Circularlymovingcornerreflectoronthehorizontalplane.
Range(m)Azimuth(m)-198-990991987354902450-245-490-735ω=55πrad/sω=35πrad/sω=15πrad/sFig.
2.
Rangecompressionresultofjammingwithr=8mandω=55πrad/s,35πrad/s,15πrad/s.
Fig.
3.
Imagingresultduetojamming.
-1665-1110-555055511101665-pi0piAzimuth(m)Phase(rad)Fig.
4.
Phasenoiseofthepairedechoesafterimaging.
(a)(b)Fig.
5.
Comparisonbetweencorrelationmapsbeforeandafterjamming.
(a)Correlationmapbeforejamming.
(b)Correlationmapafterjamming.
-1.
28-0.
96-0.
64-0.
3200.
320.
640.
961.
2800.
10.
20.
30.
40.
5Slowtime(s)Elevationerror(m)ω=15πrad/sω=35πrad/sω=55πrad/sFig.
6.
Elevationerrorcausedbycircularlymovingstrongscattererjamming.
Range(m)Azimuth(m)-621-2072066201425475-476-14262.
2660kmaL=2.
15mrL=Range(m)Azimuth(m)-713-238237712447149-148-446(a)(b)Range(m)Azimuth(m)-713-238237712447149-148-446(c)Fig.
7.
Jammingeffectsoninterferometry.
(a)Masterimagewiththejamming.
(b)Interferometricphase.
(c)Unwrappedphase.
(a)(b)Fig.
8.
ComparisonbetweenDEMsbeforeandafterjamming.
(a)DEMbeforejamming.
(b)DEMafterjamming.
15π25π35π45π55π5101520253035Azimuthspacing(m)Rotationalangularvelocity(rad/s)Fig.
9.
Theimpactofrotationalangularvelocityonazimuthspacingofpointserieswith1mr=.
11.
522.
53234567Radiusofrotation(m)Jammingcoveragealongazimuth(km)15π25π35π45π55π123456789Jammingcoveragealongazimuth(km)Rotationalangularvelocity(rad/s)(a)(b)-1-0.
6-0.
20.
20.
61010203040Azimuthtime(s)Azimuthcoverageofjamming(km)r=1m,ω=15πr=2m,ω=35πr=3m,ω=55π(c)Fig.
10.
Theimpactofdifferentparametersonjammingcoveragealongazimuth(usingtheparameterslistedinTableII).
(a)Theimpactofradiusonthecoverageat15ωπ=.
(b)Theimpactofangularvelocityonthecoveragewith1mr=.
(c)Theimpactofazimuthtimeonthecoverage.
-1-0.
6-0.
20.
20.
618.
28.
48.
68.
89x10-5Azimuthtime(s)Approximationerror(m)Fig.
11.
Theapproximationerrorof0()art.
-202-1010101202-1.
5-1-0.
500.
511.
5nDistancebiasalongazimuth(m)w=15πrad/sw=35πrad/sw=55πrad/s-1-0.
6-0.
20.
20.
61-101x10-4Azimuthtime(s)Distancebiasalongrange(m)(a)(b)Fig.
12.
Distancebiasesforthecorrespondingpointseries.
(a)Theazimuthdistancebiaswithdifferentregularvelocities.
(b)Therangedistancebiasat15rad/sωπ=.
TABLEIPARAMETERSOFTHECIRCULARLYMOVINGCORNERREFLECTORParameterValueRadiusofgyration1mAngularvelocity15πrad/sTheinitialanglevalue0.
3πradTABLEIISIMULATIONPARAMETERSOFTHEINSARSYSTEMParameterValueCarrierfrequency9.
6GHzChirprate131.
310*Hz/sPulseduration107sSamplingfrequency145MHzSensorvelocity7604m/sSquintangle0°Centerslantrange545.
1kmAltitude514.
8kmBaselinelength200mBaselineinclination0°TABLEIIISIMULATIONPARAMETERSOFTHESCENEParameterValueRangepointnumber4096Azimuthpointnumber4096JSR35dB