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InverseSyntheticAperture

RadarImagingwith MATLABAlgorithms

WileySeriesinMicrowaveandOpticalEngineering

KaiChang,Editor TexasA&MUniversity Acompletelistofthetitlesinthisseriesappearsattheendofthisvolume.

InverseSyntheticApertureRadarImaging withMATLABAlgorithms

WithAdvancedSAR/ISARImagingConcepts, Algorithms,andMATLABCodes

SecondEdition

CanerÖzdemir,Phd

MersinUniversity

Mersin,Turkey

Thissecondeditionfirstpublished2021

©2021JohnWiley&Sons,Inc.

EditionHistory

JohnWiley&Sons,Inc.(1e,2012)

Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise, exceptaspermittedbylaw.Adviceonhowtoobtainpermissiontoreusematerialfromthistitleis availableathttp://www.wiley.com/go/permissions.

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MATLAB® isatrademarkofTheMathWorks,Inc.andisusedwithpermission.TheMathWorks doesnotwarranttheaccuracyofthetextorexercisesinthisbook.Thiswork’suseordiscussionof MATLAB® softwareorrelatedproductsdoesnotconstituteendorsementorsponsorshipbyThe MathWorksofaparticularpedagogicalapproachorparticularuseoftheMATLAB® software.While thepublisherandauthorshaveusedtheirbesteffortsinpreparingthiswork,theymakeno representationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsofthiswork andspecificallydisclaimallwarranties,includingwithoutlimitationanyimpliedwarrantiesof merchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysales representatives,writtensalesmaterialsorpromotionalstatementsforthiswork.Thefactthatan organization,website,orproductisreferredtointhisworkasacitationand/orpotentialsourceof furtherinformationdoesnotmeanthatthepublisherandauthorsendorsetheinformationorservices theorganization,website,orproductmayprovideorrecommendationsitmaymake.Thisworkis soldwiththeunderstandingthatthepublisherisnotengagedinrenderingprofessionalservices.The adviceandstrategiescontainedhereinmaynotbesuitableforyoursituation.Youshouldconsult withaspecialistwhereappropriate.Further,readersshouldbeawarethatwebsiteslistedinthiswork mayhavechangedordisappearedbetweenwhenthisworkwaswrittenandwhenitisread.Neither thepublishernorauthorsshallbeliableforanylossofprofitoranyothercommercialdamages, includingbutnotlimitedtospecial,incidental,consequential,orotherdamages.

LibraryofCongressCataloging-in-PublicationData

Names:Özdemir,Caner,author.

Title:InversesyntheticapertureradarimagingwithMATLABalgorithms: withadvancedsar/isarimagingconcepts,algorithms,andmatlabcodes/ CanerOzdemir,PhDMersinUniversity,Mersin,Turkey.

Description:2ndedition.|Hoboken,NJ,USA:Wiley,2021.|Series:Wiley seriesinmicrowaveandopticalengineering|Includesbibliographical referencesandindex.

Identifiers:LCCN2020031216(print)|LCCN2020031217(ebook)|ISBN 9781119521334(cloth)|ISBN9781119521365(adobepdf)|ISBN 9781119521389(epub)

Subjects:LCSH:MATLAB.|Syntheticapertureradar.|MATLAB.

Classification:LCCTK6592.S95O932020(print)|LCCTK6592.S95(ebook) |DDC621.3848/5–dc23

LCrecordavailableathttps://lccn.loc.gov/2020031216

LCebookrecordavailableathttps://lccn.loc.gov/2020031217

CoverdesignbyWiley

Coverimage:CourtesyofCanerÖzdemir,(background)©Maxiphoto/GettyImages Setin9.5/12.5ptSTIXTwoTextbySPiGlobal,Pondicherry,India 10987654321

To: MywifeBetül, Mythreedaughters, Mybrother, Myfather, andthememoryofmybelovedmother

Contents

PrefacetotheSecondEdition xvi

Acknowledgments xix

Acronyms xx

1BasicsofFourierAnalysis 1

1.1ForwardandInverseFourierTransform 1

1.1.1BriefHistoryofFT 1

1.1.2ForwardFTOperation 2

1.1.3IFT 3

1.2FTRulesandPairs 3

1.2.1Linearity 3

1.2.2TimeShifting 3

1.2.3FrequencyShifting 4

1.2.4Scaling 4

1.2.5Duality 4

1.2.6TimeReversal 4

1.2.7Conjugation 4

1.2.8Multiplication 4

1.2.9Convolution 5

1.2.10Modulation 5

1.2.11DerivationandIntegration 5

1.2.12Parseval’sRelationship 5

1.3Time-FrequencyRepresentationofaSignal 5

1.3.1SignalintheTimeDomain 6

1.3.2SignalintheFrequencyDomain 6

1.3.3SignalintheJointTime-Frequency(JTF)Plane 7

1.4ConvolutionandMultiplicationUsingFT 11

1.5Filtering/Windowing 12

1.6DataSampling 14

1.7DFTandFFT 16

1.7.1DFT 16

1.7.2FFT 17

1.7.3BandwidthandResolutions 17

1.8Aliasing 19

1.9ImportanceofFTinRadarImaging 19

1.10EffectofAliasinginRadarImaging 23

1.11MatlabCodes 26

References 33

2RadarFundamentals 35

2.1ElectromagneticScattering 35

2.2ScatteringfromPECs 38

2.3RadarCrossSection 39

2.3.1DefinitionofRCS 40

2.3.2RCSofSimple-ShapedObjects 43

2.3.3RCSofComplex-ShapedObjects 44

2.4RadarRangeEquation 44

2.4.1BistaticCase 46

2.4.2MonostaticCase 49

2.5RangeofRadarDetection 50

2.5.1Signal-to-NoiseRatio 51

2.6RadarWaveforms 53

2.6.1ContinuousWave 53

2.6.2Frequency-ModulatedContinuousWave 56

2.6.3Stepped-FrequencyContinuousWave 59

2.6.4ShortPulse 61

2.6.5Chirp(LFM)Pulse 62

2.7PulsedRadar 69

2.7.1PulseRepetitionFrequency 69

2.7.2MaximumRangeandRangeAmbiguity 69

2.7.3DopplerFrequency 70

2.8MatlabCodes 74

References 82

3SyntheticApertureRadar 85

3.1SARModes 86

3.2SARSystemDesign 87

3.3ResolutionsinSAR 88

3.4SARImageFormation 91

3.5RangeCompression 92

3.5.1MatchedFilter 92

3.5.1.1ComputingMatchedFilterOutputviaFourierProcessing 95

3.5.1.2ExampleforMatchedFiltering 96

3.5.2AmbiguityFunction 99

3.5.2.1RelationtoMatchedFilter 100

3.5.2.2IdealAmbiguityFunction 101

3.5.2.3Rectangular-PulseAmbiguityFunction 102

3.5.2.4LFM-PulseAmbiguityFunction 102

3.5.3PulseCompression 105

3.5.3.1DetailedProcessingofPulseCompression 105

3.5.3.2Bandwidth,Resolution,andCompressionIssuesforLFMSignal 109

3.5.3.3PulseCompressionExample 110

3.6AzimuthCompression 110

3.6.1ProcessinginAzimuth 110

3.6.2AzimuthResolution 116

3.6.3RelationtoISAR 117

3.7SARImaging 118

3.8SARFocusingAlgorithms 118

3.8.1RDA 119

3.8.1.1RangeCompressioninRDA 120

3.8.1.2AzimuthFourierTransform 126

3.8.1.3RangeCellMigrationCorrection 128

3.8.1.4AzimuthCompression 129

3.8.1.5SimulatedSARImagingExample 130

3.8.1.6DrawbacksofRDA 133

3.8.2ChirpScalingAlgorithm 133

3.8.3The ω-kA 133

3.8.4Back-ProjectionAlgorithm 134

3.9ExampleofaRealSARImagery 135

3.10ProblemsinSARImaging 136

3.10.1RangeMigrationandRangeWalk 136

3.10.2MotionErrors 137

3.10.3SpeckleNoise 140

x Contents

3.11AdvancedTopicsinSAR 140

3.11.1SARInterferometry 140

3.11.2SARPolarimetry 142

3.12MatlabCodes 143 References 158

4InverseSyntheticApertureRadarImagingandItsBasicConcepts 162

4.1SARversusISAR 162

4.2TheRelationofScatteredFieldtotheImageFunctioninISAR 166

4.3One-Dimensional(1D)RangeProfile 167

4.41DCross-RangeProfile 172

4.5Two-Dimensional(2D)ISARImageFormation(SmallBandwidth,Small Angle) 176

4.5.1ResolutionsinISAR 180

4.5.1.1RangeResolution 181

4.5.1.2Cross-RangeResolution: 181

4.5.2RangeandCross-RangeExtends 181

4.5.3ImagingMultibouncesinISAR 182

4.5.4SampleDesignProcedureforISAR 185

4.5.4.1ISARDesignExample#1: “AircraftTarget” 189

4.5.4.2ISARDesignExample#2: “MilitaryTankTarget” 193

4.62DISARImageFormation(WideBandwidth,LargeAngles) 197

4.6.1DirectIntegration 198

4.6.2PolarReformatting 201

4.73DISARImageFormation 205

4.7.1RangeandCross-Rangeresolutions 209

4.7.2ADesignExamplefor3DISAR 210

4.8MatlabCodes 217 References 243

5ImagingIssuesinInverseSyntheticApertureRadar 246

5.1Fourier-RelatedIssues 246

5.1.1DFTRevisited 246

5.1.2PositiveandNegativeFrequenciesinDFT 250

5.2ImageAliasing 252

5.3PolarReformattingRevisited 255

5.3.1NearestNeighborInterpolation 255

5.3.2BilinearInterpolation 258

5.4ZeroPadding 260

5.5PointSpreadFunction 264

5.6Windowing 269

5.6.1CommonWindowingFunctions 269

5.6.1.1RectangularWindow 269

5.6.1.2TriangularWindow 269

5.6.1.3HanningWindow 272

5.6.1.4HammingWindow 272

5.6.1.5KaiserWindow 272

5.6.1.6BlackmanWindow 276

5.6.1.7ChebyshevWindow 277

5.6.2ISARImageSmoothingviaWindowing 277

5.7MatlabCodes 280 References 304

6Range-DopplerInverseSyntheticApertureRadarProcessing 306

6.1ScenariosforISAR 306

6.1.1ImagingAerialTargetsviaGround-BasedRadar 307

6.1.2ImagingGround/SeaTargetsviaAerialRadar 309

6.2ISARWaveformsforRange-DopplerProcessing 312

6.2.1ChirpPulseTrain 312

6.2.2SteppedFrequencyPulseTrain 314

6.3DopplerShift’sRelationtoCross-Range 316

6.3.1DopplerFrequencyShiftResolution 317

6.3.2ResolvingDopplerShiftandCross-Range 318

6.4FormingtheRange-DopplerImage 319

6.5ISARReceiver 320

6.5.1ISARReceiverforChirpPulseRadar 320

6.5.2ISARReceiverforSFCWRadar 321

6.6QuadratureDetection 323

6.6.1I-ChannelProcessing 324

6.6.2Q-ChannelProcessing 324

6.7RangeAlignment 326

6.8DefiningtheRange-DopplerISARImagingParameters 327

6.8.1ImageFrameDimension(ImageExtends) 327

6.8.2RangeandCross-RangeResolution 328

6.8.3FrequencyBandwidthandtheCenterFrequency 328

6.8.4DopplerFrequencyBandwidth 328

6.8.5PulseRepetitionFrequency 329

6.8.6CoherentIntegration(Dwell)Time 329

6.8.7PulseWidth 330

6.9ExampleofChirpPulse-BasedRange-DopplerISARImaging 331

6.10ExampleofSFCW-BasedRange-DopplerISARImaging 336

6.11MatlabCodes 339 References 347

7ScatteringCenterRepresentationofInverseSyntheticAperture Radar 349

7.1Scattering/RadiationCenterModel 350

7.2ExtractionofScatteringCenters 352

7.2.1ImageDomainFormulation 352

7.2.1.1ExtractionintheImageDomain:The “CLEAN” Algorithm 352

7.2.1.2ReconstructionintheImageDomain 355

7.2.2FourierDomainFormulation 362

7.2.2.1ExtractionintheFourierDomain 362

7.2.2.2ReconstructionintheFourierDomain 364

7.3MatlabCodes 368 References 382

8MotionCompensationforInverseSyntheticApertureRadar 385

8.1DopplerEffectDuetoTargetMotion 386

8.2StandardMOCOMPProcedures 388

8.2.1TranslationalMOCOMP 389

8.2.1.1RangeTracking 389

8.2.1.2DopplerTracking 390

8.2.2RotationalMOCOMP 390

8.3PopularISARMOCOMPTechniques 392

8.3.1Cross-CorrelationMethod 392

8.3.1.1ExamplefortheCross-CorrelationMethod 394

8.3.2MinimumEntropyMethod 398

8.3.2.1DefinitionofEntropyinISARImages 398

8.3.2.2ExamplefortheMinimumEntropyMethod 399

8.3.3JTF-BasedMOCOMP 402

8.3.3.1ReceivedSignalfromaMovingTarget 403

8.3.3.2AnAlgorithmforJTF-BasedRotationalMOCOMP 404

8.3.3.3ExampleforJTF-BasedRotationalMOCOMP 406

8.3.4AlgorithmforJTF-BasedTranslationalandRotationalMOCOMP 408

8.3.4.1ANumericalExample 410

8.4MatlabCodes 415 References 436

9BistaticISARImaging 440

9.1WhyBi-ISARImaging? 440

9.2GeometryforBi-IsarImagingandtheAlgorithm 444

9.2.1Bi-ISARImagingAlgorithmforaPointScatterer 444

9.2.2BistaticISARImagingAlgorithmforaTarget 448

9.3ResolutionsinBistaticISAR 449

9.3.1RangeResolution 449

9.3.2Cross-RangeResolution 450

9.3.3RangeandCross-RangeExtends 451

9.4DesignProcedureforBi-ISARImaging 452

9.5Bi-IsarImagingExamples 455

9.5.1Bi-ISARDesignExample#1 455

9.5.2Bi-ISARDesignExample#2 457

9.6Mu-ISARImaging 465

9.6.1ChallengesinMu-ISARImaging 467

9.6.2Mu-ISARImagingExample 468

9.7MatlabCodes 472 References 483

10PolarimetricISARImaging 484

10.1PolarizationofanElectromagneticWave 484

10.1.1PolarizationType 485

10.1.2PolarizationSensitivity 486

10.1.3PolarizationinRadarSystems 487

10.2PolarizationScatteringMatrix 488

10.2.1RelationtoRCS 490

10.2.2PolarizationCharacteristicsoftheScatteredWave 491

10.2.3PolarimetricDecompositionsofEMWaveScattering 493

10.2.4ThePauliDecomposition 494

10.2.4.1DescriptionofPauliDecomposition 494

10.2.4.2InterpretationofPauliDecomposition 495

10.2.4.3PolarimetricImageRepresentationUsingPauliDecomposition 496

10.3WhyPolarimetricISARImaging? 497

10.4ISARImagingwithFullPolarization 497

10.4.1ISARDatainLPBasis 497

10.4.2ISARDatainCPBasis 498

10.5PolarimetricISARImages 499

10.5.1Pol-ISARImageofaBenchmarkTarget 499

10.5.1.1The “SLICY” Target 499

10.5.1.2FullyPolarimetricEMSimulationofSLICY 499

10.5.1.3LPPol-ISARImagesofSLICY 500

10.5.1.4CPPol-ISARImagesofSLICY 502

10.5.1.5PauliDecompositionImageofSLICY 503

10.5.2Pol-ISARImageofaComplexTarget 507

10.5.2.1The “MilitaryTank” Target 507

10.5.2.2FullyPolarimetricEMSimulationof “Tank” Target 508

10.5.2.3LPPol-ISARImagesof “Tank” Target 508

10.5.2.4CPPol-ISARImagesof “Tank” Target 510

10.5.2.5PauliDecompositionImageof “Tank” Target 512

10.6FeatureExtractionfromPolarimetricImages 515

10.7MatlabCodes 515

References 529

11Near-FieldISARImaging 533

11.1DefinitionsofFarandNear-FieldRegions 534

11.1.1TheFar-FieldRegion 534

11.1.1.1TheFar-FieldDefinitionBasedonTarget’sCross-RangeExtend 534

11.1.1.2TheFar-FieldDefinitionBasedonTarget’sRangeExtend 535

11.1.2TheNear-FieldRegion 537

11.2Near-FieldSignalModelfortheBack-ScatteredField 537

11.3Near-FieldISARImagingAlgorithms 540

11.3.1 “FocusingOperator” Algorithm 540

11.3.2Back-ProjectionAlgorithm 541

11.3.2.1FourierSliceTheorem 542

11.3.2.2BPAFormulation(3DCase) 543

11.3.2.3BPAFormulation(2DCase) 544

11.4DataSamplingCriteriaandtheResolutions 546

11.5Near-FieldISARImagingExamples 547

11.5.1PointScatterersintheNear-Field:ComparisonofFar-andNear-Field ImagingAlgorithms 547

11.5.2Near-FieldISARImagingofaLargeObject 552

11.5.3Near-FieldISARImagingofaSmallObject 555

11.6MatlabCodes 560

References 569

12SomeImagingApplicationsBasedonSAR/ISAR 571

12.1ImagingSubsurfaceObjects:GPR-SAR 572

12.1.1TheGPRProblem 572

12.1.2B-ScanGPRinComparisontoStrip-MapSAR 577

12.1.3FocusedGPRImagesUsingSAR 577

12.1.3.1GPRFocusingwith ω-kAlgorithm(ω-kA) 579

12.1.3.2GPRFocusingwithBPA 582

12.1.3.3OtherPopularGPRFocusingTechniques 589

12.2Thru-the-WallImagingRadarUsingSAR 590

12.2.1ChallengesinTWIR 591

12.2.2TechniquestoImproveCross-RangeResolutioninTWIR 591

12.2.3TheUseofSARinTWIR 592

12.2.4ExampleofSAR-BasedTWIR 594

12.3ImagingAntenna-PlatformScattering:ASAR 596

12.3.1TheASARImagingAlgorithm 597

12.3.2NumericalExampleforASARImagery 603

12.4ImagingPlatformCouplingBetweenAntennas:ACSAR 605

12.4.1TheACSARImagingAlgorithm 606

12.4.2NumericalExampleforACSAR 609

12.4.3ApplyingACSARConcepttotheGPRProblem 611 References 615

Appendix 619 Index 628

PrefacetotheSecondEdition

Inthefirsteditionofthebook,Itriedtocovermostoftheaspectsofinversesyntheticapertureradar(ISAR)imagingstartingfromFourieranalysistosome advancedISARconceptssuchasrange-DopplerISARprocessingandISARmotion compensationtechniques.Themaingoalwastopresentaconceptualdescription ofISARimageryandtheexplanationofbasicISARresearchtopics.Althoughthe primaryaudiencewouldbegraduatestudentsandotherinterestedresearchersin thefieldsofelectricalengineeringandphysics,Ihopedthatcolleaguesworkingin radarresearchanddevelopmentorinarelatedindustrymightalsobenefitfrom thebook.

Ithasbeenmorethaneightyearssincethepublicationofthefirstedition.Since then,IhavebeenreallygratefulthatIhavereceivedpositiveresponsesfromthe researchersandcolleaguesthatareinterestedand/orinvolvedinradarimaging, andespeciallyISARimaging.Undoubtedly,ISARhasbeengainingmoreattention amongresearchers,scholars,andengineersasemergingnewdevelopmentsin ISARresearchhavebeenreportedbyvariouscolleaguesdaybyday.

Inthissecondeditionofthebook,Ihavetriedtoincludetherecentprogress madeinISARimagingresearchandalsogiveinsightstomoreadvancedconcepts. Therefore,inthiseditionofthebook,Ihavemadethefollowingalterationsand additions:

• Allthechaptersinthefirsteditionhavebeenrevisedincludingallthetexts, equations,andfigureswithsomeadditions.Typosinthefirsteditionhavealso beencorrected.

• Chapter3thatisdevotedtotheissuesofsyntheticapertureradar(SAR)hasbeen extendedtoincludetheSARfocusing/processingalgorithmssuchasrangeDoppleralgorithm(RDA),back-projectionalgorithm(BPA)andfrequencywavenumberalgorithm(ω-kA).TheMatlabcodesforthesealgorithmsare beingprovidedwiththeassociatednumericalexamples.Briefexplanationsof

otherSARfocusing/processingalgorithmsincludingchirpscalingalgorithm (CSA)andphaseshiftalgorithm(PSA)havealsobeenmentioned.

• InChapters4,5,7,and12wherewehandlevariousaspectsofISARimaging technology,newscatteredfieldrawdat aandthecorrespondingISARimages thataremorevisuallyattractivearep resentedtogetherwiththeassociated Matlabcodesthatcanbeusedtogeneratetheseimages.

• Atotalofthreenewchaptershavebeenwrittentocoverthetopicsthatwerenot consideredinthefirsteditionandalsotoincludemoredetailedsubjectsofISAR imagingtobeabletoreflecttherecentresearchstudies.Thesearelistedbelow:

– The “BistaticISAR(Bi-ISAR)Imaging” conceptiscoveredinChapter9.While theISARimagingalgorithmspresentedinpreviouschaptersarebasedon monostaticusageofISARimaging,weintroducetheformulationofISAR imagingforthebistaticusagesbypresentingkeyaspectssuchasresolutions inrange/cross-rangedirectionsandusagelimitations.Also,extensionofBiISARtomultistaticISAR(Mu-ISAR)imagingisderivedwiththeassociated Matlabexamples.AgeneralassessmentofBi-ISARandMu-ISARimaging toconventionalmonostaticISARimagingisbeingmadethroughoutthechapterbycomparingtheoutcomesofquantitativemetricsandgivingtheconcludingstatementsabouttheiradvantagesanddisadvantagesbasedonthese measurableevaluations.

– InChapter10,wehaveaddedanewandexcitingresearchtopicofISARcalled “PolarimetricISARImaging.” AsthetraditionalISARimagingalgorithmsare basedonlyonasinglepolarizationofthebackscatteredelectricfield,wedemonstrateinthischapterthatveryexcitingfeaturesofthetargetcanbe extractedwiththeuseofotherpossiblepolarizationsforthereflectedwave. PolarizationdecompositiontechniquesarebeingintroducedandPauli decompositionschemeistakenasthetooltobeappliedtothedifferentpolarizationISARimagesinthisbook.TheformulationandtheusageofPauli decompositiontechniquearepresentedtogetherwithitsMatlabcodes.Variousrealisticsimulationexamplesbasedonlinearpolarization,circularpolarization,andalsoPaulidecompositionaregiventogetherwithobtained polarimetricISARimages.Ithasbeendemonstratedthroughtheexamples thatpolarizedISARimagesdefinitelyincreasetherecognitionandclassificationoftargetsbyprovidingincreasednumberofextractedtargetfeatures.

– Thankstotherecentdevelopmentinthemicrowavecircuittechnologyand antennadesign,ISARimagingalgorithmshavebeenstartedtobeusedinthe near-fieldregion.Therefore,Ihaveaddedanewpartentitled “Near-field ISARimaging ” asChapter11.Thenear-fieldISARimagingalgorithmsare beingintroduced.Twoofthemcalled “Focusingoperator” andthebackprojectionbasedfocusingalgorithmsaregivenbypresentingtheirtheoretical formulationandalgorithmstepstogetherwithcorrespondingMatlabcodes.

Also,numericalandmeasuredexamplesbasedonrealscenariosarebeing shared.

• InChapter12inwhichsomeexamplesbasedonSAR/ISARimagingtechnologiesareprovided,IhavepreviouslyintroducedalgorithmscalledantennaSAR (ASAR)andantennacouplingSAR(ACSAR)astheuniqueradarimagingalgorithmstoimageantennamountedonaplatform-to-radarreceiverinteraction overthetargetandtoimageplatformcouplingovertheantennasmounted onatarget,respectively.Inthiseditionofthebook,Ihaveaddedsomenew applicationssuchas ground-penetratingradar (GPR)and through-the-wallimagingradar (TWIR)thatalsomakeuseofSAR/ISARimagingalgorithms.MeasuredexamplesofGPRandTWIRradarimagesareprovidedtodemonstratehow SAR/ISARimagingalgorithmscanbeeffectivelyusedinsomepopularradar imagingapplications.

Ihopethat,withtheneweditionofthebook “InverseSyntheticApertureRadar ImagingwithMATLABAlgorithms,” thereaderwouldbenefitmoreintermsof abovementionednewISARimagingtopicsandalsofromtheMatlabcodesprovidedattheendofchapters.

AllMATLABfilesmaybeaccessedonthefollowingFTPsite:ftp://ftp.wiley. com/public/sci_tech_med/inverse_synthetic.

CanerÖzdemir

Mersin,October2020

Acknowledgments

Iwouldliketoaddressspecialthankstothepeoplebelowfortheirhelpandsupportduringthepreparationofthisbook.First,Iamthankfultomywife,Betüland mythreechildrenfortheirpatienceandcontinuoussupportwhilewritingthis book.IamverygratefultoDr.HaoLing,EmeritusProfessorinEngineeringof theUniversityofTexasatAustinforbeingavaluablesourceofknowledge,ideas, andalsoinspirationthroughoutmyacademiccarreer.Hehasbeenagreatadvisor sinceImethim,andhisguidanceonscientificresearchispricelesstome.

Iwouldliketoexpressmysincerethankstomyformergraduatestudents;Dr. ŞevketDemirci,Dr.EnesYiğit,Dr.BetülYılmaz,Dr.DenizÜstün,ÖzkanKırık, andDr.HakanIşıkerwhohavehelpedcarryingoutsomeoftheresearchpresented inthisbook.IwouldalsoliketothankmygraduatestudentRasheedKhankanfor hishelpinpreparingreferences.

Lastbutnotleast,IwouldliketoconveymyspecialthankstoDr.KaiChangfor invitingmetowritethefirstandthensecondeditionofthebook.Withouthiskind offer,thisbookprojectwouldnothavebeenpossible.

CanerÖzdemir

Acronyms

1DOne-dimensional

2DTwo-dimensional

3DThree-dimensional

ACSARAntennacouplingsyntheticapertureradar

ADCAnalog-to-digitalconverter

ANNArtificialneuralnetwork

ASARAntennasyntheticapertureradar

ATCAutomatictargetclassification

ATRAutomatictargetrecognition

Bi-ISARBistaticinversesyntheticapertureradar

BPABack-projectionalgorithm

CADComputeraideddesign

CDFCumulativedensityfunction

CFARConstantfalsealarmrate

COContrastoptimization

Co-polCo-polarization

CPCircularpolarization

Cross-polCross-polarization

CSAChirpscalingalgorithm

CWContinuouswave

DCRDihedralcornerreflectors

DFTDiscreteFouriertransform

DTVDigitaltelevision

EFIEElectricfieldintegralequation

EMElectromagnetic

ESMExplodingsourcemodel

FMFrequencymodulated

FMCWFrequencymodulatedcontinuouswave

FTFouriertransform

GOGeometricoptics

GPRGround-penetratingradar

GPSGlobalpositioningsystem

GWNGaussianwhitenoise

HHorizontal

HHHorizontal–horizontal

HSAHyperbolicsummationalgorithm

HVHorizontal–vertical

IInphase

IDFTInversediscreteFouriertransform

IFTInverseFouriertransform

IMUInertialmeasurementunit

InSARInterferometricSAR

ISARInversesyntheticapertureradar

JTFJointtime-frequency

KBKbytes

KMAKirchhoffmigrationalgorithm

LLeft

LFMLinearfrequencymodulated

LFMCWLinearfrequencymodulatedcontinuouswave

LHCPLeft-handcircularpolarized

LHEPLeft-handellipticallypolarized

LLLeft–left

LOSLineofsight

LPLinearpolarization

LRLeft–right

MBMbytes

MDAMap-driftautofocus

MFIEMagneticfieldintegralequation

MIMOMultiple-inputmultiple-output

MOCOMPMotioncompensation

Mu-ISARMulti-staticinversesyntheticapertureradar

PECPerfectelectricconductor

PGAPhasegradientautofocus

P-ISARPassiveinversesyntheticapertureradar

POPhysicaloptics

PolSARPolarimetricsyntheticapertureradar

PPPProminentpointprocessing

PRFPulserepetitionfrequency

PRIPulserepetitioninterval

PSDPowerspectraldensity

PSFPointspreadfunction

PSLRPeak-to-sideloberatio

PSMAPhase-shiftmigrationalgorithm

PSRPoint-spread-response

QQuadrature

QDQuadraduredetection

RRight

RCMRangecellmigration

RCMCRangecellmigrationcorrection

RCSRadarcrosssection

RDARange-doppleralgorithm

RFRadiofrequency

RGBRedgreenblue

RHCPRight-handcircularpolarized

RHEPRight-handellipticallypolarized

RLRight–Left

RLOSRadarlineofsight

RRRight–right

RxReceiver

[S]Polarizationscatteringmatrix

SACShiftandcorrelate

SARSyntheticapertureradar

SBRShootingandbouncingray

SFCWSteppedfrequencycontinuouswave sincSinuscardinalis

SNRSignal-to-noiseratio

SPUSignalprocessingunit

STFTShort-timeFouriertransform

TCRTrihedralcornerreflector

TFDSTime-frequencydistributionseries

TWIRThrough-the-wallimagingradar

TWRThrough-the-wallradar

TxTransmitter

VVertical

VHVertical–horizontal

VNAVectornetworkanalyzer

VVVertical–vertical

ω-kAFrequency-wavenumberalgorithm

xxii Acronyms

BasicsofFourierAnalysis

1.1ForwardandInverseFourierTransform

Fouriertransform(FT)isacommonandusefulmathematicaltoolthatisutilized ininnumerousapplicationsinscienceandtechnology.FTisquitepracticalespeciallyforcharacterizingnonlinearfunctionsinnonlinearsystems,analyzingrandomsignals,andsolvinglinearproblems.FTisalsoaveryimportanttoolinradar imagingapplicationsasweshallinvestigateintheforthcomingchaptersofthis book.BeforestartingtodealwiththeFTandinverseFouriertransform(IFT),a briefhistoryofthisusefullinearoperator,anditsfoundersarepresented.

1.1.1BriefHistoryofFT

JeanBaptisteJosephFourier,agreatmathematician,wasbornin1768,Auxerre, France.Hisspecialinterestinheatconductionledhimtodescribeamathematical seriesofsineandcosinetermsthatcouldbeusedtoanalyzepropagationanddiffusionofheatinsolidbodies.In1807,hetriedtosharehisinnovativeideaswith researchersbypreparinganessayentitledas OnthePropagationofHeatinSolid Bodies.TheworkwasexaminedbyLagrange,Laplace,Monge,andLacroix. Lagrange’soppositionscausedtherejectionofFourier’spaper.Thisunfortunate decisioncostcolleaguestowaitfor15moreyearstomeethisremarkablecontributionstomathematics,physics,andespeciallyonsignalanalysis.Finally,his ideaswerepublishedthruthebook TheAnalyticTheoryofHeat in1822 (Fourier1955).

DiscreteFouriertransform(DFT)wasdevelopedasaneffectivetoolincalculatingthistransformation.However,computingFTwiththistoolinthenineteenth centurywastakingalongtime.In1903,C.Rungehasstudiedontheminimization

InverseSyntheticApertureRadarImagingwithMATLABAlgorithms:WithAdvancedSAR/ISAR ImagingConcepts,Algorithms,andMATLABCodes,SecondEdition.CanerÖzdemir. ©2021JohnWiley&Sons,Inc.Published2021byJohnWiley&Sons,Inc.

2 1BasicsofFourierAnalysis

ofthecomputationaltimeofthetransformationoperation(Runge1903).In1942, DanielsonandLanczoshadutilizedthesymmetrypropertiesofFTtoreducethe numberofoperationsinDFT(DanielsonandLanczos1942).Beforetheadventof digitalcomputingtechnologies,JamesW.CooleyandJohnW.Tukeydevelopeda fastmethodtoreducethecomputationtimeofDFToperation.In1965,they publishedtheirtechniquethatlateronhasbecomefamousasthefastFourier transform(FFT)(CooleyandTukey1965).

1.1.2ForwardFTOperation

TheFTcanbesimplydefinedasacertainlinearoperatorthatmapsfunctionsor signalsdefinedinonedomaintootherfunctionsorsignalsinanotherdomain.The commonuseofFTinelectricalengineeringistotransformsignalsfromtime domaintofrequencydomainorvice-versa.Moreprecisely,forwardFTdecomposesasignalintoacontinuousspectrumofitsfrequencycomponentssuchthat thetimesignalistransformedtoafrequencydomainsignal.Inradarapplications, thesetwoopposingdomainsareusuallyrepresentedas “spatial-frequency(or wave-number)” and “range(distance).” SuchuseofFTwillbeoftenexamined andappliedthroughoutthisbook.

TheforwardFTofacontinuoussignal g(t)where ∞ < t < ∞ isdescribedas

where representstheforwardFToperationthatisdefinedfromtimedomainto frequencydomain.

ToappreciatethemeaningofFT,themultiplyingfunctionexp( j2π ft)and operators(multiplicationandintegration)ontherightofsideofEq.1.1should beexaminedcarefully:Thetermexp j2π f i t isacomplexphasorrepresentation forasinusoidalfunctionwiththesinglefrequencyof “fi. ” Thissignaloscillates withthesinglefrequencyof “fi” anddoesnotcontainanyotherfrequencycomponent.Multiplyingthesignalininterest, g(t)withexp j2π f i t providesthesimilaritybetweeneachsignal,thatis,howmuchof g(t)hasthefrequencycontentof “fi. ” Integratingthismultiplicationoveralltimeinstantsfrom ∞ to ∞ willsum the “fi” contentsof g(t)overalltimeinstantstogive G(fi)thatistheamplitudeof thesignalattheparticularfrequencyof “fi. ” Repeatingthisprocessforallthefrequenciesfrom ∞ to ∞ willprovidethefrequencyspectrumofthesignalrepresentedas G(f).Therefore,thetransformedsignalrepresentsthecontinuous spectrumoffrequencycomponents;i.e.representationofthesignalin “frequency domain.”

1.2FTRulesandPairs 3

1.1.3IFT

ThistransformationistheinverseoperationoftheFT.IFT,therefore,synthesizes afrequency-domainsignalfromitsspectrumoffrequencycomponentstoits timedomainform.TheIFTofacontinuoussignal G(f)where ∞ < f < ∞ is describedas

wheretheIFToperationfromfrequencydomaintotimedomainisrepresentedby 1 .

1.2FTRulesandPairs

TherearemanyusefulFourierrulesandpairsthatcanbeveryhelpfulwhenapplyingtheFTorIFTtodifferentreal-worldapplications.Wewillbrieflyrevisitthem toremindthepropertiesoftheFTtothereader.ProvidedthatFTandIFTare definedasinEqs.1.1and1.2,respectively,FTpairisdenotedas

andthecorrespondingalternativepairisgivenby

Basedonthesenotations,thepropertiesofFTarelistedbrieflybelow.

1.2.1Linearity

If G(f)and H(f)aretheFTsofthetimesignals g(t)and h(t),respectively,thefollowingequationisvalidforthescalars a and b.

Therefore,theFTisalinearoperator.

1.2.2TimeShifting

Ifthesignalisshiftedintimewithavalueof to,thenthecorrespondingfrequency signalwillhavetheformof

1.2.3FrequencyShifting

Ifthetimesignalismultipliedbyaphasetermofexp j2π f o t ,thentheFTofthis timesignalisshiftedinfrequencyby fo asgivenbelow

1.2.4Scaling

Ifthetimesignalisscaledbyaconstant a,thenthespectrumisalsoscaledwiththe followingrule

1.2.5Duality

Ifthespectrumsignal G(f)istakenasatimesignal G(t),then,thecorresponding frequencydomainsignalwillbethetimereversalequivalentoftheoriginaltime domainsignal, g(t)as

1.2.6TimeReversal

Ifthetimeisreversedforthetime-domainsignal,thenthefrequencyisalso reversedinthefrequencydomainsignal.

1.2.7Conjugation

Iftheconjugateofthetime-domainsignalistaken,thenthefrequency-domain signalconjugatedandfrequency-reversed.

1.2.8Multiplication

Ifthetime-domainsignals, g(t)and h(t)aremultipliedintime,thentheirspectrum signals G(f)and H(f)areconvolvedinfrequency.

1.3Time-FrequencyRepresentationofaSignal 5

1.2.9Convolution

Ifthetime-domainsignals, g(t)and h(t)areconvolvedintime,thentheirspectrum signals G(f)and H(f)aremultipliedinthefrequencydomain.

1.2.10Modulation

Ifthetime-domainsignalismodulatedwithsinusoidalfunctions,thenthefrequency-domainsignalisshiftedbytheamountofthefrequencyatthatparticular sinusoidalfunction.

1.2.11DerivationandIntegration

Ifthederivativeorintegrationofatime-domainsignalistaken,thenthecorrespondingfrequency-domainsignalisgivenasbelow.

1.2.12Parseval’sRelationship

AusefulpropertythatwasclaimedbyParsevalisthatsincetheFT(orIFT)operationmapsasignalinonedomaintoanotherdomain,theirenergiesshouldbe exactlythesameasgivenbythefollowingrelationship.

1.3Time-FrequencyRepresentationofaSignal

WhiletheFTconceptcanbesuccessfullyutilizedforthestationarysignals,there aremanyreal-worldsignalswhosefrequencycontentsvaryovertime.Tobeableto displaythesefrequencyvariationsovertime;therefore,jointtime–frequency(JTF) transforms/representationsarebeingused.

Figure1.1 Thetime-domainsignalof “prince” spokenbyalady. 6 1BasicsofFourierAnalysis

1.3.1SignalintheTimeDomain

Theterm “timedomain” isusedwhiledescribingfunctionsorphysicalsignals withrespecttotimeeithercontinuousordiscrete.Thetime-domainsignalsare usuallymorecomprehensiblethanthefrequency-domainsignalssincemostof thereal-worldsignalsarerecordedanddisplayedversustime.Commonequipmentistoanalyzetime-domainsignalsisthe oscilloscope.InFigure1.1,atimedomainsoundsignalisshown.Thissignalisobtainedbyrecordingofanutterance oftheword “prince” byalady.Bylookingattheoccurrenceinstantsinthe x-axis andthesignalmagnitudeinthe y-axis,onecananalyzethestressoftheletters insidetheword “prince.”

1.3.2SignalintheFrequencyDomain

Theterm “frequencydomain” isusedwhiledescribingfunctionsorphysicalsignalswithrespecttofrequencyeithercontinuousordiscrete.Frequency-domain representationhasbeenproventobeveryusefulininnumerousengineeringapplicationswhilecharacterizing,interpreting,andidentifyingsignals.Solvingdifferentialequations,analyzingcircuits,signalanalysisincommunicationsystemsare fewamongmanyotherswherefrequency-domainrepresentationismuchmore

domain signal

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