Principles of Modern Radar - Volume 2 1891121537

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6.8 Autofocus 251Range (m)50403020100−10−20Range (m)50403020100−10−20FIGURE 6-21Example SARimagery [15]exhibiting phaseerror effects: (a) Noerror. (b) Quadraticerror. (c) Sinusoidalerror. (d) Randomerror.−30−30−40−50−50−40−30−20−10010Cross-Range (m)(a)20304050−40−50−50−40−30−20−10010Cross-Range (m)(b)203040505050404030302020Range (m)100−10Range (m)100−10−20−20−30−30−40−50−50−40−30−20Cross-Range (m)(c)−1001020304050−40−50−50−40−30−20Cross-Range (m)(d)−1001020304050the fact that phase errors occuring at the radar result in spatially invariant effects in thecorresponding image. This spatial invariance is a strong advantage because it allows asignificant amount of averaging to be performed over the scene to obtain a good estimateof the phase error. For cases in which the artifacts are localized, the image can be chippedinto small regions and analyzed separately. This is the case for stripmap SAR, for example.Autofocus techniques are characterized as being either parametric or nonparametric.The former operate by estimating the values associated with a phase error model, such asthe quadratic coefficent β or some other polynomial fit, while the latter do not. Parametrictechniques are generally good for correcting low-frequency errors, and nonparametricapproaches are well-suited to removing random errors. There is some degree of overlapbetween the two approaches, but it is reasonable to include both in a practical SARimage formation processor since they are complementary. A parametric algorithm is firstapplied to remove the quadratic phase component and improve focus. This is followed bya nonparametric technique whose purpose is to remove the random phase error to improveimage contrast. We now give an example of each type.
252 CHAPTER 6 Spotlight Synthetic Aperture RadarFIGURE 6-22Steps for the phasedifference autofocusalgorithm. (Adaptedfrom Carraraet al. [4].)Range-compressedimage domainDivide into two equalsubaperturesConjugateMultiplyFourier transformMagnitudeSum over rangeFind cross-range peakof cross-correlationFind QPE coefficient6.8.1 Phase Difference AutofocusPhase difference autofocus (PDA) is a noniterative parametric technique for estimatingthe quadratic phase error present in a SAR image [4]. The procedure is diagrammedin Figure 6-22. If we consider a complex-valued SAR image to be our source of data,we first inverse Fourier transform in the cross-range dimension. This new domain correspondsroughly to the slow-time (or azimuth or pulse) domain of the data and is the inputfor PDA. The data are then divided into a pair of equal-duration slow-time blocks. Theblocks are known as subapertures because their Fourier transforms should yield the sameimagery [22], having coarser cross-range resolution and independent speckle realizations.Each subaperture now contains half of the original quadratic phase. These new phaseterms can be approximated by a linear phase plus a residual quadratic phase. The linearcomponent is proportional to the quadratic phase error coefficient β and causes thesubaperture-based images to shift in opposite directions. The residual quadratic phasecauses each subaperture image to be slightly defocused. PDA operates by cross-correlatingthe image pair and measuring the offset of the resulting peak to estimate β.The next step is to multiply the subapertures after having first taken the complex conjugateof one of them. Recall from Table 6-1 that the operation of conjugate multiplicationin one Fourier domain is the same as correlation in the other. The data are then Fouriertransformed giving the cross-range cross-correlation function evaluated at each range bin.We then take the magnitude of the cross-correlation and then average over all ranges toobtain a single estimate of the subaperture image cross-correlation function. The offset of
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Principles of Modern Radar
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Published by SciTech Publishing, an
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Brief ContentsPreface xvPublisher A
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xContents3.6 Adaptive MIMO Radar 10
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xiiContents9.3 Adaptive Jammer Canc
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xivContents15.3 Multisensor Trackin
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xviPrefacehas always been the unlik
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Publisher AcknowledgmentsTechnical
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Editors and ContributorsVolume Edit
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xxiiEditors and ContributorsDr. Lis
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xxivEditors and ContributorsMr. Ara
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2 CHAPTER 1 Overview: Advanced Tech
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1.3 Radar and System Topologies 5FI
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1.4 Topics in Advanced Techniques 7
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1.6 References 15TABLE 1-1Summary o
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PART IWaveforms and SpectrumCHAPTER
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20 CHAPTER 2 Advanced Pulse Compres
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2.2 Stretch Processing 35is applied
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2.2 Stretch Processing 37TABLE 2-1
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2.5 Stepped Frequency Waveforms 61T
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2.5 Stepped Frequency Waveforms 63w
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2.5 Stepped Frequency Waveforms 69I
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2.9 References 812.7.4 SummaryWhile
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2.9 References 83[27] Taylor, Jr.,
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2.10 Problems 85shift across the pu
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88 CHAPTER 3 Optimal and Adaptive M
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3.2 Optimum MIMO Waveform Design fo
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3.4 Optimum MIMO Design for Target
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3.4 Optimum MIMO Design for Target
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3.5 Constrained Optimum MIMO Radar
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108 CHAPTER 3 Optimal and Adaptive
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3.6 Adaptive MIMO Radar 111SINR Los
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3.10 Problems 115[22] W. Y. Hsiang,
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3.10 Problems 1179. A constrained o
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120 CHAPTER 4 MIMO Radarperformance
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4.3 The MIMO Virtual Array 123separ
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4.4 MIMO Radar Signal Processing 12
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134 CHAPTER 4 MIMO RadarFIGURE 4-7T
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136 CHAPTER 4 MIMO Radar4.5.2 MIMO
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138 CHAPTER 4 MIMO Radarnamely, R
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140 CHAPTER 4 MIMO RadarTABLE 4-2 P
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142 CHAPTER 4 MIMO RadarSINR Loss (
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144 CHAPTER 4 MIMO Radar[10] H. V.
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Radar Applications of SparseReconst
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5.1 Introduction 149δ = M/N, the u
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152 CHAPTER 5 Radar Applications of
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5.2 CS Theory 163While the notion o
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5.2 CS Theory 165as , where is a b
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5.3 SR Algorithms 167than the norm
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5.3 SR Algorithms 169the value of o
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5.3 SR Algorithms 171takes special
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5.3 SR Algorithms 173The function f
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5.3 SR Algorithms 175of the TV norm
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5.3 SR Algorithms 177One can argue
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5.3 SR Algorithms 179probability ma
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5.3 SR Algorithms 181only a subset
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5.4 Sample Radar Applications 183pr
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5.4 Sample Radar Applications 185We
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5.4 Sample Radar Applications 187th
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5.4 Sample Radar Applications 189tu
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5.4 Sample Radar Applications 191Ra
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5.4 Sample Radar Applications 193Ta
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Page 225 and 226: 200 CHAPTER 5 Radar Applications of
Page 236 and 237: Spotlight SyntheticAperture RadarCH
Page 238 and 239: 6.1 Introduction 213• Image quali
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Page 242 and 243: 6.2 Mathematical Background 2172π
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Page 264 and 265: 6.5 Image Reconstruction 239FIGURE
Page 266 and 267: 6.6 Image Metrics 241The contrast r
Page 268 and 269: 6.6 Image Metrics 243Along-track am
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Page 285 and 286: 260 CHAPTER 7 Stripmap SAR3 m SAR O
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Page 313 and 314: 288 CHAPTER 7 Stripmap SARand in th
Page 316 and 317: 7.4 Range-Doppler Algorithms 291to
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Page 325 and 326: 300 CHAPTER 7 Stripmap SAR33 cycles
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302 CHAPTER 7 Stripmap SARCrossrang
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304 CHAPTER 7 Stripmap SARfrom freq
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7.5 Range Migration Algorithm 307r,
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310 CHAPTER 7 Stripmap SARkx (rad/m
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316 CHAPTER 7 Stripmap SARThe diffe
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320 CHAPTER 7 Stripmap SARLet us re
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322 CHAPTER 7 Stripmap SARThe resul
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324 CHAPTER 7 Stripmap SARscene. Th
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326 CHAPTER 7 Stripmap SARdriven by
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328 CHAPTER 7 Stripmap SARTABLE 7-3
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330 CHAPTER 7 Stripmap SARFIGURE 7-
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332 CHAPTER 7 Stripmap SAR7.10 REFE
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334 CHAPTER 7 Stripmap SAR6. [MATLA
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Interferometric SAR andCoherent Exp
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8.1 Introduction 3398.1.1 Organizat
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8.1 Introduction 341Rsabnv rw x ,w
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8.2 Digital Terrain Models 343FIGUR
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8.3 Estimating Elevation Profiles U
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352 CHAPTER 8 Interferometric SAR a
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8.5 InSAR Processing Steps 365ξ ta
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8.5 InSAR Processing Steps 3670.1 0
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8.5 InSAR Processing Steps 373While
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8.6 Error Sources 375The second met
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8.6 Error Sources 377If sufficient
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Adaptive Digital BeamformingCHAPTER
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9.1 Introduction 403c k = clutter s
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408 CHAPTER 9 Adaptive Digital Beam
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9.2 Digital Beamforming Fundamental
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9.3 Adaptive Jammer Cancellation 42
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9.5 Wideband Cancellation 447FIGURE
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454 CHAPTER 10 Clutter Suppression
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10.2 Space-Time Signal Representati
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10.5 STAP Fundamentals 4810−5−1
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10.6 STAP Processing Architectures
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10.7 Other Considerations 4911 CPIM
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10.9 Summary 49310.7.3 Computationa
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10.10 References 495[12] Fenner, D.
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10.11 Problems 497the PSD in Figure
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11.2 Colored Space-Time Exploration
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11.2 Colored Space-Time Exploration
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506 CHAPTER 11 Space-Time Coding fo
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11.8 References 525Cost reduction o
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11.9 Problems 52711.9.2 Equivalence
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530 CHAPTER 12 Electronic Protectio
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12.2 Electronic Attack 535TABLE 12-
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12.2 Electronic Attack 541variation
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12.5 Antenna-Based EP 557are adjust
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12.6 Transmitter-Based EP 561polari
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12.11 Summary 583TABLE 12-4Summary
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12.14 Problems 585[9] Stimson, G.W.
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Introduction to RadarPolarimetryCHA
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13.1 Introduction 591and precipitat
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13.1 Introduction 593S: target scat
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13.2 Polarization 597After substitu
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13.2 Polarization 599zFIGURE 13-4Po
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13.3 Scattering Matrix 601left-hand
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604 CHAPTER 13 Introduction to Rada
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13.4 Radar Applications of Polarime
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13.4 Radar Applications of Polarime
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13.5 Measurement of the Scattering
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13.5 Measurement of the Scattering
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13.8 References 623• Lee, Jong-Se
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13.8 References 625[32] Kraus, J.D.
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13.9 Problems 627with the result in
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Automatic Target RecognitionCHAPTER
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14.2 Unified Framework for ATR 633P
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14.3 Metrics and Performance Predic
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14.3 Metrics and Performance Predic
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14.4 Synthetic Aperture Radar 639TA
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14.4 Synthetic Aperture Radar 641Te
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14.4 Synthetic Aperture Radar 64314
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14.4 Synthetic Aperture Radar 645Un
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14.4 Synthetic Aperture Radar 64714
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14.4 Synthetic Aperture Radar 649se
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14.4 Synthetic Aperture Radar 651th
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14.5 Inverse Synthetic Aperture Rad
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14.5 Inverse Synthetic Aperture Rad
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14.6 Passive Radar ATR 657radar sys
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14.7 High-Resolution Range Profiles
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14.9 Further Reading 661take a targ
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14.10 References 663[19] Q. H. Pham
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14.10 References 665[56] M. Martore
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14.10 References 667[92] E. Libby,
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Multitarget, MultisensorTrackingCHA
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15.1 Review Of Tracking Concepts 67
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15.1 Review Of Tracking Concepts 67
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678 CHAPTER 15 Multitarget, Multise
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15.2 Multitarget Tracking 683TABLE
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15.2 Multitarget Tracking 685remove
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15.5 Further Reading 69515.4 SUMMAR
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15.6 References 697[11] Blair, W.D.
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15.7 Problems 6992. Common metrics
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⎡⎤3 0 0 0 0 00 3 0 0 0 0P 2 =0
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Human Detection With Radar:Dismount
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environment that may mask the gener
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D s % = Boulic-Thalmann model param
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16.2 Characterizing the Human Radar
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714 CHAPTER 16 Human Detection With
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16.4 Technical Challenges in Human
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16.4 Technical Challenges in Human
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16.5 Exploiting Knowledge for Detec
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16.7 Further Reading 729enable not
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16.8 References 731[13] Broggi, A.,
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16.8 References 733[53] G.E. Smith,
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16.8 References 735Conference on So
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16.9 Problems 737FIGURE 16-13Pendul
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740 CHAPTER 17 Advanced Processing
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17.3 Direct Signal and Multipath/Cl
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17.4 Signal Processing Techniques f
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17.5 2D-CCF Sidelobe Control 787TAB
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17.6 Multichannel Processing for De
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17.10 References 815While far from
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17.10 References 817[20] Chetty, K.
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17.11 Problems 819[52] Gao, Z., Tao
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17.11 Problems 8215. Using the sign
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824 Appendix A: Answers to Selected
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ResolutionResolution withDimension
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830 IndexASAR. See Advanced SAR (AS
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832 IndexCross-polarization (XPOL),
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834 IndexExciter-based EP (cont.)fr
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836 IndexInterferencecolored noise,
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838 IndexMoving target indication (
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840 IndexPOI. See Probability of in
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842 IndexSaturated (constant amplit
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844 IndexStripmap SAR (cont.)remote
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846 IndexWWald sequential test, com
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