Principles of Modern Radar - Volume 2 1891121537

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5.2 CS Theory 157The combined space-time steering vector for a target is then given as the Kronecker productof the temporal and spatial steering vectors, that is,a( f s , f d ) = a t ( f d ) ⊗ a s ( f s )For a given range bin, the vector a( f s , f d ) represents the data that the radar would collectover a CPI if only a single target having unit scattering amplitude were present at theangle-Doppler location encoded by f s and f d . Specifically, the steering vector a( f s , f d )corresponds to a single column of the A matrix for this MTI problem.Let us discretize the frequency variables into N s ≥ J spatial frequency bins andN d ≥ K Doppler frequency bins spaced uniformly across the allowed ranges for eachvariable to obtain N = N s N d unique steering vectors. We can organize the resultingsteering vectors into a matrix A ∈ C M×N . Neglecting range ambiguities, we can definethe scene reflectivity function at a given range as x ∈ C N , where the rows of x areindexed by angle-Doppler pairs 8 ( f s , f d ). We then obtain the linear relationship betweenthe collected data and the scene of interest asy = Ax + ewhere e in this case will include the thermal noise, clutter, and other interference signals.A more realistic formulation would include measured steering vectors in the matrix A.Thus, we see that the data for a multichannel pulsed radar problem can be placed easilyinto the framework (5.1).5.2.2.4 CommentsThe overall message is that most radar signal processing tasks can be expressed in terms ofthe linear model (5.1). Additional examples and detailed references can be found in [17].We should also mention that both of these examples have used the “standard” basisfor the signal of interest: voxels for SAR imaging and delay-Doppler cells for MTI. Inmany cases, the signal of interest might not be sparse in this domain. For example, aSAR image might be sparse in a wavelet transform or a basis of canonical scatterers. 9 Asanother example, in [18], the authors explore the use of curvelets for compressing formedSAR images. Suppose that the signal is actually sparse in a basis such that x = α,with α sparse. In this case, we can simply redefine the linear problem asy = Aα + e (5.10)to obtain a model in the same form with the forward operator A. Indeed, many of theearly CS papers were written with this framework in mind with A = , where isthe measurement operator, and is the sparse basis. In this framework, one attempts todefine a measurement operator that is “incoherent” from the basis . We will not dwellon this interpretation of the problem and refer the interested reader to, for example, [19].8 Note that x in this context is the same image reflectivity function used in common STAP applications [15].9 Selection of the appropriate sparse basis is problem dependent, and we refer the reader to the literaturefor more detailed explorations.
158 CHAPTER 5 Radar Applications of Sparse Reconstruction5.2.3 Regularization of the Linear Model through SparsityWe now turn our attention to the inverse problem of estimating x true from the noisy datay. As mentioned in Section 5.2.1, since δ
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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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Page 167 and 168: 142 CHAPTER 4 MIMO RadarSINR Loss (
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Page 172 and 173: Radar Applications of SparseReconst
Page 174 and 175: 5.1 Introduction 149δ = M/N, the u
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Page 188 and 189: 5.2 CS Theory 163While the notion o
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Page 192 and 193: 5.3 SR Algorithms 167than the norm
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Page 200 and 201: 5.3 SR Algorithms 175of the TV norm
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Page 204 and 205: 5.3 SR Algorithms 179probability ma
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208 CHAPTER 5 Radar Applications of
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Spotlight SyntheticAperture RadarCH
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6.1 Introduction 213• Image quali
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6.2 Mathematical Background 215andf
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6.2 Mathematical Background 2172π
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220 CHAPTER 6 Spotlight Synthetic A
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6.4 Sampling Requirements and Resol
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6.4 Sampling Requirements and Resol
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6.5 Image Reconstruction 239FIGURE
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6.6 Image Metrics 241The contrast r
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6.6 Image Metrics 243Along-track am
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6.7 Phase Error Effects 245TABLE 6-
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260 CHAPTER 7 Stripmap SAR3 m SAR O
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262 CHAPTER 7 Stripmap SAR• RMA i
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264 CHAPTER 7 Stripmap SARH 0 (ω)
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268 CHAPTER 7 Stripmap SARTABLE 7-1
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274 CHAPTER 7 Stripmap SARFIGURE 7-
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276 CHAPTER 7 Stripmap SAR−500Sce
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7.3 Doppler Beam Sharpening Extensi
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288 CHAPTER 7 Stripmap SARand in th
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7.4 Range-Doppler Algorithms 291to
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7.4 Range-Doppler Algorithms 293For
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296 CHAPTER 7 Stripmap SAR−150Col
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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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