Principles of Modern Radar - Volume 2 1891121537

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9.9 Problems 451[32] Golub, G.H. and Van Loan, C.F., Matrix Computations, 3d ed., Johns Hopkins UniversityPress, 1996.[33] Anderson, E., et al., LAPACK Users’ Guide, 3d ed., Society for Industrial and Applied Mathematics,Philadelphia, PA, 1999.[34] Rader, C.M., ”VLSI Systolic Arrays for Adaptive Nulling,” IEEE Signal Processing Magazine,July 1996.[35] Farina, A., Antenna-Based Signal Processing Techniques for Radar Systems, Artech House,Boston, MA, 1992.[36] Special Issue on Adaptive Antennas, IEEE Transactions on AP, vol. 24, September 1976.[37] Weiss, s., et al., “An Efficient Scheme for Broadband Adaptive Beamforming,” in AsilomarConf. Sig. Sys. Comp., Monterey, CA, November 1999.[38] Vaidyanathan, P.P. “Multirate Digital Filters, Filter Banks, Polyphase Networks, and Applications:A Tutorial,” Proceedings of the IEEE, vol. 78, no. 1, pp. 56–93, January 1990.[39] Fliege, N.J., Multirate Digital Signal Processing: Multirate Systems—Filter Banks—Wavelets,Wiley, New York, 1994.[40] Aalfs, D.D., Brown, G.C., Holder, E.J., and Beason, B., “Adaptive Beamforming for WidebandRadars,” in Proceedings of the International Radar Symposium, Munich, Germany, pp. 983–992, September 15–27, 1998.9.9 PROBLEMS1. What is the equation for the availability of an N-channel DBF system that can toleratethe failure of any two receivers? What is the general form of the equation foravailability where P is the number of failed receivers that can be tolerated?2. The (3:1) overlapped subarray layout for the 64-element linear array used to generateFigures 9-17 and 9-18 has six subarrays instead of eight. Why?3. How could the example array from problem 2 be changed so that it will have eight3:1 overlapped subarrays?4. Derive the Wiener filter solution for the optimum adaptive weights by minimizing themean squared error of the beamforming output.5. Derive the maximum SINR solution for the optimum adaptive weights.6. Derive the LCMV solution using the method of Lagrange multipliers.7. According to the principle of orthogonality, the output, y(n), of the optimal filter isorthogonal to the error (i.e., E[y(n)e*(n)] = 0). Use this relationship to derive theoptimal solution for the weights.8. Write an expression for the covariance matrix of a plane wave in the presence ofnoise that is independent and identically distributed. The expression should be interms of the steering vector for the plane wave signal, the signal power, and the noisepower.9. Using the matrix inversion lemma, write an expression for the inverse of the covariancematrix from problem 6.(Matrix inversion lemma: a matrix of the form A = B −1 + CD −1 C H has an inversegivenbyA −1 = B + BC(D + C H BC) −1 C H B).
452 CHAPTER 9 Adaptive Digital Beamforming10. In Figure 9-25, why is the max SINR value for the two-element array equal to 3 dB?11. Derive the equation for the instantaneous cross-correlation of a white noise jammerafter stretch processing that was given in Section 9.5.4.12. Verify the equation given in Section 9.5.4 for jammer cross-correlation averaged overK time samples.
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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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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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Page 426 and 427: Adaptive Digital BeamformingCHAPTER
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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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17.10 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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