Space/time/frequency methods in adaptive radar - New Jersey ...

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107also presented. The Sample Matrix Inversion (SMI), Generalized sidelobe canceler(GSC), Eigencanceler, and fixed transforms techniques are all introduced. Targetcancellation and closed form expressions for the SMI and eigencanceler are presented.An expression for fixed transforms is also shown.Reduced-rank methods for STAP based on the signal model were presented inChapter 4. Reduced-rank methods with known and unknown covariance matriceswere analyzed. The analysis is carried out in the framework of the minimum variancebeamformer and the generalized sidelobe canceller. A method was developed toevaluate the theoretical performance of reduced-rank techniques when the rankreductionis carried out by a fixed transform. The PC-SMI technique was recommendedwhen the steering vector lies mostly in the interference subspace, andconversely, when the steering vector is mainly in the noise subspace, the eigencancelermethod should be applied.The application of several reduced-rank methods to the STAP problemwas studied by analysis, simulations, and analysis of real data (in Chapter 5).The motivation for the application of reduced-rank methods is that the STAPproblem is inherently low-rank. Restriction of the number of degrees of freedomthrough the application of reduced-rank methods has the advantage of providingrobust covariance matrix estimates resulting in improved performance over SMI.A taxonomy of reduced-rank methods was presented and specific methods wereanalyzed. The CSNR was defined as a figure of merit for the array performancewhen the interference covariance matrix is estimated from a training set. Variousadaptive methods are compared according to their CSNR performance. A generalexpression for the CSNR density function was developed for reduced-rank methodsutilizing fixed transforms. When compared to the CSNR of SMI, reduced-rankmethods exhibit fewer degrees of freedom and a bias term. While best performanceis obtained using transforms based on the eigendecomposition (data dependent),
108the loss incurred by the application of fixed transforms (such as the discrete cosinetransform) is relatively small. The main advantage of fixed transforms is the availabilityof efficient computational procedures for their implementation. The effectsof calibration errors and covariance training ranges were also presented. It wasillustrated that adaptive radar is susceptible to signal cancellation when the targetit included in the training data. It was shown that signal cancellation with theSMI, CSM, DCT and DFT is sensitive to the SNR and magnitude of the pointingerrors. The eigencanceler is much more robust than the SMI with respect to signalcancellation.
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Copyright Warning & RestrictionsThe
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ABSTRACTSPACE/TIME/FREQUENCY METHOD
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SPACE/TIME/FREQUENCY METHODS IN ADA
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APPROVAL PAGESpace/Time/Frequency M
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ACKNOWLEDGMENTI would like to begin
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ChapterPage3.2.1 Non-Adaptive Beamf
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FigurePage2.22 Scalogram of a linea
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CHAPTER 1INTRODUCTIONVarious space,
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3the target. In this work we study
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5support consists of a population o
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7processing. This is explained by t
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92.1 An Overview of Synthetic Apert
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11Figure 2.2 SAR cross-range Dopple
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13Through the expression for the on
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15Illumination pattern onEarth's su
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17Figure 2.6 Time-frequency descrip
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19Figure 2.7 Computation of the sho
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21Figure 2.9 Spectrogram of a multi
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23where 9/ is the Hilbert transform
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Figure 2.11 Gabor Transform of a si
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272.3.3 Continuous Wavelet Transfor
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29Figure 2.13 Time-Frequency resolu
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Figure 2.14 Scalogram of a sine wav
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Figure 2.16 Regions of influence co
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Figure 2.17 WVD transform of a sine
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37Figure 2.18 Example of WVD cross
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39(a) Contour plot of the WVD of a
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41(a) Contour plot of the STFT of a
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43(a) Contour plot of the Gabor exp
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452.5 Time-Frequency Analysis in No
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47Consequently, when the slope S, i
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49where:Doppler phase shift due to
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51(a) Contour plotFigure 2.24 SAR i
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53(a) Contour plotFigure 2.26 SAR i
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55calculated in each case. In this
Page 72 and 73: 57(a) Moving target with synthetic
Page 74 and 75: Figure 2.31 SAR with 2 moving targe
Page 76 and 77: 61Figure 3.1 Space-time adaptive ar
Page 78 and 79: 63Figure 3.3 Airborne radar basic g
Page 80 and 81: subspace is formed using the remain
Page 82 and 83: 67where k is a gain constant and R
Page 84 and 85: 69The scalar beamformed noise estim
Page 86 and 87: 71are the desired signal, interfere
Page 88 and 89: CHAPTER 4REDUCED-RANK PROCESSINGThe
Page 90 and 91: 75Figure 4.2 Reduced-rank GSCThis m
Page 92 and 93: 77This relation establishes an equi
Page 94 and 95: 79The conditioned SNR is a random v
Page 96 and 97: 81The performance of the GSC proces
Page 98 and 99: 83For large interference eigenvalue
Page 100 and 101: 85the steering vector s, and the ve
Page 102 and 103: 87(a) CSNR vs Rank order for other
Page 104 and 105: 89Figure 5.4 CSNR vs Rank order for
Page 106 and 107: 91Figure 5.6 Theoretical and simula
Page 108 and 109: 93Figure 5.8 CSNR vs CNRThe signal
Page 110 and 111: 950.80.80.6 0.6~(5'0.4IC!J0.40.20.2
Page 112 and 113: 97the spatial domain. The target is
Page 114 and 115: 99(a) Training outside the target r
Page 116 and 117: 101(a) Training around the target r
Page 118 and 119: 103Figure 5.15 Angle scan with the
Page 120 and 121: CHAPTER 6CONCLUSIONSThis work has b
Page 124 and 125: APPENDIX ADISCRETE COSINE TRANSFORM
Page 126 and 127: 111This matrix is formed using the
Page 128 and 129: REFERENCES1. Leon Cohen. Time-frequ
Page 130 and 131: 11523. Franz Hlawatsch and G. Faye
Page 132 and 133: 11750. Daniel F. Marshall. A two st
Page 134 and 135: INDEXanalytic signal, 21array imper
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