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

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83For large interference eigenvalues, the elements of A. 27 1 are negligible, and Equation4.29 can be approximated withSince the vector Elr is the noise subspace with respect to the rank p interference, thisPC-SMI is equivalent to a noise subspace canceler. Thus under the assumption thatthe interference eigenvalues are very large, the density of pr is given by Equation4.26. The overall CSNR is p pbpr . For PC-SMI, pb sliqrces is the projection ofthe steering vector s onto the eigenvector q r . For the eigencancelerare the same, it would seem that the eigencanceler would always be preferable.This conclusion however is based on the assumption that the elements of .4 1 arenegligible. In general, PC-SMI is recommended when the steering vector lies mostlyin the interference subspace, and conversely, when the steering vector is mainly inthe noise subspace, the eigencanceler method should be applied.
CHAPTER 5NUMERICAL RESULTSNumerical results presented in this chapter were derived from computer simulationsas well as from processing real data collected by the DARPA sponsored Mountain-Topprogram. Simulated data is used to compare the various techniques that have beenpresented in earlier chapters. The Mountain-Top data is used to demonstrate theperformance of the various techniques on real-world data. Analysis of the Mountain-Top data reveals target cancellation due to mismatch between the true received signalvector and the steering vector used in weight calculation as well as the training areaused for the calculation of the covariance matrix.5.1 Simulated DataThe simulation model used an V = 8 element array with n = 4 taps at each element.The clutter was located in the angular sector of 0 to 30 degrees. The input clutter-tonoiseratio (CNR) was 10 dB at each antenna. In Figures 5.1(a), 5.2(a), and 5.5(a),two jammers were located at 15 and 20 degrees with a jammer-to-noise ratio (JNR) of10 dB at each antenna. The interference subspace rank is bound by r < 1/-1- K- 1 = 11.The bound would be achieved for interference that covers the full space-Dopplerdomain. For the sample covariance matrix used in the simulation, the clutter doesnot cover the whole space-Doppler domain and the interference rank was found to be6. The steering vector was set at 50 degrees, and at a normalized Doppler frequencyof 0.4. The effect of the assumed rank p of the interference subspace on the averageCSNR is shown in Figure 5.1(a). For each method, the CSNR was computed fromEquation 4.17.The eigencanceler's weight vector used in Equation 4.17 is given by Equation4.24. For the DCT and DFT reduced-rank transformations, T was constructed from84
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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
Page 48 and 49: Figure 2.16 Regions of influence co
Page 50 and 51: Figure 2.17 WVD transform of a sine
Page 52 and 53: 37Figure 2.18 Example of WVD cross
Page 54 and 55: 39(a) Contour plot of the WVD of a
Page 56 and 57: 41(a) Contour plot of the STFT of a
Page 58 and 59: 43(a) Contour plot of the Gabor exp
Page 60 and 61: 452.5 Time-Frequency Analysis in No
Page 62 and 63: 47Consequently, when the slope S, i
Page 64 and 65: 49where:Doppler phase shift due to
Page 66 and 67: 51(a) Contour plotFigure 2.24 SAR i
Page 68 and 69: 53(a) Contour plotFigure 2.26 SAR i
Page 70 and 71: 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 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 122 and 123: 107also presented. The Sample Matri
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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