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

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67where k is a gain constant and R is the colored noise true covariance matrix. TheWiener filter can be interpreted as a cascade of a whitening filter for the interference,followed by a matched filter. This solution requires the knowledge of thetrue covariance matrix R.3.2.3 Sample Matrix InversionIn practice, the true covariance matrix of the interference R is unknown a priori andneeds to be estimated from a limited set of the secondary data (noise and interference)as given in Equation 3.8.Substituting R for the true covariance matrix, R, in Equation 3.18 yields thefollowing solutionThe covariance matrix used for this solution has been estimated from a finite numberof secondary samples. Therefore, this solution for the weights is not optimal.The conditioned signal-to-colored noise ratio (CSNR) is defined as the ratio ofthe actual signal-to-colored noise ratio (SNR) to the optimal SNR. The optimal SNRresults when the covariance is known. Colored noise refers to the white noise andinterference. If K 2N snapshots are used to estimate R in Equation 3.8, Reedet al.[15] showed that this solution in Equation 3.19 achieves a CSNR at the outputof the array with a mean of 0.5. A 3 dB loss with respect to the optimal SNR is aCSNR with a mean of 0.5. The CSNR is a random variable bounded between 0 and1 because the covariance matrix is estimated using Equation 3.8 and the resultingsignal-to-noise ratio is a random variable.3.2.4 Generalized Sidelobe Canceller (GSC)The Generalized sidelobe canceller (GSC) is a general form of a linearly constrainedadaptive beamforming algorithm[48]. It adapts to minimize mean square error (MSE)
68Figure 3.4 Full-rank GSC processorin a system while implementing a look direction constant gain constraint[49]. TheGSC is implemented by partitioning the received signal with filters w, and W, asshown in Figure 3.4. This Kxl beamforming filter takes the formwhere 1 is a vector whose elements are all 1. The desired signal is blocked from theadaptive processor by W 3 , the N x K signal blocking matrix, with N < K. The fullrow rank matrix W, is made up of rows ai where ai1 = 0 for i = 1, 2, • • • , K.The K x 1 dimensional received signal vector at time k is represented by x(k).The input K x K covariance matrix is denoted bydimensional noise subspace is given by,The scalar beamformed output is
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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
Page 32 and 33: 17Figure 2.6 Time-frequency descrip
Page 34 and 35: 19Figure 2.7 Computation of the sho
Page 36 and 37: 21Figure 2.9 Spectrogram of a multi
Page 38 and 39: 23where 9/ is the Hilbert transform
Page 40 and 41: Figure 2.11 Gabor Transform of a si
Page 42 and 43: 272.3.3 Continuous Wavelet Transfor
Page 44 and 45: 29Figure 2.13 Time-Frequency resolu
Page 46 and 47: 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 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 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
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11750. Daniel F. Marshall. A two st
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INDEXanalytic signal, 21array imper
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