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

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APPENDIX ADISCRETE COSINE TRANSFORMIn discrete Wiener filtering, the filter is represented by G, an M x M matrix. Theestimate of the data vector 3C 1Swhere z = x N and N is the noise vector. The use of orthogonal transforms yielda G that contains a large number of elements that can be set to zero as they arerelatively small in magnitude.The Karhunen-Loeve transform (KLT) is optimal in respect to variance distribution[60] and estimation using the mean-square error [61]. There is no generalalgorithm that enables the fast computation of the KLT [60]. The KLT is aperformance basis to which many orthogonal transforms are compared, includingthe Walsh-Hadamard transform (WHT), discrete Fourier transform (DFT), andthe Haar transform (HT). The discrete cosine transform (DCT) is an orthogonaltransform that closely compares to the KLT [62].The DCT of a data sequence xm , m = 0, 1, • • • , (M — 1) is defined aswhere Gk is the kth DCT coefficient.The inverse discrete cosine transform (IDCT) is defined as109
APPENDIX BCOLUMN STACKED FIXED TRANSFORMSAs introduced in section 3.1, processing in the STAP model is carried out in the Ndimensional signal space resulting from stacking the snapshot column-wise. Whena fixed transform is used, a matrix form for the transform would be beneficial forprocessing the signal.A one-dimensional discrete N point Fourier transform may be written asA two-dimensional DFT that results from stacking the transform as done whencreating the vector for STAP processing, is created using the form,This may be represented in matrix form as110
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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
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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 122 and 123: 107also presented. The Sample Matri
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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