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

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85the steering vector s, and the vectors corresponding to the p principal componentsof each transformation. The CSNR was computed from Equation 4.19. In case ofthe CSM method, the matrix U was constructed as in Equation 4.12 substitutingestimated values for unknown quantities. The CSM weight vector was subsequentlyevaluated from Equation 4.8. The curves shown represent averages of 5000 runs.CSM provides slightly better performance when the rank is underestimated. TheDCT-based method seems to be the least affected by overestimating the rank of theinterference subspace.The effect of the assumed rank p of the interference subspace on the averageCSNR is shown in Figure 5.1. For each method, the CSNR was computed fromEquation 4.17. In the case of the the particular scenario considered without jammers(Figure 5.1(a)), all methods peak near an interference subspace rank of p = 4, the truerank of the interference subspace. In the scenario considered with jammers (Figure5.1(b)), the eigencanceler and CSM methods peak near an interference subspace rankof p = 6, the true rank of the interference subspace. The DCT method peaks near aninterference subspace rank of p 8 while the DFT method peaks near an interferencesubspace rank of p = 7. The different rank values required by each method for bestperformance, are indicative of different capabilities to concentrate the power in a fewprincipal values.Several other methods are compared in Figure 5.2(a): PC-SMI, reduced-rankGSC, DFT-based CSM, and DCT-based CSM [21, 22]. The PC-SMI weight vectorwas computed from Equation 4.28. The reduced-rank GSC weight vector wasevaluated using Equation 4.8, where the matrix U consisted of the p principal eigenvectorsof Ra, = ARAH. The CSM methods shown in the figure are not discussedin this work; details on those methods can be found in [21, 22]. At their respectiveoptimal rank orders, the CSNR peak values for the eigencanceler, CSM, PC-SMIand reduced-rank GSC are in close agreement.
86(a) CSNit vs Hank order - without jammers(b) CSNR vs Rank order - with jammersFigure 5.1 CSNR vs Rank order
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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
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 98 and 99: 83For large interference eigenvalue
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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