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

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55calculated in each case. In this scenario, the remaining signal was related to themoving target, or the original boat target. The masking technique is dependenton the various levels of the chirp signals and will not work in all scenarios. Thetransform window sizes are the same as in the examples of the previous section.For the case of the WVD, the original target's relative velocity was notestimated due to the cross-terms found in the WVD. A contour plot for the outputof the WVD is shown in Figure 2.28 and the cross-terms are clearly visible and donot allow the technique used to estimate the target parameters. For the case ofthe STFT, the target's relative velocity was estimated to be 7.2 meters/sec. Thecontour plot for the output in the case of the STFT is shown in Figure 2.29. Inthe case of the Gabor expansion, the target's relative velocity was estimated to be6.5 meters/sec. The contour plot for the output in the case of the Gabor expansionis shown in Figure 2.30. Finally, for the case of the scalogram (CWT), the target'srelative was estimated to be 5.2 meters/sec. The contour plot for the scalogram isshown in Figure 2.31.As can be seen from the resulting estimated relative velocities, the numericalresults from the successful techniques are similar to the examples previouslydiscussed. This scenario demonstrates the property of linear transformation forthe various time-frequency transformations used in this work.In the SAR processing, various time-frequency analysis techniques have beenused to analyze the track and determine the velocity of a moving target. Each of thetechniques examined exhibited a sharp threshold effect in the input SNR requiredto estimate the instantaneous frequency (IF) of a simulated linear FM signal. Theoptimality of the Wigner-Ville distribution for the determination of the IF of a signalwas verified by comparing the results of the simulation to the Cramer-Rao bound onthe estimation of the IF. If the TF representation contains signal elements that donot allow certain types of processing, a 'mask' may successfully used to block certain
Figure 2.28 SAR with 2 moving targets processed using WVDsignal elements from the TF plane and allow the desired processing. With each TFprocessing technique, the relative velocity mismatch introduced by the motion of asingle moving target (a boat) was less than 6% of the SAR platform velocity.
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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
Page 20 and 21: 5support consists of a population o
Page 22 and 23: 7processing. This is explained by t
Page 24 and 25: 92.1 An Overview of Synthetic Apert
Page 26 and 27: 11Figure 2.2 SAR cross-range Dopple
Page 28 and 29: 13Through the expression for the on
Page 30 and 31: 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 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
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CHAPTER 6CONCLUSIONSThis work has b
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107also presented. The Sample Matri
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APPENDIX ADISCRETE COSINE TRANSFORM
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111This matrix is formed using the
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REFERENCES1. Leon Cohen. Time-frequ
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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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