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

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93Figure 5.8 CSNR vs CNRThe signal cancellation effects on the various STAP techniques under investigationare shown in Figures 5.9 and 5.10. In these figures, the SNR axis is based onFigure 5.9 shows the effects of SNR and the pointingerror on the array gain using Equation 3.34. There are no phase and amplitude errorsso ci = \/1/N. The target is at bore sight (9d = 0°) and the interference angle is 15°.As shown in the figures, when the SNR is small the pointing errors have the leasteffect on the array gain. As the SNR increases, the performance degrades for a smallpointing error as the SMI's mainlobe narrows. The •eigencanceler's performance isacceptable up to an SNR of 15 dB but decreases as the SNR approaches the INR.This is due to the shift of the first eigenvector towards the desired signal as the SNRapproaches the INR. The CSM performs better than the SMI at low SNR however itis not as acceptable as the eigencanceler. The input signal in this case was one signaland one interferer. The Eigencanceler and CSM perform well with one transformterm. However, due to the way that the fixed transforms perform, their performance
94is unacceptable with one term. The DCT and DFT techniques were performed withp = 5. In this case, the DCT's performance is similar to the SMI. The DFT is alsosimilar to the SMI with the exception of several spikes at low SNR as the pointingerror is increased. These are due to the way that the DFT processes the input signal.Additional terms in the DFT processing will reduce these effects.Figure 5.10 show the effects of the phase and pointing errors. There are noamplitude errors and the phase errors are modeled as a zero-mean Gaussian randomvariable. The phase errors were evaluated using 50 Monte Carlo runs. The SMIexhibits a larger degradation in the array gain than the eigencanceler in the caseof both pointing and phase errors. The eigencanceler exhibits almost no loss ofperformance for phase errors up to 8° while the SMI gain is decreased to 1/2 forphase errors with a standard deviation of 5°. The CSM shows good performancefor phase errors up to 6°. The DCT gain is decreased to 1/2 for phase errors witha standard deviation of 8'. The DFT's performance is similar to that of the SMI.As illustrated before, the eigencanceler's pointing error is less than that of the othertechniques.5.2 Mountain-Top DataThe performance of the various reduced-rank methods are compared to oneanother when applied to the Mountain-Top dataset . This data was collectedfrom commanding sites (mountain tops) and radar motion is emulated using atechnique developed at Lincoln Laboratories [58]. The sensor consists of 14 elementsand the data is organized in coherent pulse intervals (CPI) of 16 pulses. For thedataset analyzed here, the clutter was located around 245 degrees azimuth andthe target was at 275 degrees and at a Doppler frequency of 156 Hz. A synthetictarget was introduced in the data at 275 degrees and 156 Hz. Note that the clutterand target have the same Doppler frequency, hence separation is possible only in
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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
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 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 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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