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

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37Figure 2.18 Example of WVD cross termswhere the time signal is of length 11r', band-limited tcand n, k, and m are the discrete variables corresponding to the continuous variablest, f, and T.The discrete-time values may be converted to the corresponding continuoustimevalues using the transformations:where ƒ, is the sampling frequency which must be at least 2ƒ, to satisfy the Nyquistcriterion where ƒm is the maximum frequency of the signal. Notice that Equation2.37 may be viewed as a slightly modified Discrete Fourier transform.
382.4 Time-Frequency Analysis of Linear FMThis section describes the estimation of the instantaneous frequency using the fourpreviously introduced TF analysis techniques; the Short-Time Fourier transform, theGabor expansion, the Continuous Wavelet transform and the Wigner-Ville distribution.Analytic expressions for the output of each method to a given linear FMsignal are developed and it is shown how the chirp rate can be extracted using eachtechnique. The performance in the presence of additive white Gaussian noise iscompared with the Cramér-Rao bound analytically for the WVD and by simulationsfor all four techniques.2.4.1 The Wigner-Ville Distributionthe WVD is given byusing Equation 2.32 explicitly. For the discrete finite time duration waveform z(n)..a n2T2eJ2 , the WVD is given byThe magnitude squared of the WVD is then given byconverges to the well known limiting form Equation 2.39.Figure 2.19(a) shows the WVD of a linear FM signal with a chirp rate of 0.00117Hz/sec. The window size of the WVD is 64 points. A 3-D mesh plot of this signal isshown in Figure 2.19(b). The chirp may be seen clearly in these figures.
Page 1 and 2: Copyright Warning & RestrictionsThe
Page 3 and 4: ABSTRACTSPACE/TIME/FREQUENCY METHOD
Page 5 and 6: SPACE/TIME/FREQUENCY METHODS IN ADA
Page 7: APPROVAL PAGESpace/Time/Frequency M
Page 10 and 11: ACKNOWLEDGMENTI would like to begin
Page 12 and 13: ChapterPage3.2.1 Non-Adaptive Beamf
Page 14 and 15: FigurePage2.22 Scalogram of a linea
Page 16 and 17: CHAPTER 1INTRODUCTIONVarious space,
Page 18 and 19: 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 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 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
Page 132 and 133:
11750. Daniel F. Marshall. A two st
Page 134 and 135:
INDEXanalytic signal, 21array imper
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