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

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3the target. In this work we study a number of techniques for extracting the targetmotion parameters from the SAR data. Those parameters may then be subsequentlyused to adjust the processing to focus on the moving object.The signal received from a target moving over a stationary background can bemodeled as samples of a chirp signal embedded in noise. Therefore the problem ofestimating the motion parameters is equivalent to the estimation of a chirp signalin a noisy environment. Time-frequency Distributions (TFD) are mappings of informationcontained in a time series into functions of time and frequency. TFD's havebeen proven powerful tools for analyzing signals with time varying properties [1] [2].In particular, TFD's can be applied to the estimation of the parameters of the linearFM signal (chirp). Various authors have used TFD for estimating the instantaneousfrequency(IF) of a signal in noisy environments.Boashash et. al. compare the performance of a number of algorithms used todetermine the IF [3]. White estimated the IF of a noisy signal using TFD techniques[4]. Lovell compares the performance of TFD's in the Cohen's class with other IFestimation techniques such as the zero crossing estimator and an estimator based onlinear regression in the signal phase [5]. Boashash showed [6] that the Cross Wigner-Ville distribution (XWVD) method provides the best performance in terms of theSNR threshold which meets the Cramér-Rao bound. Harris and Salem comparedthe Wigner-Ville distribution (WVD) to various FM discriminators [7]. The Wigner-Ville distribution has also been applied to the analysis of SAR data for the purposeof extracting the motion parameters of a moving target [8, 9, 10]. The Short-TimeFourier transform (SIFT) and the Gabor expansion are of special interest beinglinear and thus not exhibiting cross-terms when multiple time-varying signals areanalyzed. Auslander et. al. compared the performance of the Gabor expansion andShort-Time Fourier transform in the presence of noise [11]. Morlet's wavelet [12, 13]is based on a Gaussian and is an extension of Gabor's basic idea for a more efficient
4representation of seismic data [13]. This wavelet has also been used to process SARsignals [14].1.2 Space-time Adaptive ProcessingSpace-time adaptive processing (STAP) radar performance has been for some time atopic of considerable interest to the radar community. The need for adaptive methodsarises in practice when statistical properties of the interference are not known andneed to be inferred from the observed data. STAP is a system that linearly combinesthe spatial samples from the elements of an antenna array and the temporal samplesthat are provided by the successive pulses of a multiple-pulse waveform. An arraybeamformer and target Doppler filter are combined to create a STAP weight vector.In the ideal case, STAP provides a coherent gain on target while suppressing clutterand jamming by forming angle and Doppler response nulls. The weight vector isdynamically determined based on the data received by the system. Since a weightvector is optimized for a specific angle and Doppler, STAP systems may computemultiple weight vectors to cover the target angles and Doppler frequencies of interest.A primary difficulty in STAP is the dimension of the adaptive weight vector thatcan become large. As this dimension becomes larger, the required sample supportfor STAP detection also needs to increase. In optimum filter theory, the interferencecovariance is assumed known. This is not directly applicable to practical problems,but it is the start from which adaptive filtering theory is developed. The optimalNeyman-Pearson detector for a known signal vector in colored Gaussian noise witha known covariance matrix is linear, i.e., it is constructed from a linear combinationof the inputs to the space-time array. In practice, the interference+noise covariancematrix is typically not known. A well-known solution to that is the sample matrixinversion (SMI) method, that substitutes an estimate for the true noise covariancematrix expression in the linear detector [15]. It is also well-known that if the sample
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 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
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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
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Figure 2.31 SAR with 2 moving targe
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61Figure 3.1 Space-time adaptive ar
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63Figure 3.3 Airborne radar basic g
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subspace is formed using the remain
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67where k is a gain constant and R
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69The scalar beamformed noise estim
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71are the desired signal, interfere
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CHAPTER 4REDUCED-RANK PROCESSINGThe
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75Figure 4.2 Reduced-rank GSCThis m
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77This relation establishes an equi
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79The conditioned SNR is a random v
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81The performance of the GSC proces
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83For large interference eigenvalue
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85the steering vector s, and the ve
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87(a) CSNR vs Rank order for other
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89Figure 5.4 CSNR vs Rank order for
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91Figure 5.6 Theoretical and simula
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93Figure 5.8 CSNR vs CNRThe signal
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950.80.80.6 0.6~(5'0.4IC!J0.40.20.2
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97the spatial domain. The target is
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99(a) Training outside the target r
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101(a) Training around the target r
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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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