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

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CHAPTER 6CONCLUSIONSThis work has brought together various methods used to study synthetic apertureradar (SAR) and space-time adaptive processing (STAP) radar systems. As statedpreviously, radar systems may be processed with various space, time and frequencytechniques. Advanced radar systems are required to detect targets in the presenceof jamming and clutter and this interference is seen by the radar systems in variousways. To perform interference cancellation, multidimensional filtering over thespatial and temporal domains is required. Uncertain knowledge of the clutter andjamming environment requires systems that perform data-adaptive processing.For SAR, a technique for extracting the target motion parameters from thedata was introduced. The technique was based on processing the signal with varioustime-frequency distributions. The parameters may then be subsequently used ina SAR system to adjust the processing to focus on the moving object within thefield. The signal received from a target moving over a stationary background can bemodeled as samples of a chirp signal embedded in noise.STAP radar performance was studied with the focus on the problem that,in STAP, the dimension of the adaptive weight vector can become large. As thisdimension becomes larger, the required sample support for STAP detection also needsto increase. Publications have shown the advantages of various forms of reduced-rankprocessing over the full-rank SMI. Given a rank reducing transformation, adaptationcan take place in the subspace spanned by the principal components of the transform(interference subspace methods) or in the complementary subspace (noise subspacemethods). The transforms are either fixed (such as discrete Fourier transform - DFT,or discrete cosine transform - DCT) or data dependent such as the eigencanceler orthe cross-spectral metric (CSM). Reduced-rank methods are important for STAP105
106radar, where a large number of degrees of freedom may be available. For a uniformarray and for fixed PRF, the space-time clutter covariance matrix is essentially lowrankdue to the inherent oversampling nature of the STAP architecture. As hasbeen demonstrated, the space-time radar problem is well suited to the application oftechniques that take advantage of the low-rank property.An overview of the various time-frequency techniques studied were given inChapter 2. The response of each technique used was shown when analyzing a sinewave and a multicomponent signal. Basic properties associated with each techniquewere also introduced. The time-frequency techniques were used to estimate SARtarget parameters. This work was based on the concept that a signal received in aSAR system from a target moving over a stationary background may be modeled assamples of a chirp signal embedded in noise and the problem of estimating the motionparameters of this moving target is equivalent to the estimation of a chirp signal in anoisy environment. The application of four specific TF analysis techniques: the shorttimeFourier transform, the Gabor expansion the Continuous Wavelet transform andthe Wigner-Ville distribution, to the estimation of the relative along-track velocitybetween the SAR platform and a moving target were presented. It was shown thatvarious TF analysis techniques may be used to analyze thè track of a moving targetwith SAR. Each of the TF analysis techniques examined display a sharp thresholdeffect when used to obtain the instantaneous frequency of a signal. The optimalityof the WVD for the determination of the IF was verified and compared to theresults obtained for the cases of the STFT the Gabor expansion and the CWT.In the simulations performed, the STFT was closer to the Cramér-Rao bound thanthe Gabor expansion and the CWT. In all cases, the relative velocity mismatchintroduced by the boat motion was less than 6% of the SAR platform velocity.Chapter 3 introduced the space-time adaptive processing signal environment.The definitions and mathematical model of the signals used for the STAP work was
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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
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43(a) Contour plot of the Gabor exp
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452.5 Time-Frequency Analysis in No
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47Consequently, when the slope S, i
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49where:Doppler phase shift due to
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51(a) Contour plotFigure 2.24 SAR i
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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 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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