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

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CHAPTER 1INTRODUCTIONVarious space, time, and frequency techniques may be used to process signals originatingfrom radar systems. These techniques are utilized in advanced radar systemsthat are capable of detecting targets in environments containing jamming and clutter.Clutter and jamming affect radar systems in various ways. Ground clutter observedby an airborne platform may be extended in both angle and range. Platform motioncauses the ground clutter to be spread in Doppler frequency. Jamming signals arelocalized in angle and spread over all Doppler frequency. To perform interferencecancellation, multidimensional filtering over the spatial and temporal domains isrequired. Uncertain knowledge of the clutter and jamming environment requires theuse of systems that perform data-adaptive processing.Time-frequency distributions are mappings of information contained in a timeseries into functions of time and frequency. TFDs have been proven to be powerfultools for signal analysis and processing. In Synthetic Aperture Radar (SAR) systems,the SAR returns may be processed with different time-frequency distributions toanalyze specific characteristics of targets within the radar return. The dopplerfrequency in SAR is not a fixed quantity but it is linear in time. TFDs may beused where localization of this information is needed. SAR systems may be used inapplications requiring high resolution imaging.Space-time adaptive processing (STAP) refers to the simultaneous processingof the spatial samples from an array antenna and the temporal samples providedby the echos from multiple pulses of a radar coherent processing interval (CPI). InSTAP, signals are varying in space and doppler but the doppler is fixed over theprocessing interval. In the case of STAP, reduced rank techniques may be applied
2that take advantage of the low-rank property of the space-time covariance matrix.STAP is applicable for target tracking and detection.1.1 SAR Processing using Time-frequency DistributionsSynthetic Aperture Radar (SAR) systems operating in stripmap mode are designedto produce two-dimensional, high resolution images of the earth's surface. This highresolution is obtained by utilizing the relative motion between the radar and theobserved scene. The knowledge of the platform motion allows the synthesis of a longantenna, along the flight direction, and the resulting high spatial resolution. Theechoes corresponding to successive transmitted pulses exhibit a phase shift varyingwith the time as a function of the relative motion between the radar and eachbackscattering element. Due to the motion of the radar platform, each point onthe ground reflects an echo having a Doppler shift proportional to the radar velocityvector along the line of sight. Points at different distances are separated in time, bytransmitting a chirp signal and then applying a range compression. Points at thesame distance, but observed from different angles, exhibit different Doppler shifts.Targets moving along-track (in parallel with the SAR platform) appear as adefocused object superimposed on the ground map. The defocused image is causedby the mismatch between the SAR processing parameters and the signals returnedfrom the moving target. To achieve high resolution in the azimuth dimension, theSAR collects and integrates samples of signals received from the same range. Fora fixed rate of relative motion, and for a target at a specified range and azimuthlocation, the phase of the SAR return is a quadratic function of time. The phaserate of change (the Doppler frequency) is then a linear function of time, and theDoppler rate is constant. SAR processing is tuned to the Doppler rate calculatedfor geostationary imaging. The blurring of a moving target can then be correctedby carrying out the SAR processing using the actual Doppler rate associated with
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 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 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
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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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