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Target Shadow Profile Reconstruction in Forward Scatter Radar Target Shadow Profile Reconstruction in Forward Scatter Radar Stanislav Zdravkov Hristov A thesis submitted to The University of Birmingham for the degree of DOCTOR OF PHILOSOPHY School of Electrical, Electronic and Systems Engineering 31st March 2017 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. ABSTRACT This thesis is dedicated to the matter of imaging (further explained as profile recon- struction) in Forward Scatter Radars (FSR). Firstly, an introduction to radar systems, including forward scatter radar, is made, then an introduction to the scalar theory of diffraction and principles of holography follows. The application of holographic imaging principles in the microwave domain is studied. The practical modelling of forward scatter radar target signals is made, based on the theoretical expectations and approximations outlined. Theoretical background of the imaging in FSR is made, based on previously published work. A novel approach for profile reconstruction is introduced based on the practices of holographic imaging, together with simulated results. Experimental set-ups used in the feasibility proof are described and experimental results are presented for 8 different targets in both a single-node and multistatic configurations. Preliminary accur- acy analysis of these reconstructed target profiles is done, outlining practical application issues and domain of accuracy. Quantitative measures of the accuracy of the reconstructed images are defined. ACKNOWLEDGEMENTS First and foremost I want to thank Dr. Marina Gashinova and Prof. Mike Cherniakov for giving me the possibility to grasp the exciting world of scientific research, and all their help and guidance along the way. But mostly for their patience during my PhD studies. Also, I want to thank all the colleagues within the group - Dimitris Tzagkas, Alp Sayin, Alessandro De Luca, to name a few, and Liam Daniel and Edward Hoare, for their help and all the constructive discussions we have had. And I'd like to thank my mother, my father, my friends for the nice memories and good time during the years of my PhD study. CONTENTS 1 Introduction 1 1.1 Basics of Radar ................................ 1 1.2 Topology of bistatic radar systems ...................... 6 1.2.1 The radar equation for bistatic radar ................. 8 1.2.2 Resolution in Bistatic Radar ..................... 9 1.3 Radar Imaging ................................. 12 1.3.1 Real Aperture Radar ......................... 13 1.3.2 Synthetic Aperture Radar ....................... 15 1.3.3 Inverse SAR .............................. 16 1.4 Aim and problem setting of the thesis .................... 19 1.5 Thesis outline ................................. 20 2 Fundamentals of FSR 22 2.1 Introduction .................................. 22 2.2 Topology of FSR ................................ 23 2.3 Shadowing effect: stationary target ...................... 24 2.4 Shadowing effect: moving target crossing the baseline ............ 34 2.4.1 Doppler signature ........................... 41 2.5 Extraction of target trajectory parameters from the signature ........ 48 2.5.1 Optimal signal processing ....................... 48 2.5.2 Extraction of target trajectory parameters via analysis of the FSR spectrogram .............................. 51 2.5.3 Extraction of target trajectory parameters through the use of a multi-static FSR system ........................ 53 2.6 Conclusion ................................... 56 3 Principles of diffraction, holography and their application for FSR analysis 58 3.1 Scalar Theory of Diffraction .......................... 59 3.1.1 Interference and coherence of waves ................. 60 3.1.2 Huygens-Fresnel principle ....................... 61 3.1.3 Fresnel-Kirchhoff (FK) diffraction theory ............... 65 3.1.4 Fresnel-Kirchoff diffraction integral solutions for simple shapes ... 67 3.1.5 Rayleigh-Sommerfield (RS) Theory .................. 73 3.1.6 Babinet's principle ........................... 76 3.1.7 Conclusion ............................... 78 3.2 Basics of Holographic Imaging ........................ 79 3.2.1 Principle of holography ........................ 79 3.2.2 In-line holography ........................... 83 3.2.3 Digital in-line holography ....................... 86 3.3 Application of Holography to Radio waves .................. 89 3.3.1 Microwave holograms and optical reconstruction ........... 91 3.3.2 In-line microwave holography ..................... 92 3.3.3 FSR as a radio-holographic system .................. 93 3.4 Conclusion ................................... 94 4 Signal modelling in Forward Scatter Radar 96 4.1 Introduction .................................. 96 4.2 Model for point-like target and rectangular plate ............... 97 4.3 Signal modelling for extended target ..................... 99 4.3.1 SISAR ................................. 100 4.3.2 Signal modelling via the numerical solution of the Fresnel-Kirchoff diffraction integral ........................... 105 4.4 Modelling of two-dimensional target signatures ............... 113 4.4.1 Fresnel-Kirchhoff diffraction integral based two-dimensional target signature ................................ 114 4.4.2 Rayleigh-Sommerfield (RS) diffraction integral based two-dimensional target signature ............................ 118 4.5 Conclusion ................................... 120 5 Imaging in FSR and development of Target Shadow Profile Reconstruction 122 5.1 State of the art of target imaging in FSR .................. 123 5.1.1 SISAR ................................. 123 5.1.2 Modified SISAR ............................ 124 5.2 Target Shadow Profile Reconstruction algorithm ............... 127 5.2.1 FSR signal as a hologram ....................... 127 5.2.2 Application of holographic reconstruction to FSR signatures .... 131 5.3 Properties of the reconstructed profiles .................... 135 5.4 Two-dimensional profile reconstruction .................... 137 5.5 Initial results from simulations ........................ 145 5.6 Conclusion ................................... 149 6 Experimental validation of Target Shadow Profile Reconstruction algorithm 150 6.1 Hardware used for experimental verification ................. 151 6.1.1 Single-node FSR system for ground moving target .......... 151 6.1.2 Software defined radio ......................... 153 6.2 Experimental results .............................. 157 6.2.1 Initial experimental results with plates ................ 159 6.2.2 Initial experimental results with car targets .............. 165 6.2.3 Results of 2x2 multi-static configuration ............... 176 6.2.4 Profile dependence on state of windows of car targets ........ 185 6.3 Conclusion ................................... 188 7 Initial accuracy analysis of profile reconstruction 190 7.1 Introduction .................................. 190 7.2 Accuracy of the target profile ......................... 191 7.2.1 Resolution of reconstructed target profile .............. 191 7.2.2 Criteria of accuracy estimations of target profile ........... 195 7.3 Effect of trajectory estimation errors on the reconstructed results ...... 206 7.3.1 Error in estimation of speed ...................... 207 7.3.2 Error in estimation of crossing angle ................. 207 7.3.3 Error in estimation of crossing point ................. 210 7.4 Auto-focusing of the TSPR algorithm output ................ 212 7.5 Dependence on target trajectory ....................... 214 7.5.1 Crossing point ............................. 214 7.5.2 Crossing angle ............................. 216 7.5.3 Arbitrary motion of target ...................... 218 7.6 Influence of clutter on the image reconstruction ............... 220 7.6.1 Simulation results ........................... 221 7.7 Conclusion ................................... 224 8 Conclusion and further work 226 8.1 Conclusion ................................... 226 8.2 Summary .................................... 227 8.3 Further work .................................. 231 A Crossing time estimation 234 B Hardware properties 236 B.1 1.192 GHz single node FSR transceiver .................... 236 B.1.1 Power budget calculation ....................... 239 B.2 Patch antennas designed by Liam Daniel ................... 241 B.3 Power Calibration of the USRP-2950R .................... 244 C Publications 247 LIST OF FIGURES 1.1 A typical radar system ............................. 2 1.2 Radar classification by topology: monostatic (a), bistatic (b) and forward scatter (c) radar systems. ........................... 6 1.3 2D Bistatic radar geometry in a north-referenced coordinate system .... 7 1.4 Ovals of Cassini for a reference bistatic radar system for constant SNR values of 0, 5, 10 and 15 dB. ......................... 9 1.5 Bistatic range cells .............................. 10 1.6 Geometry for angle resolution in bistatic radar ................ 12 1.7 Side-looking airborne RAR .......................... 14 1.8 Illustration of the difference between real antenna aperture beamwidth,
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