Passive bistatic radar imaging of aircraft using FM broadcast signals

... main goal of our work is to build radar images of aircraft using passive bistatic radar signals The use of the FM band for that purpose is motivated by the geographic prevalence of radio broadcasting... 4.7 Simulation Of PBR Images Using Low Frequency Signals 4.7.1 Simulation Of Passive Bistatic Radar Image 4.7.2 Simulation Of Passive bistatic Radar Image Using Actual Airplanes... 1.4 Contribution Of The Thesis The main contributions of the thesis are : • The feasibility study of a passive bistatic radar system using the radio broadcasting FM signals for imaging airplanes

PASSIVE BISTATIC RADAR IMAGING OF AIRPLANES BY USING FM RADIO BROADCASTING SIGNALS ABIVEN PIERRICK A THESIS SUBMITTED FOR THE DEGREE OF MASTER ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2014 Declaration I hereby declare that this thesis is my original urork aad it has been written by me in its entirety. I have duly acknowledged all the sources of information which harre been used in the thesis. This thesis has also not been submitted for any degre in any university previously. ? fr&lv[.N Pie^^i.{ ZS S,r*u27a9 o Acknowledgments This work could not have been performed without the contributions of various persons. those persons all guided me and supported at some time along my work. I would like to thank my supervisor Professor Lim Teng Joon, Professor in the departement of Electrical and Computer Engineering of the National University of Singapore, for advising me all along the thesis and providing me the possibility of working on an exiting topic. I also thank him to let me work with another research laboratory of the Nanyang Technological University. I also wish to thank Doctor Jonathan Pisane, research scientist at the Temasek Laboratory of Nanyiang Technological University, for the technical discussions that we had during the last 10 months of my thesis and for his comments that helped me to write this thesis. I also wish to thank Doctor Danny Tan Kai Pin for his invaluable help for the experiments that could not have been without him. I also wish to thank Doctor Fr´ed´eric Brigui and Doctor Mehdi Air ighil for the informal discussion on their respective field of expertise which provides me a better understanding on passive radar technologies. I wish to thank all my family and friends that supported me during the thesis. Especially, I would like to thank my friends who convinced me to join the NUS running team and allowed me to meet a large number of amazing persons. Finally, I wish to thank all the persons I forgot to mention here. ii Summary A conventional Airport Surveillance Radar (ASR) system must transmit a signal in order to detect approaching aircraft, and thus a frequency band has to be allocated to the ASR system. Passive bistatic radar (PBR) systems, on the other hand, reuse electromagnetic signals already present in order to detect, localize and identify an object within a given area. PBR is a well-known topic but prior research has mainly focused on detection and estimation, and relatively little work has been done on PBR imaging. The use of the FM band for that purpose is motivated by the geographic prevalence of radio broadcasting and the large size of an FM cell, and is the subject of this thesis. Firstly, the tomography principles applied to radar imaging are presented for the monostatic configuration and then generalized to the bistatic configuration. Secondly, the feasibility of using FM radio broadcasting signals is studied for imaging airborne aircraft using a realistic configuration and a validation of the theoretical work is done using a bright point model. The feasibility of the PBR imaging is considered for the Singaporean configuration which has two transmitters, one in Johor Bahru (Malaysia) and the other in Bukit Timah(Singapore). Thirdly, a second validation of the theory is undertaken by developing a new tool for simulating the electromagnetic field reflected off an object based on the NEC2 program. It is based on the transformation of a CAD model given by free license software to an interpretable model for NEC2 that composes of wire coordinates only. PBR images are built from the simulated RCS obtained. Finally an experimental data collection campaign has been executed to compare the theory and the simulation with the reality in the Singapore vicinity by using the FM radio broadcasting signal iii transmitted from Bukit Batok (Singapore) and airplanes approaching Changi Airport. A PBR system has been built and is able to track and detect targets but the too low power of the reflected signals prevents us from extracting the RCS of the targets and from generating their PBR images. The main contribution is the successful construction of interpretable PBR images given a realistic configuration and limited trajectories for the airplanes based on simulated data. It also provides a new tool for obtaining an estimation of the RCS of an airplane at a low frequency for a limited cost. Moreover, a PBR system has been built and was able to detect and to track real targets landing and taking off at Changi airport. Finally, all the work was derived for a special configuration but the methodology can be easily applied in other configurations. iv Contents Acronyms xi 1 Introduction 1.1 Targets Considered . . . . . . . . . . 1.2 Radar . . . . . . . . . . . . . . . . . 1.2.1 Monostatic Radar Description 1.2.2 Bistatic Radar Description . . 1.2.3 Passive Radar . . . . . . . . . 1.2.4 Radar Imaging . . . . . . . . 1.3 Notation . . . . . . . . . . . . . . . . 1.4 Contribution Of The Thesis . . . . . 1.5 Organisation Of The Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 2 3 4 5 6 6 7 2 Principles Of Passive Bistatic Radar Imaging 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Radar Cross-Section And Radar Image Definition . . . . . . . . . . . 2.2.1 Electrical Field Modeling . . . . . . . . . . . . . . . . . . . . . 2.2.2 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Radar Cross Section . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Radar Image . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 A Tomography Approach To Bistatic Radar Imaging . . . . . . . . . 2.3.1 Radon Transform And Projection Slice Theorem . . . . . . . . 2.3.2 Tomography Principles Applied To Monostatic Radar imaging 2.3.3 Tomography Principles Applied To Bistatic Radar Imaging . . 2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 8 9 9 10 11 13 14 14 16 22 25 3 Characteristic Of The Singaporean Configuration 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Practical PBR imaging . . . . . . . . . . . . . . . . . . . . 3.2.1 Block Diagram Of The PBR System Considered . . 3.2.2 PBR imaging implementation . . . . . . . . . . . . 3.2.3 Resolution . . . . . . . . . . . . . . . . . . . . . . . 3.3 Actual Configuration Constraints . . . . . . . . . . . . . . 3.3.1 General Presentation Of The Bistatic Configuration 3.3.2 Transmitters Constraints . . . . . . . . . . . . . . . 3.3.3 Airplanes Trajectory Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 26 27 27 28 29 30 30 31 34 v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . And . . . . . . . . . . . . 35 4 Simulated Electromagnetic Airplane Model 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Electromagnetic Model And Simulation . . . . . . . . . . . . . . . . . . . 4.3.1 The Importance Of A Conformal Mesh . . . . . . . . . . . . . . . 4.3.2 Maxwell’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 E-Field Reflected Off A Sphere And The Electromagnetic Regions 4.3.4 Electromagnetic Simulation . . . . . . . . . . . . . . . . . . . . . 4.3.5 The Methods Of Moments (MoM) . . . . . . . . . . . . . . . . . . 4.3.6 The NEC2 Software . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.7 Constraints Of NEC2 . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 From CAD Model To NEC2 Interpretable Model . . . . . . . . . . . . . . 4.5 Validation Of The Approach And Limitations . . . . . . . . . . . . . . . 4.5.1 Verification On A Sphere . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Estimation Of The Computation Time And Memory Required . . 4.5.3 Remaining Limitations . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Simulation Of Radar Cross Section Of Airplanes . . . . . . . . . . . . . . 4.6.1 RCS At Different Frequencies . . . . . . . . . . . . . . . . . . . . 4.6.2 Variation Of RCS In Function Of An Orientation Error Of The Airplanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Simulation Of PBR Images Using Low Frequency Signals . . . . . . . . . 4.7.1 Simulation Of Passive Bistatic Radar Image . . . . . . . . . . . . 4.7.2 Simulation Of Passive bistatic Radar Image Using Actual Airplanes Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 41 42 43 43 44 46 47 48 48 49 51 57 57 58 60 61 61 5 Passive Bistatic Radar Using Real Data 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Design Of The Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 General Description Of The Real Data Collection And Processing 5.2.2 Acquisition Of Measured And Reference Signals . . . . . . . . . . 5.2.3 Generation Of RD Map And Extraction Of RCS . . . . . . . . . . 5.2.4 Synchronization And Filtering Of The ADSB Data . . . . . . . . 5.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Range Doppler Map Obtained . . . . . . . . . . . . . . . . . . . . 5.3.2 RCS Extraction Of Commercial Airliner By Using Real Data . . . 5.3.3 Discussion On The Passive Bistatic Radar System Built . . . . . . 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 69 70 70 71 72 74 76 76 77 81 81 3.4 3.5 3.3.4 Consequence On The Fourier Space Coverage . . . . Example Of Radar Images Generated By Using Bright Point Actual Airplane Trajectory . . . . . . . . . . . . . . . . . . . 3.4.1 Bright-Point Model . . . . . . . . . . . . . . . . . . . 3.4.2 Passive Bistatic Radar Images . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi . . . . Model . . . . . . . . . . . . . . . . 37 37 38 40 62 64 64 65 67 6 Conclusion 6.1 Summary Of The Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Overcoming NEC2 limitations . . . . . . . . . . . . . . . . . . . . 6.2.2 Improving the extraction of the CRCS from real data measurements 6.2.3 Use of multiple FM station transmitters and receivers . . . . . . . 6.2.4 Considering another signal . . . . . . . . . . . . . . . . . . . . . . vii 83 83 85 85 86 86 86 List of Tables 3.1 Parameters used for the bistatic radar . . . . . . . . . . . . . . . . . . . . viii 32 List of Figures 1.1 1.2 1.3 A general description of a radar system . . . . . . . . . . . . . . . . . . . The bistatic configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . Block diagram of radar imaging processing developed in this thesis. . . . 2.1 2.2 2.3 2.4 Block diagram of radar imaging processing and focus on this Chapter. Description of the polarization . . . . . . . . . . . . . . . . . . . . . . A monostatic configuration. . . . . . . . . . . . . . . . . . . . . . . . A bistatic configuration. . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 3.2 Block diagram of the simulated PBR imaging system. . . . . . . . . . . . Geometric configuration used for the ISAR imaging using a passive bistatic radar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Difference between the Mean Bandwidth (MBW) and the Full Width at Half Maximum (FWHM). Reproduced from [1]. . . . . . . . . . . . . . . . Singaporean configuration considered for the ISAR imaging using a passive bistatic radar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Presentation of the parameters used in the power link budget equation [2]. Representation of the frequency, expressed in MHz, repartition available from the two transmitters considered. . . . . . . . . . . . . . . . . . . . . Trajectories of commercial airliners in the Cartesian representation. . . . Trajectory represented in the (α, β)-representation. . . . . . . . . . . . . Covered Fourier domain with those transmitters by five targets. . . . . . Covered Fourier domain with those transmitters by only one target. . . . Bright point model descritpion. . . . . . . . . . . . . . . . . . . . . . . . PBR images of 5 bright points using a real trajectory. . . . . . . . . . . . PBR image of 9 bright points using a real trajectory. . . . . . . . . . . . 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 4.1 4.2 4.3 4.4 4.5 4.6 4.7 . . . . . . . . Block diagram of the radar imaging processing. . . . . . . . . . . . . . . CAD model and conformal wire model of a F16 fighter airplane. . . . . . Radar cross section of metal sphere from Mie’s theory. . . . . . . . . . . Block diagram of the processing for obtaining a NEC2c interpretable model from a CAD model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of a face divided in four sub-faces and the wires model derivated from it. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of a face crossed by a wire and the modification of the wires structure induced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RCS of a 10-m sphere with 5376 faces. . . . . . . . . . . . . . . . . . . . ix 2 4 5 9 12 17 23 27 28 29 30 32 33 34 35 36 37 38 39 39 43 44 47 52 54 56 57 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 RCS of a 10-m sphere with 5376 faces when ka = 5.3, i.e at 50 MHz. . . CPU time needed in function of the number of segments, with a fixed number of incident and scattered angle. . . . . . . . . . . . . . . . . . . . CPU time needed in function of the number of incident and reflected angles. Airplane CAD model used for PBR imaging. . . . . . . . . . . . . . . . . Influence of the frequency on the bistatic RCS. . . . . . . . . . . . . . . . Influence of an azimuth error on the bistatic RCS. . . . . . . . . . . . . . Influence of an elevation mistake on the bistatic RCS. . . . . . . . . . . . Monostatic radar images two different airplanes with or without their shape using a 360 degrees range of angles. . . . . . . . . . . . . . . . . . . . . . PBR images of two different airplanes with a 20 degree constant bistatic angle and an aspect angle ranging from 230 to 350 degrees. . . . . . . . . Fourier space considered for the PBR imaging. . . . . . . . . . . . . . . . Influence of an elevation mistake on the bistatic RCS. . . . . . . . . . . . Block diagram of the processing chain for experimental data. . . . . . . . Block diagram of the extraction of RCS from real data. The improvement provided by our work is emphasized by the yellow background . . . . . . Example of ADSB data smoothed by a polynomial function of degree 6 and its influence on the aspect angle and Doppler shift at the different instant of a trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . RD map obtained by using FM signals and the station at 93.8 MHz. . . . Example of target tracking on RDMap3. . . . . . . . . . . . . . . . . . . Example of Doppler shift and bistatic range estimated from ADSB data and tracked from RDMap3. . . . . . . . . . . . . . . . . . . . . . . . . . Representation of the ratio between the peak value corresponding to the reflected path and the noise level on RDMap3 . . . . . . . . . . . . . . . Example of power received and RCS computed. . . . . . . . . . . . . . . Polar representation of the RCS of a target in function of the aspect angle α and its bistatic angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . x 58 59 60 61 62 63 64 66 67 67 68 70 71 75 76 77 78 79 80 80 Acronyms ADC Analog to digital converter. ADSB Automatic dependent surveillance-broadcast. ASR Airport surveillance radar. ATR Automatic target recognition. B-Field Magnetic field. CAD Computer-aided design. CIT Computation integration time. COLLADA Collaborative design activity. CPU central processing unit. CRCS Complex radar cross-section. E-Field ElectricalField. FM Frequency modulation. FWHM Full width at half maximum. HFA High frequency asymptotic. xi LNA Low noise amplifier. MBW Mean bandwidth. NEC Numerical electromagnetic code. NTU Nanyang Technological University. OS Operating system. PBR Passive bistatic radar. PEC Perfect electric conductor. RCS Radar cross-section. RD Range-Doppler. RF Radio frequency. SNR Signal-to-noise ratio. SR-CRCS Square root of the complex radar cross-section. TL@NTU Temasek Laboratory at Nanyang Technological University. TL@NTU Worldwide Interoperability for Microwave Access. VAC Visual approach chart. XML Extensible markup language. xii Chapter 1 Introduction The main goal of our work is to build radar images of aircraft using passive bistatic radar signals. The use of the FM band for that purpose is motivated by the geographic prevalence of radio broadcasting and the large size of an FM cell. The thesis covers the feasibility study of such a system, its design, its simulation, and its implementation. 1.1 Targets Considered In the first part of the thesis, the targets considered are air target models obtained from CAD models. The targets ranged from fighter jets to private jets. In the second part, the targets considered are actual commercial airplanes thanks to the proximity with Changi Airport and the possibility to obtain exact flight information of the airplanes in real time. Moreover, the trajectories considered for the imaging are actual trajectories of airplanes in and around Singapore. 1.2 Radar The term radar comes from RAdio Detection And Ranging and originally described a system that uses the electromagnetic wave for detecting the presence of an object and 1 Chapter 1 1.2. Radar determining its position. A full radar system is composed of a transmitter, a receiver and a signal processing chain, as represented in Figure 1.1. Figure 1.1: A general description of a radar system 1.2.1 Monostatic Radar Description A radar system is called monostatic if the transmitting antenna and the receiving antenna are co-located. In a monostatic configuration, the delay τ is related to the range R from the antenna to the receiver, the Doppler shift fD to the range-rate VR (also called radial velocity), and the power to the reflectivity coefficient of the object such that R= τ , 2c VR = λ PR = fD , 2 PT GT GR λ2 σ (4π)3 R4 LLoss (1.1) (1.2) (1.3) where c is the light velocity, PT is the transmitted power, PR is the received power, λ the wavelength, σ the reflectivity coefficient of the object, GT and GR the gain of the transmitting and receiving antenna respectively, and LLoss is the loss of our system. Equation (1.3), called the power budget of the reflected path, determines the size of the detection cell. If isotropic antennas are used by both transmitter and receiver, the detection range is then a disk that depends on the signal to noise ratio (SNR) required 2 Chapter 1 1.2. Radar for detection. 1.2.2 Bistatic Radar Description A bistatic radar refers to a radar system where the receiver and the transmitter are not co-located. The bistatic radar configuration is described in Figure 1.2. New parameters are introduced for describing the bistatic configuration such as the baseline distance L, and the bistatic range RB such that RB = RT S + RRS − L (1.4) where RRS is the distance between the scattered point and the receiver and RT S the distance between the scattered point and the transmitter. In that configuration, the delay can be related to the bistatic range RB , the Doppler shift to the bistatic rangerate, and the ratio between the transmitted and received power to the bistatic reflectivity function. The relation between the signal parameters and the geographic parameters are given by RT S + RRS − L = τ , c fD d (RT S + RRS − L) = λ , dt 2 PRS = PT GT GR λ2 σB 2 (4π)3 RRS RT2 S LLoss (1.5) (1.6) (1.7) where σB the bistatic reflection coefficient. Moreover, a new parameter appears in a bistatic configuration called the bistatic angle β and is defined as the angle between the transmitter, the scattered object, and the receiver. The monostatic configuration corresponds to a bistatic configuration where the bistatic angle and the baseline distance are null. The bistatic detection range is an oval of Cassini defined by a constant product of the distance transmitter-object and receiver-object, and 3 Chapter 1 1.2. Radar Figure 1.2: The bistatic configuration. it is derived from Equation (1.7). 1.2.3 Passive Radar A passive radar is a radar system which takes advantage of an illuminator of opportunity to replace the transmitter in a radar system. Such systems make use of existing radiated signals already available and so have discretion properties for the radar itself, and do not require a new frequency spectrum slot [3]. Recently, a renewed interest in bistatic radar has been seen, due to the widespread deployment of cellular communication equipment, and thus the possibility of using the cellular infrastructure for detection, estimation, and tracking [4, 5]. In [6], Griffiths investigated the use of various wireless digital signals for detection and estimation of targets, which presents good ambiguity functions, but their low geographic spread or the small coverage of their cells decreases the interest for those signals or increases the complexity of those systems. For instance, the use of WiMAX as an illuminator of opportunity was discussed in [7] for ground imaging but its limited availability impairs its practical value. In [6], Griffiths also analyzed various analog signals as illuminators of opportunity and proved that the resolution achievable by using FM band signals is too low for practical detection and estimation applications. However, despite the low image resolution, radio broadcasting FM signals appears to be a good candidate for imaging airplanes thanks to the widespread use of the technology 4 Chapter 1 1.2. Radar and the typical large size of the FM cells. In [8], Daoult et al. investigated the construction of passive radar images of synthetic air targets flying synthetic trajectories from the signal of a single FM station. In this thesis, the construction of passive radar images using CAD-modeled and real airplanes flying actual trajectories. 1.2.4 Radar Imaging The radar image of a target is the distribution of its elementary scattering coefficients. A radar image is generally presented as a two dimension map where each pixel intensity/color represents the amplitude of the elementary scattering coefficient at this position, usually represented in a dB scale. A radar image is obtained by doing a multitude of processing. In this thesis, the processing, as represented in Figure 1.3, is divided into two main parts: • The extraction of the radar cross section (RCS) of airplanes. • The construction of a passive bistatic radar (PBR) image. The first block calculates the RCS of the target given simulated or real observations, a process that will be described in the next chapter. The extracted RCS is then passed to the second block to obtain a radar image. This second process will also be discussed in the next chapter. Environment parameters FM Data Extract RCS RCS Build PBR image Radar Image Figure 1.3: Block diagram of radar imaging processing developed in this thesis. 5 Chapter 1 1.3 1.3. Notation Notation In the thesis, unless otherwise specified, the following notation will be used for a variable “x”: • a real number in R is denoted by x, • a complex number in C is denoted by x, • a vector in Rn or Cn is denoted by x, • a matrix (in R or C) is denoted by X. 1.4 Contribution Of The Thesis The main contributions of the thesis are : • The feasibility study of a passive bistatic radar system using the radio broadcasting FM signals for imaging airplanes applied to the Singaporean configuration. • The use of low frequency signals to build radar image in a constrained environment based on the principles of tomography from simulated data. • The construction of a conformal model interpretable by NEC2 based on a basic CAD model available online. • The simulation of a scattered field of small airplanes using NEC2. • The realization of a tracking system based on both FM data and ADSB data. • The processing of the FM data to find the complex RCS of airplanes. 6 Chapter 1 1.5 1.5. Organisation Of The Thesis Organisation Of The Thesis The thesis is organized as follows. Chapter 2 presents the electromagnetic and radar background needed for the understanding of the radar image generation. It presents the principles of tomography used for the construction of radar images. Chapter 3 presents the feasibility study of the passive bistatic radar system designed in this thesis. The chapter discusses the constraints introduced by a true bistatic configuration and their influence on the quality of the radar images obtained by our passive bistatic radar. Chapter 4 presents the electromagnetic tools used for the electromagnetic simulation and the simulation results. It also describes the method used for building a NEC2 interpretable model from a CAD model. Chapter 5 presents the design of the passive bistatic radar system built to extract the radar cross section of airplanes. The limitations of the system built are underlined and solutions for overcoming them are presented. Chapter 6 summarizes the work performed in this thesis and provides ideas for future developments. 7 Chapter 2 Principles Of Passive Bistatic Radar Imaging 2.1 Introduction In this chapter, the focus is put on the radar image generation from the complex radar cross section (CRCS) of the airplanes. The radar imaging is based on the tomography principles presented in [2, 9]. In Section 2.2, we define the concepts of CRCS and radar image. In Section 2.3, after introducing the Radon Transform and the projection theorem, the relation between the RCS and the radar images is derived for the monostatic configuration and then for the bistatic configuration. The development performed in this Chapter is then used in Chapter 3, 4 and 5 for the construction of radar images. The diagram in Figure 2.1 represents the passive bistatic radar considered and it underlines the focus put on the radar imaging part in this Chapter. 8 Chapter 2 2.2. Radar Cross-Section And Radar Image Definition Environment parameters FM Data Extract RCS RCS Build PBR image Radar Image Chapter 2 focus Figure 2.1: Block diagram of radar imaging processing and focus on this Chapter. 2.2 Radar Cross-Section And Radar Image Definition 2.2.1 Electrical Field Modeling A real-valued sinusoidal signal x(t) = A cos(ωt + θ) can be expressed as Re[Aejωt ejθ ] and we refer to Aejθ as the fixed phasor, and Aejωt ejθ as the time-varying phasor. The electric field (E-Field) transmitted by a point source can be modeled as in [10] E(r, t) = E0 (r)ej (ωt−k·r) , (2.1) where the vector E(r, t) is the E-Field at a position r of polar coordinates centered on the point source at a time t, E0 (r) its amplitude, ω its angular frequency, and k is the wave vector. The E-Field is propagating in the direction of the wave vector k, therefore the E-Field is described by two components orthogonal to the wave vector k. Moreover the wave vector k generally depends on the position. From Equation (2.1), it is obvious that the E-Field can be separated into time and space functions, as follows. 9 Chapter 2 2.2. Radar Cross-Section And Radar Image Definition E(r, t) = E0 (r)e−j k·r ejωt (2.2) = E(r)e jωt E(r) and E(r, t) are both called phasors and describe the E-Field. The phasor E(r) is referred to as the fixed phasor and E(r, t) as the time-varying phasor. It is also important to point out that both phasors are complex-valued and that the E-Field is the real part of the time-varying phasor. The amplitude of the E-Field E0 (r) depends on the model considered. In a near field condition, the usual assumption is that the amplitude of the E-Field is inversely proportional to the range from the transmitter, i.e. E0 (r) = E0 , |r| (2.3) where E0 is a constant that can be determined by boundary conditions. If the amplitude of the E-Field respects the condition in Equation (2.3), the wave is called a spherical wave. In a far-field condition, a usual hypothesis is that the amplitude of the E-Field is not range dependent and the wave is then called a plane wave. 2.2.2 Polarization As said previously, the E-Field can be described by two orthogonal components to the direction of propagation given by the wave vector k. For the purpose of the demonstration and without any lost of generality, we assume a propagation over the z-axis and so the E-field initial can be described as: 10 Chapter 2 2.2. Radar Cross-Section And Radar Image Definition   E0x (r)    E0 (r) =  E0y (r)   0 (2.4) The polarization of an electromagnetic wave refers to the relation between the two components orthogonal to the propagation direction. Different polarizations exist, including • Circular polarization : If the two orthogonal components |E0x | and |E0y | are equal but E0x and E0y have a 90-degrees phase difference. • Linear polarization : If the two orthogonal components E0x or E0y have the same phase. • Elliptical polarization : If the two orthogonal components E0x and E0y have 90degrees phase difference and amplitude, none of them are null. The linear polarization is the most used for radar system and two polarizations are mainly used called the Horizontal (H) polarization and the Vertical (V) polarization. By considering cylindrical coordinates centered at the antenna, we can defined in each point of the space a local basis represented in Figure 2.2. The V polarization is defined as a polarization such that the E-Field is only in the Uθ direction whereas in a H polarization the E-Field is pointing in the Uφ . 2.2.3 Radar Cross Section Monostatic Radar Cross-Section Definition Previously, we spoke about the power received by the receiver and it was linked to the reflectivity coefficient σ, which is also called the radar cross-section (RCS). It is defined as in [11] by σ = lim 4π|r|2 |r|→∞ |ER (r)|2 |ET (0)|2 , (2.5) 11 Chapter 2 2.2. Radar Cross-Section And Radar Image Definition Figure 2.2: Description of the polarization where ER (r) denotes the reflected E-Field observed by a receiver located at a position r sufficiently far away from the object and ET (0) the incident electric field at the target in a far field condition. The RCS of an object depends mainly on its shape, its size, its materials, the frequency, the polarization, and the aspect angle. The complex radar cross-section (CRCS) σ is introduced from the definition of the RCS given in [12] 2 σ = lim 4π|r| |r|→∞ ER (r) ET (0) 2 e j k·r , (2.6) where the exponential term is added for fixing the phase of the CRCS in the far-field region. Finally, the square root of the CRCS (SR-CRCS) is defined as √ σ = lim |r|→∞ √ 4π|r| ER (r) ET (0) ej k·r , (2.7) The dependency on environment parameters is not expressed in Equations (2.5), (2.6) and (2.7) for simplicity purpose. In the following section the environment parameters 12 Chapter 2 2.2. Radar Cross-Section And Radar Image Definition dependency is pointed out by denoting the RCS σ(α, k) where α and k are the aspect angle and the wavenumber. Bistatic Radar Cross Section Definition In a similar way we can also define the bistatic radar-cross section σB by Equation (2.8), σB = lim |rRS |→∞ 4π|rRS |2 |ER (rRS )|2 |ET (0)|2 . (2.8) In a bistatic configuration, the reflected E-Field is also taken at a position r sufficiently far away from the object and the incident E-Field is the one near the target in a far field condition. We also need to introduce a bistatic CRCS σB from the definition of the RCS given in [12] σB = lim |rRS |→∞ 2 4π|rRS | ER (rRS ) ET (0) 2 j k·rRS e , (2.9) where the exponential term is added for fixing the phase of the CRCS in the far-field. Finally, the bistatic square root of the CRCS (SR-CRCS) is defined such that: √ σB = lim |rRS |→∞ √ 4π|rRS | ER (rRS ) ET (0) ej k·rRS , (2.10) The dependency on environment parameters is not expressed in Equations (2.8), (2.9) and (2.10) for simplicity purpose. In the following section the environment parameters dependency is pointed out by denoting the RCS σ(α, β, k) where α, β, and k are the aspect angle, the bistatic angle and the wavenumber. 2.2.4 Radar Image As mentioned in Chapter 1, the radar image is the distribution of its elementary scattering coefficients. In this thesis, we only consider a two dimensional radar image, i.e. the scattering coefficients are projected onto a two dimensional plane. If we consider a scene 13 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging Ω with only discrete scattering points, the radar image is denoted as S(x, y) and defined as √ S(x, y) = σω δxω ,yω (x, y) (2.11) ω∈Ω where the symbol δx,y denotes the 2 dimensional Kronecker function, √ σω the SR-CRCS of the scattering point at the position ω, xω and yω are the x- and y-coordinates of the point ω. In a nutshell, the radar image gives us information about the position of the scattering points and their reflectivity coefficient. 2.3 A Tomography Approach To Bistatic Radar Imaging The tomography principle used for the radar image generation is based on the Radon transform and the projection slice theorem. It consists in building a 2D image of a scene from a multitude of 1D information of the scene with different points of view [9]. Therefore, Radon transform and projection slice theorem are presented before deriving the tomography principle applied to radar image generation. The relation between the √ SR-CRCS σB and the radar image S(x, y) is used in Chapters 3, 4 and 5. 2.3.1 Radon Transform And Projection Slice Theorem Radon Transform The Radon transform is the integral transform of a 2D-function over a straight line. For a given function f defined on R2 , the Radon transform is defined as [9] +∞ Rf (α, u) = f (u cos(α) + v sin(α), u sin(α) − v cos(α))dv, (2.12) −∞ where u and v are two real variables. We consider the parametric equations 14 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging x = u cos(α) + v sin(α) (2.13) y = u cos(α) − v sin(α) with u fixed and v a variable. This pair of equations describes a line in the x-y plane, and therefore, the Radon transform is a line integral. Projection Slice Theorem The Radon transform is closely related to the Fourier Transform and this relation is captured in the projection slice theorem or Fourier slice theorem [9]. The one-dimensional Fourier transform of a function f : R2 → R is given by +∞ fˆ(ωx ) = f (x, y)e−j2πxωx dx, (2.14) −∞ and the two-dimensional Fourier transform of f (x, y) is given by +∞ +∞ fˆ(ωx , ωy ) = f (x, y)e−j2π(xωx +yωy ) dxdy, −∞ (2.15) −∞ The Radon transform of the function f is then considered as a function of the u variable only and is denoted by Rf,α . Its Fourier transform is then computed by +∞ +∞ ˆ f,α (ωu ) = R f (u cos(α) + v sin(α), u sin(α) − v cos(α))e−j2πuωu dvdu −∞ (2.16) −∞ A rotation matrix Rα of rotation angle α is introduced. u is a vector from R2 with coordinates (u, v), and Px is the operator for the projection onto the x-axis. We can rewrite the previous equation as +∞ +∞ ˆ f,α (ωu ) = R f (Rα−1 u)e−j2πPx (u)ωu dvdu −∞ (2.17) −∞ 15 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging The change of variable u = Rα x where x is a vector from R2 with coordinates (x, y) gives us +∞ +∞ −∞ +∞ −∞ +∞ ˆ f,α (ωu ) = R f (x)e−j2πPx (Rα x)ωu dxdy f (x)e−j2πx·(αωu ) dxdy = −∞ (2.18) −∞ = fˆ(αωu ), where α is a vector from R2 with coordinates (cos(α), sin(α)). Equation (2.18) explicitly relates the Radon transform and Fourier transform, and is a statement of the projection slice theorem. Equation (2.18) also shows that the inverse Fourier transform gives us an explicit formula for the inversion of the Radon transform. 2.3.2 Tomography Principles Applied To Monostatic Radar imaging The monostatic configuration is described in this section in order to explain the tomographic principles applied to radar imaging. It is described in [9] for a monostatic configuration and a chirp pulse. In this section, assuming a monostatic configuration and an ISAR configuration, the imaging principle is described for a more general signal. Figure 2.3 shows the monostatic configuration used for the mathematical description of the tomography principles applied to the monostatic radar imaging where ω denotes an elementary element of the object being tracked, O is the center of the object, r(x, y) the range between the radar and the elementary points considered and rO the range between the center of the object and the radar. First, we consider an aspect angle α null, i.e. the line of sight and the x-axis are collinear. The incident E-Field is assumed to be far field and a bright point model is used for the object, i.e. the object can be described as a sum of discrete scatterers, so that the 16 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging Figure 2.3: A monostatic configuration. reflected total E-Field is a discrete sum of reflected, attenuated, and delayed incident E-Field reflected by each scatter points. Thus, the reflected field is modeled by the fixed-phasor given by ER (rR ) = Aω Sω EI (rT ), (2.19) ω∈Ω where rR and rT are the receiver and transmitter positions in the local basis centered at O of the object Ω, respectively, EI (rT ) is the incident E-Field fixed-phasor, ER (rR ) is the reflected E-Field fixed-phasor, Aω the attenuation and delay coefficient associated with the scattering point ω , and Sω the reflection coefficient associated with the scattering point ω . Since a monostatic configuration is considered, thus we have r = rR = rT . The reflection coefficient depends on the polarization of the incident E-Field and the reflected E-Field of interest. The reflection coefficients between the different polarization HH, HV, VH and VV define the scattering matrix.   SV V S= SHV  SV H   SHH (2.20) In the following, we consider only a unique linear polarization for the receiver and the transmitter, thus the same notation is used for the scattering matrix and the reflectivity coefficient. The attenuation and delay term Aω can be expressed by 17 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging e−j2k·r Aω = √ 2 π|r| (2.21) where k is the wave vector and r is the position of the scattered element from the radar position (r = rR = rT ). The object is considered to be continuous spatially and thus the received signal is a Riemann sum of attenuated and delayed signals reflected by each elementary volume of the object, as in Aω · Sω · EI (r)dω, ER (r) = (2.22) ω∈Ω where dω is the elementary volume. A local base centered on the object Ω is considered and the scattering coefficients are replaced by the radar image defined in (2.11), then we have ER (r) = e−2j k·r(x,y) · ET (r)dxdy, S(x, y) √ 2 π|r(x, y)| (x,y)∈R2 (2.23) By using a first order approximation of the denominator, and using the Cartesian coordinates, we have ER (r) = S(x, y) (x,y)∈R2 e−2j √ (r0 +x)2 +y 2 √ 2 πr0 · ET (r)dxdy, (2.24) Then we consider a second order approximation for the exponent of the numerator and we find that 18 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging |r(x, y)| = (r0 + x)2 + y 2 = (r0 + x) y r0 + x (1 + 2 (2.25) ≈ r0 + x Thanks to Equations (2.24)-(2.25), we have e−2jk(r0 +x) ER (r) = S(x, y) √ · ET (r)dxdy, 2 πr0 (x,y)∈R2 −2jkx S(x, y)e = dxdy (x,y)∈R2 e−2jkr0 √ · ET (r), 2 πr0 (2.26) In Equation (2.26), we can separate the variables x and y and so we obtain e−2jkr0 · ET (r) ER (r) = √ 2 πr0 S(x, y)dy e−2jkx dx, x∈R (2.27) y∈R The term between the bracket in Equation (2.27) is the Radon transform of the reflection coefficients. By reusing the notation introduced in (2.14), we obtain e−2jkr0 ER (r) = √ · ET (r) 2 πr0 e−2jkr0 = √ · ET (r) 2 πr0 RS (0, x)e−2jkx dx, x∈R (2.28) −2jkx RS,0 (x)e dx, x∈R ˆ S,0 (ω) of RS,0 (ω). Then it can The remaining integral is the 1D Fourier Transform R be written as e−2jkr0 ˆ S,0 (2k) ER (r) = √ · ET (r) · R 2 πr0 (2.29) 19 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging By using Equation (2.6), the CRCS is 2 σ = lim 4π|r| |r|→∞ 4π|r|2 = lim |r|→∞ 4πr02 ≈ lim r0 →∞ ER (r) ET (0) 2 j k·r e ˆ S,0 (2k) R , 2 ET (r) j k·r−2jkr0 e ET (0) , (2.30) 2 ET (r)e−jkr0 ˆ RS,0 (2k) ET (0) , As far-field conditions are assumed, the transmitted E-Field is a plane wave, so we have ET (0) = ET (r)e−jkr0 (2.31) Substituting (2.31) in (2.30), we obtain ˆ S,0 (2k) σ(0, k) = R 2 (2.32) The CRCS of an object is then the square of the 1D-Fourier Transform of the Radon transform of the reflectivity coefficients of the object. The value of the CRCS obtained depends on the frequency, the position of the antenna, the polarization and the shape of the object. The notation σ(0, k) indicates that the CRCS has been computed at a null aspect angle and at a wavenumber k.The polarization considered for the transmitter and the receiver is out of the scope of the derivation. So we have, ˆ S,0 (2k) = √σ(0, k) R where √ (2.33) σ(0, k) denotes the SR-CRCS presented previously in Section 2.2.3. Second, we assumed that the radar is still over the x-axis as plotted in Figure 2.3. The radar is still considered at a distance r0 but now the angle between the line of sight 20 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging and the x-axis is −α, it is as we considered a rotation of the object of an angle α. Then the Equation (2.25) changes such that |r(x, y)| = (r0 + x cos(α) + y sin(α))2 + (−x sin(α) + y cos(α))2 = (r0 + x cos(α) + y sin(α)) 1+ −x sin(α) + y cos(α) r0 + x cos(α) + y sin(α) 2 (2.34) ≈ r0 + x cos(α) + y sin(α) By going through the derivation again by using the relation given in Equation (2.34), Equation (2.33) is generalized to ˆ S,α (2k) = √σ(α, k), R (2.35) And then we find that for any aspect angle α the SR-CRCS is the Fourier transform of the Radon transform of the object’s reflectivity function. By using the projection slice theorem stated in Equation (2.18), we can rewrite the Fourier transform of the reflectivity function S such that √ ˆ S(α2k) = σ(α, k), (2.36) where α is the vector of coordinates (cos(α), sin(α)) corresponding to an aspect angle α. We introduce a change of variable such that ωx = 2k cos(α) (2.37) ωy = 2k sin(α) The relation can thus be written ˆ x , ωy ) = √σ(α(ωx , ωy ), k(ωx , ωy )) S(ω (2.38) 21 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging Using the inverse Fourier transform, we have S(x, y) = 1 (2π)2 √ σ(α(ωx , ωy ), k(ωx , ωy ))ej(ωx x+ωy y) dωx dωy , (2.39) (ωx ,ωy )∈R2 By using the aspect angle α and the wavenumber k we have S(x, y) = 1 (2π)2 √ σ(α, k)ej2k(cos(α)x+sin(α)y) |4k|dαdk, k∈R (2.40) α∈[0,2π] Equation (2.40) then shows the relation between the SR-CRCS and the radar image. 2.3.3 Tomography Principles Applied To Bistatic Radar Imaging Second, a bistatic configuration is considered in order to apply the tomography principles to passive bistatic radar imaging. Figure 2.4 shows the bistatic configuration used for the mathematical description of the tomography principles applied to the bistatic radar imaging, where ω denotes an elementary element of the object, O the center of the object. A Cartesian and a polar basis are centered in O and the x-axis is in the direction of the bisector of the angle between the transmitter, the center O and the Receiver. Moreover, rT (x, y) is the range between the transmitter and the elementary points considered, rR (x, y) the range between the receiver and the elementary points considered, rTO the range between the center of the object and the transmitter, rRO the range between the center of the object and the receiver and β the bistatic angle between the line of sight between the receiver and the object center and the line of sight between the transmitter and the center of the object. In a same way that in Section 2.3.2, the incident E-Field is assumed in a far field conditions and it is then considered as a plane wave. Therefore, the received E-Field can 22 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging Figure 2.4: A bistatic configuration. be written as ER (rR ) = SB (x, y) (x,y)∈R2 ej(kT ·rT (x,y)+kR ·rR (x,y)) √ · ET (rT )dxdy, 2 πrR (x, y) (2.41) where kT is the wavenumber associated to the transmitted E-Field, kR is the wavenumber associated to the received E-Field, rR (x, y) the position of the elementary scattering point from the receiver, rT (x, y) the position of the elementary scattering point from the transmitter, and SB (x, y) the bistatic radar image. As previously, we use a first order approximation at the denominator and a second order approximation on the exponential term. By using the cosine law, the distance between an elementary point and the transmitter is 23 Chapter 2 2.3. A Tomography Approach To Bistatic Radar Imaging rT (x, y) = RT2 0 + ρ2 − 2ρRT0 cos(π − ϕ − β/2) = (RT0 + ρ cos(ϕ − β/2))2 + ρ2 (1 + cos(ϕ − β/2)2 ) =(RT0 ρ2 (1 + cos(ϕ − β/2)2 ) + ρ cos(ϕ − β/2)) 1 + RT0 + ρ cos(ϕ − β/2) (2.42) ≈(RT0 + ρ cos(ϕ − β/2)) In the same way, we obtain the following relation for the range between the receiver and the elementary point rR (x, y) ≈ RT0 + ρ cos(ϕ + β/2) (2.43) Therefore, the bistatic range is rR (x, y) + rT (x, y) ≈ RT0 + RR0 + 2ρ cos(ϕ) cos(β/2) (2.44) By using the Cartesian coordinates shown in Figure 2.4, the bistatic range can be written as rR (x, y) + rT (x, y) ≈ RT0 + RR0 + 2x cos(β/2) (2.45) Now, the object is rotated from an aspect angle −α and that the local (x,y) Cartesian base is attached to the object then the relation becomes rR (x, y) + rT (x, y) ≈ RT0 + RR0 + 2 cos(β/2) (x cos(α) + y sin(α)) (2.46) By going through the derivation in Section 2.3.2 again by using the relation given in 24 Chapter 2 2.4. Conclusion Equation (2.46), a relation between the bistatic CRCS and the radar image is that √ SˆB (α4k cos(β/2)) = σB (α, β, k) (2.47) The change of variable used is then ωx = 2 k cos(α) cos(β/2) (2.48) ωy = 2 k sin(α) cos(β/2) Finally, the bistatic radar image can be reconstructed by using the relation SB (X, Y ) = 1 (2π)2 √ σB (α, β, k)ej2 cos(β/2)k(cos(α)X+sin(α)Y ) |4k cos(β/2)2 |dαdk, k∈R+ α∈[0,2π] (2.49) 2.4 Conclusion In this Chapter, we presented the principles of tomography applied to a monostatic configuration and its generalization for a bistatic configuration. The tomography principles will be used in Chapters 3, 4, and 5 of this thesis for building PBR images of airplanes from the FM radio broadcasting system in Singapore. A relation between the CRCS and the radar image, characterized by its reflectivity coefficients, was pointed out. Differences between the theory and its implementation will be pointed out in the following Chapters. 25 Chapter 3 Characteristic Of The Singaporean Configuration 3.1 Introduction The purpose of this chapter is to show that the radio FM broadcasting system in Singapore can be used as an illuminator of opportunity for constructing PBR images. The influence of an actual configurations on different parameters such as the range of detection, the frequency, the aspect angle and bistatic angle is studied. Finally, the influence of the actual configuration on the Fourier space coverage and thus the achievable resolution is presented. In Section 3.2, the practical implementation of the theory developed in Chapter 2 is presented and the resolution of an image is introduced as a performance measure. In Section 3.3, the performance of the system is studied by analyzing the link budget equation, the available frequencies in Singapore and the different bistatic parameters. Finally, the Fourier space domain fulfilled is estimated and the theoretical achievable resolution is computed. In Section 3.4, the quality of the radar image is discussed according to the limited FM Band and the limited variation of the aspect angle in a Singaporean con- 26 Chapter 3 3.2. Practical PBR imaging text. The discussion is done on image generated from a bright-point model and the radar imaging presented in Chapter 2. 3.2 3.2.1 Practical PBR imaging Block Diagram Of The PBR System Considered The influence of actual airplanes trajectories on PBR images is studied in this chapter. In that purpose,PBR simulated system is built such that the inputs are the frequency used, the bright points considered and the ADSB data measured and the output of the PBR simulated system is a radar image. The block diagram of the PBR system built is in Figure 3.1. Frequency Bright-point model Compute E-Field E-Field RCS Extraction RCS Build PBR image Radar Image Angles ADSB Data Extract aspect and bistatic angles Angles Figure 3.1: Block diagram of the simulated PBR imaging system. The bistatic and aspect angles are extracted from actual trajectories extracted from the information given by the ADSB system available on all commercial airliner. The E-Field is computed according to those angles and to those frequencies, the bright-points positions and their scattering coefficients. The CRCS is then extracted from the E-Field. Finally, radar images are constructed from the CRCS obtained and the different aspect and bistatic angles using the Equation (2.49). 27 Chapter 3 3.2.2 3.2. Practical PBR imaging PBR imaging implementation The bistatic geometry used in this Chapter is summarized in Figure 3.2, where we denote by TX the transmitter, RX the receiver, S the scattering airplane, u the bistatic vector, V the direction of travel of the aircraft, β the bistatic angle and α is the aspect angle. Figure 3.2: Geometric configuration used for the ISAR imaging using a passive bistatic radar. As shown in Chapter 2, the radar image of an object can be obtained from its CRCS. The PBR image is obtained by using a brute force computation such that S(xi , yj ) = 4 c2 fk cos( k l 4πfk βl βl 2 √ ) σB ej c cos( 2 (xi cos(αl )+yj sin(αj )) k,l 2 (3.1) where (xi , yj ) corresponds to the Cartesian coordinates of the pixel located at the ith column andj th rows and, k and l are the indexes of summation. The radar image S(x, y) considered in this thesis is a 60-meters large square grid with a pixel size of 20 cm which is far beyond the resolution achievable by the system and the wavelength considered but provides smooth PBR images. The practical relation between the CRCS and the PBR images is then a discrete Fourier transform with effect of windowing which is discussed in the following Section 3.2.3. The PBR imaging is represented by the block diagram Build 28 Chapter 3 3.2. Practical PBR imaging PBR image in Figure 3.1. 3.2.3 Resolution In this work, the term resolution refers to the definition given by C.Jakowatz [9] and correspond to the Mean Bandwidth (MBW) in spectral analysis. As described in Chapter 2, the PBR image S(x, y) consists in a 2D Fourier transform of the SR-CRCS. The resolution of a PBR image S(x, y) is proportional to the inverse of the windows aperture introduced by the limited value of CRCS in the Fourier space. Another definition of the resolution in the literature is referring to the Full Width at Half Maximum (FWHM),the difference between the two definitions is shown on Figure 3.3. Relations between the two definitions depends on the window effect created by the limited number of aspect angles and frequency. Figure 3.3: Difference between the Mean Bandwidth (MBW) and the Full Width at Half Maximum (FWHM). Reproduced from [1]. The best achievable down-range and cross-range resolutions denoted by ρx and ρy , respectively, are demonstrated in [13] and are given by ρx = c , 2∆f cos(β/2) (3.2) 29 Chapter 3 3.3. Actual Configuration Constraints and ρy = c , 2fc ∆α cos(β/2)) (3.3) where c is the light velocity, ∆f the bandwidth of our signal of opportunity, fc the carrier frequency, ∆α the variation of the aspect angle. An PBR image is called interpretable if the resolution of the PBR system is significantly smaller than the dimension of the targets. 3.3 3.3.1 Actual Configuration Constraints General Presentation Of The Bistatic Configuration Figure 3.4 shows the actual Singaporean configurations studied in this thesis. The receiver used is situated in Nanyang Technological University (NTU), the two transmitters are located in Bukit Batok (Singapore) and Johor Bahru (Malaysia). The trajectories of the airplanes imaged are then the trajectories of airplane taking off or landing at the Changi Airport in the South-East of Singapore. Figure 3.4: Singaporean configuration considered for the ISAR imaging using a passive bistatic radar. 30 Chapter 3 3.3.2 3.3. Actual Configuration Constraints Transmitters Constraints Power Constraints Firstly, it is important to check if the received power is sufficiently high for being able to differentiate the reflected path from the cluster and the noise and thus to built PBR image. The power PRD received by the direct path and the power PRS received by the reflected path on the target are given by PT GT R GRT λ2 , (4π)3 RT2 R LLoss (3.4) PT GT S GRS λ2 σB , 2 (4π)3 RRS RT2 S LLoss (3.5) PRD = PRS = where PT is the transmitted power, λ is the wavelength, LLoss are the loss of the system, σ is the radar cross section, Gij the directional gain for the i antenna to the direction of the j object, Rij is the distance between the i and j object and the subscripts i and j refers to the transmitter T , the receiver R and the scattering object S. In Chapter [?] and [?], the antenna considered is supposed to be isotropic and thus the directional gain is constant. The parameters previously discussed are represented in Figure 3.5 On the other hand, the noise power Pn is given by : Pn = F kT0 Bn , (3.6) where F is the noise factor, k the Boltzmann constant, T0 the noise temperature and Bn the bandwidth. Using the Parameters found in Table 3.1, we have a SNR of: • For the received direct Path signal from Bukit Batok (Singapore): 97 dB 31 Chapter 3 3.3. Actual Configuration Constraints Figure 3.5: Presentation of the parameters used in the power link budget equation [2]. • For the received reflected Path signal from Bukit Batok (Singapore): 16.4 dB • For the received direct Path signal from Johor Bahru (Malaysia): 88 dB • For the received reflected Path signal from Johor Bahru (Malaysia): 10.2 dB The data measured experimentally tends to confirm those values. Parameters Value Frequency available Bukit Batok 88.3 − 100.3 MHz Frequency available Johor Bahru 87.4 − 107.5 MHz Distance receiver-transmitter Bukit BatokRRT 10.6 km Distance receiver-transmitter Johor Bahru RRT 30.5 km Transmitted power PT · GT S 10 kW Antenna gain receiver GRS 10 dB Radar cross-section σB 20 dB Effective bandwidth Bn 200 kHz Noise temperature T0 290 K Receiver noise figure F 1 Table 3.1: Parameters used for the bistatic radar 32 Chapter 3 3.3. Actual Configuration Constraints Frequency Available For PBR Imaging The geometric constraints were discussed previously, another constraint is the frequency used by the different signals available at the illuminator of opportunity. Figure 3.6 shows the minimum, first quarter, last quarter and maximum frequency available for both transmitters, only FM stations with enough transmitted power are kept. The transmitters from Bukit Batok (Singapore) is in general using lower frequency than the transmitter in Johor Bahru (Malaysia), moreover the frequency are concentrated in a 12 MHz bandwidth for both transmitters. Finally, the non-uniform repartition of the frequency explains why the convolution backprojection algorithm of the polar format algorithm are not considered for the generation of radar image in our work since they required data on almost uniform grid in the Fourier space. For the processing, the whole bandwidth available from the two configurations are considered. Those constraints on the frequency used are fixed by the location of the passive system but they are independent of the trajectory followed by the airplanes contrary to the other constrained parameters. Figure 3.6: Representation of the frequency, expressed in MHz, repartition available from the two transmitters considered. 33 Chapter 3 3.3.3 3.3. Actual Configuration Constraints Airplanes Trajectory Constraints Airplanes Trajectory In A Cartesian Space The airplane trajectories are determined by the civil aviation authority of the country and are described on a visual approach chart (VAC). In this thesis, the actual airplanes trajectories are determined empirically by using an automatic dependent surveillancebroadcast (ADSB) system recording the flight information sent by the the airplanes. Figure 3.7 shows an example of some trajectory followed by the airplanes in the Cartesian space. Since the illuminator of opportunity is a FM transmitter, and we assume that the radiation pattern of the transmitting antenna is directed in direction of the ground, the power of the signal received from a reflection off high-altitude targets is supposed too weak and consequently only targets below 6000 meters are kept. Trajectory of the aircraft in the Cartesian Space 6000 5000 z−axis 4000 T T R 1 25 3000 2000 1000 0 5 0 0 4 −5 −10 x 10 y−axis −15 −5 10 3 4 5 4 x 10 x−axis Figure 3.7: Trajectories of commercial airliners in the Cartesian representation. Airplanes Trajectory In α − β Space As we have seen previously in section 3.2.3, the resolution of an image depends on the amplitude of variation of the aspect angle, the variation of the bistatic angle and the frequency available. In that section, the constraint on the aspect angle and the bistatic angle are discussed. Figure 3.8 represents the different targets in the space defined by 34 Chapter 3 3.3. Actual Configuration Constraints the aspect angle α and the bistatic angle β, it is referred to as the (α, β)-representation. Bistatic Angle in fonction of the Aspect Angle(Singapore) Aspect Angle (Degree) 200 100 1 2 3 4 5 0 −100 −200 0 5 10 Bistatic Angle (Degree) 15 20 Bistatic Angle in fonction of the Aspect Angle (Malaysia) Aspect Angle (Degree) 200 100 1 2 3 4 5 0 −100 −200 0 5 10 15 20 25 30 Bistatic Angle (Degree) 35 40 45 Figure 3.8: Trajectory represented in the (α, β)-representation. The representation shows that the bistatic angle remains small along all the trajectories while the variation of the aspect angle varies over several decades of degrees, those limited variations are due to the limited number of trajectory available for the commercial airplanes. 3.3.4 Consequence On The Fourier Space Coverage The different parameters constrained by the location of the PBR system and the trajectory of the airplane were discussed previously. All those parameters have an influence on the RCS of the airplanes, the RCS position in the Fourier space and thus it has an influence on the resolution achievable by the system. The resolution of the system depends on the area fulfilled in the Fourier space, Figure 3.9 shows the RCS points that we can obtain in the Fourier space representation from actual commercial airliner. The positions in the Fourier space corresponds to a point at a distance f cos(β/2) from the center and in a direction α, where f is the frequency, β the bistatic angle and α the aspect angle. 35 Chapter 3 3.3. Actual Configuration Constraints (a) Transmitter in Singapore (b) Transmitter in Malaysia Figure 3.9: Covered Fourier domain with those transmitters by five targets. In Figure 3.10a and Figure 3.10b, a single trajectory is presented and it provides enough RCS to fulfilled a sufficiently large part of the Fourier Domain to construct an interpretable image with a resolution close to 15 meters in down-range and few meters in cross-range. According to Equation 3.3, the cross-range resolution is inversely proportional to the amplitude of the aspect angle variation, the cross-range resolution is then 11 meters for a 10 degrees aspect angle amplitude of variation, and 5.5 meters for a 20 degrees aspect angle amplitude of variation. In the trajectory represented in Figure 3.10, the resolution achievable is then close to 1 meter in cross-range. The signals transmitted by both transmitters are using different parts of the FM band. Most of the FM station transmitted from the antenna in Johor Bahru are using the upper part of the radio FM band while the transmitter in Bukit Batok are using only the lower radio FM band. Moreover, the bistatic angle is generally higher for the transmitter in Malaysia, so the data collected from the two transmitters are projected over a close area into the Fourier space. 36 3.4. Example Of Radar Images Generated By Using Bright Point Model And Actual Chapter 3 Airplane Trajectory Fourier Domain (Singapore) Fourier Domain (Malaysia) 100 100 50 50 v−axis 150 v−axis 150 0 0 −50 −50 −100 −100 −150 −150 −100 −50 0 u−axis 50 100 150 −150 −150 −100 (a) Transmitter in Singapore −50 0 u−axis 50 100 (b) Transmitter in Malaysia Figure 3.10: Covered Fourier domain with those transmitters by only one target. 3.4 Example Of Radar Images Generated By Using Bright Point Model And Actual Airplane Trajectory 3.4.1 Bright-Point Model As assumed in section 2.3.2 for the derivation of Equation 2.18, the object Ω is supposed to be a sum of discrete scattering point and then the reflected E-Field can be written as a sum of scattered E-Field ER = s √ σs −jk(rRSs +rT Ss ) √ e EI 4πrRS (3.7) where ER is the reflected E-Field, EI the incident E-Field, rT Ss the transmitter to scatter√ ing point distance, rT Ss the receiver to scattering point distance, and σs the reflection coefficient associated to the scattering point s. Then the square root of the CRCS can be written as 37 150 3.4. Example Of Radar Images Generated By Using Bright Point Model And Actual Chapter 3 Airplane Trajectory √ −jk(rRSs +rT Ss ) σs e σΩ = (3.8) s where √ σΩ is the square root of the CRCS of the object Ω. The model obtained for the CRCS of the object is then the CRCS obtained by using the bright point model, Figure 3.11 summarized the bright point modeling principles. The bright point model is used for the E-Field computation and then for obtaining of the RCS. It is represented by the block diagram Compute E-Field and RCS Extraction in Figure 3.1. Figure 3.11: Bright point model descritpion. 3.4.2 Passive Bistatic Radar Images A first set of images is done by using a simulated object with 5 bright points, 4 of which are separated by a distance of 10 meters from the center point, as shown in Figure 3.12. Five points are visually identified by using the transmitter in Johor Bahru (Singapore) whereas the separation between two points is under the theoretical resolution of 15 meters for the down-range resolution. This can be explained by the definition used for the resolution. The resolution of a target is defined as the dimension of the area around a scattered point, where the intensity of a pixel is comprised between the intensity of the scattered point and 3dB less than this value, then by using this definition the resolutions observed is close to the theoretical resolutions. For the trajectory of interest, the images using the transmitters of Malaysia have a better resolution mainly due to the larger frequency 38 3.4. Example Of Radar Images Generated By Using Bright Point Model And Actual Chapter 3 Airplane Trajectory bandwidth available for the FM band signals adn the larger variation of aspect angle. −30 −30 −42 −20 −40 −42 −20 −10 −46 0 −48 10 −50 y−axis, meters y−axis, meters −44 −52 20 −44 −10 −46 0 −48 10 −50 20 −52 −54 30 −54 30 −20 0 x−axis, meters −20 20 (a) Using the transmitter in Malaysia. 0 x−axis, meters 20 (b) Using the transmitter in Singapore. Figure 3.12: PBR images of 5 bright points using a real trajectory. A 40-meter-long object is then simulated by 9 bright points. Figure 3.13 represents the PBR image constructed for this model and the position of the 9 bright points. The different bright points are less easily identifiable but the shape of the radar image gives us an estimation of the target. Even with a low-resolution, it is possible to differentiate the two models and thus the PBR image appears to be a good candidate for applications such as identification and classification of targets. −30 −42 −20 y−axis, meters −44 −10 −46 0 −48 10 −50 −52 20 −54 30 −20 0 x−axis, meters 20 Figure 3.13: PBR image of 9 bright points using a real trajectory. It can be thus concluded that PBR images of bright point targets can be constructed with real configuration constraints and FM signals. Even though the resolution of the 39 Chapter 3 3.5. Conclusion images is low, the size of the object is distinguishable and thus provides us information about the targets that can be used for ATR applications for instance. 3.5 Conclusion In this Chapter, we presented the feasibility study of a PBR imaging system using the radio FM broadcasting system available in Singapore and the resolution reaches by the PBR images. Two transmitters were considered, one at Johor Bahru (Malaysia) and one at Bukit Batok (Singapore), the receiver was located at Nanyang Technological University (Singapore). The power link budget indicates that a practical PBR system in this configurations must be able to built PBR images of commercial flight taking off or landing at the Changi Airport (Singapore). The resolution obtained from the PBR system from both transmitters were from 15 meters for the range resolution and 14 meters per 10 degree aspect angle which should be sufficient for being able to identify a commercial airliner but probably not enough for a civil jet or fighter jet. 40 Chapter 4 Simulated Electromagnetic Airplane Model 4.1 Introduction The purpose of this thesis is the design of a PBR system able to image an airborne airplane flying in a trajectory encountered in practice, using measurements obtained by an experimental testbed. Before describing the results obtained using testbed measurements of real signals in the next chapter, in this chapter we will build a simulated scattered Efield by using NEC2 that can accommodate any system configuration, as long as an electromagnetic model of the target is available. We will discuss how to build such a model. In the previous Chapter, we have seen that a radar image can be built using the CRCS of an object. In this Chapter, the simulation of the E-Field reflected off a target is studied and the E-Field obtained is processed in order to extract the CRCS of the target and hence to build a radar image of it. An electromagnetic model is needed for the computation of the E-Field. The model is built from a Computer-aided design (CAD) model. The scattered E-Field is then simulated by the Numerical Electromagnetics Code (NEC2) and can be used for the computation of the CRCS of targets. Actual measured 41 Chapter 4 4.2. General Description trajectories of airplanes and FM signals available in Singapore are considered for the construction of radar images. Section 4.2 presents the PBR system studied in this Chapter and point out the novelty of it. Section 4.3 describes the electromagnetic model required, the electromagnetic simulations tools used and their constraints. Section 4.4 is then focused on the construction of a NEC2-interpretable model. In Section 4.5, the validation of our electromagnetic model applied to a sphere is presented and an estimation of the processing time and memory requirement is also undertaken, while the limitations of our work are also underlined. Finally, in Section 4.6, the CRCS of small airplanes obtained by our work is discussed and radar images are presented in Section 4.7. 4.2 General Description Figure 4.1 represents the block diagram of the processing performed in this chapter. The actual trajectories of airplanes are obtained by using an ADSB system from which the aspect and bistatic angles are extracted. The CAD airplane model is imported to MATLAB and modified to provide a NEC2-interpretable model. The available frequency at the Bukit Batok transmitters, the aspect and bistatic angles and the NEC2-interpretable model are used to build NEC2 input files. Afterwards, NEC2 computes the scattered EField and gives us an output file from which the CRCS is determined using Equation (2.9). Finally, the radar imaging processing discussed in Chapter 2 and implementated in Chapter 3 is used for obtaining a PBR image from the CRCS. By comparing the block diagrams in Figures 3.1 and 4.1, the main difference between Chapter 3 and Chapter 4 corresponds to the computation of the E-Field and the creation of interpretable models for electromagnetic simulations. Therefore, only those two points will be discussed in the following sections. 42 Chapter 4 4.3. Electromagnetic Model And Simulation CAD model ADSB Data CAD model interpretation Frequency Conformal Model Angles NEC2 Extract aspect and bistatic angles E-Field RCS Extraction Angles RCS Build PBR image Radar Image Figure 4.1: Block diagram of the radar imaging processing. 4.3 4.3.1 Electromagnetic Model And Simulation The Importance Of A Conformal Mesh Our approach consists of the simulation of the RCS of an object from its CAD model. On the one hand, we assume that the object is a Perfect Electric Conductor (PEC), which means that the current density and the E-Field inside the object are null according to Ohm’s law and thus the current is only distributed on the surface of the object. On the other hand, the Faraday cage principle is based on the fact that the E-Field inside an enclosure delimited by a mesh of a conducting material is null and the current density is confined to the outside of the Faraday cage [14]. Based on those two principles, we assume that the object we want to determine the RCS of can be modeled by a wire mesh 43 Chapter 4 4.3. Electromagnetic Model And Simulation as in [8]. The following conditions have to be respected by the mesh to be able to model an object : • The mesh has to be sufficiently small in comparison to the wavelength of the incident wave. • The mesh has to be free of any wires inside the object in order to avoid propagation inside. If the wires respect those two conditions, the wire model is then called conformal in this thesis. Figure 4.2a shows the original CAD-model and Figure 4.2b shows a conformal mesh respecting the conditions above. (a) ACD model (b) Conformal wire model Figure 4.2: CAD model and conformal wire model of a F16 fighter airplane. 4.3.2 Maxwell’s Equation The modern theory of electromagnetism is based on four differential equations called the Maxwell’s equations [15] ∇·E = ρ , ε0 (4.1) 44 Chapter 4 4.3. Electromagnetic Model And Simulation ∇ · B = 0, ∇×E =− (4.2) ∂B , ∂t ∇ × B = µ 0 J + ε0 ∂E ∂t (4.3) , (4.4) where ∇· is the divergence operator, ∇× the curl operator, E is the electric field (EField), B is the magnetic field (B-Field), J the current density, ρ the charge density, ε0 the permittivity of free space and µ0 the permeability of free space. Those four relations link together the electric field, the magnetic field, and the current density on the surface of the object in our environment. A second form of Maxwell’s equations can also be obtained by using an integral form of those equations. By using Maxwell’s equations, we can derive the wave equation 1 ∂ 2F − ∇2 F = 0, 2 2 c ∂t (4.5) where F is either the B-Field or the E-Field. The general solution of this equation is a superposition of wave [14] such that F (r, t) = G(ωt − k · r) + H(ωt − k · r), (4.6) where G and H are generalized function, k is the wave vector and ω the pulsation. Moreover for a valid solution, the wave vector should respect the condition |k| = k = ω , c (4.7) where k is called the wavenumber and c is the speed of light. Thanks to a sufficient number of initial and boundary conditions, a unique solution can solve the problem [16]. An analytical expression exists for simple shapes like a sphere, an infinite plate or a cylinder [17], but no analytical solution is available in the literature for more complex shapes such as cars, airplanes or ships. Therefore, electromagnetic simulation tools have 45 Chapter 4 4.3. Electromagnetic Model And Simulation to be used to estimate the RCS of complex targets. 4.3.3 E-Field Reflected Off A Sphere And The Electromagnetic Regions The E-Field reflected off an object is the unique solution of Maxwell’s equations satisfying all boundary conditions imposed by the object, analytical solution for an arbitrary objects are usually difficult to obtain but analytical solutions have been demonstrated for a few canonical objects [17, 18]. The example of the scattering E-Field by a sphere is briefly discussed in this section and the three electromagnetic regions are introduced using the sphere as a reference. Figure 4.3 represents the analytical solution of the RCS of a sphere as a function of the ratio between the circumference of a sphere and the wavelength derived by Mie [14], the relation between the E-Field and the RCS has been shown previously in Equations (2.6)-(2.8). Three electromagnetic regions are defined [19, 20] and presented on the figure: • The Rayleigh region, where the RCS is proportional to the frequency and when the wavelength is much larger than the circumference of the sphere. • The resonance region, where the RCS is neither proportional to the frequency nor independent of the frequency and when the circumference of the sphere is close to the wavelength. • The optical region, where the RCS is independent of the wavelength and when the wavelength is much smaller than the circumference of the sphere. The three regions are easily identifiable for a sphere but they also appear for ordinary objects [21] and the three regions depend on the ratio between the size of the object and the wavelength. Most radar systems work at high frequencies ranging from a few Gigahertz to tens of Gigahertz at which the wavelength ranges from a few centimeters to a few decimeters and so the scattering region is the optical region for objects such as 46 Chapter 4 4.3. Electromagnetic Model And Simulation Figure 4.3: Radar cross section of metal sphere from Mie’s theory. ships, airplanes, trucks, cars or even sometimes humans. Therefore, many electromagnetic tools have been developed to simulate the RCS of objects at high frequency. On the other hand, FM signals occupy much lower frequencies and few electromagnetic tools have been developed for simulating the RCS of objects in the FM band. 4.3.4 Electromagnetic Simulation An electromagnetic problem such as the estimation of the E-Field reflected off an object requires the solution of the Maxwell’s Equations with appropriate boundary conditions as explained previously. Currently, there exists two families of solution methods: • High frequency asymptotic (HFA) approaches. • Numerical methods based on finite elements model. High Frequency Asymptotic Approaches The HFA approaches are only approximations but save a lot of processing time when they can be applied. They assume the wavelength λ to be much smaller than the object’s dimensions, which means that the scattering mechanisms are assumed to occur in the optical region. The HFA family is divided into two subfamilies, the first one is based on 47 Chapter 4 4.3. Electromagnetic Model And Simulation the Snell-Descartes equation and referred to as field-based such as the Geometrical Optics (GO) [22], the second one referred to as current-based such as the Physical Optics. For those two families, improvements [23–26] were developed by adding diffraction law at the cost of more processing in order to be more accurate. They are commonly used for RCS simulation using classic radar. Numerical Methods The numerical methods are based on discretization. The numerical methods family can also be divided into two subfamilies, one subfamily is based on the solving of integral equations such as Method of the Moments (MOM) [16, 27] while the second subfamily is based on the solving of differential equations such as the Finite Difference Time Domain (FDTD) method [28]. Finally, those two subfamilies can be further divided into 2 subfamilies according to the use of either a time domain approach or a frequency approach. 4.3.5 The Methods Of Moments (MoM) Among the different numerical methods, the method of moments (MoM) is very popular in radar domain [29–31]. The method of moments (MoM) is fully described in [16]. The MoM solves the electromagnetic integral equation by a discretization of the problem so that it is transformed into a linear algebraic problem. Many numerical tools can be found in the literature to solve the electromagnetic equation, some of which are presented in [30, 31]. The choice of solver depends mainly on the model available for a target but two simulations should converge to the same solution if a similar model is used. 4.3.6 The NEC2 Software The New Electromagnetic Code (NEC2) is based on the MoM applied to a wire mesh model. The wire model describes the model structure, each wire being divided into segments which the NEC2 software uses those segments for the electromagnetic computation. 48 Chapter 4 4.3. Electromagnetic Model And Simulation The NEC2 software is based on solving the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE) derived in [32]. The EFIE (resp. MFIE) gives a linear relation between the E-Field (resp. H-Field) and the current density in each segment such as E = GI (4.8) where the vector E contains the incident E-Field evaluated at the center of the segment, I the current density in each field and G is a matrix such that Gij is the E-Field at the center of the ith segment due to the j th segment, the size of the square matrix G is then the number of segments considered in the model. Firstly, NEC2 inverses this system by using an LU decomposition and then the Gauss pivot method [33] I = G−1 E = U −1 L−1 E , (4.9) where L and U are the lower and upper triangular matrix of the LU decompposition. The scattered E-Field is then computed from the value of the current density on the wires. 4.3.7 Constraints Of NEC2 NEC2 has certain constraints due to its implementation or the underlying physics. In this paragraph the constraints are listed and explained. The next Section will then explain the approach undertaken for dealing with those limitations. Length Of Segments First of all, we need to point out the differences between a segment and a wire. A wire is an edge of a face and can be divided in segments. A segment is then an elementary element used for the computation of the current density and then the scattered E-Field. The length ∆ of a segment should respect the following conditions 49 Chapter 4 4.3. Electromagnetic Model And Simulation 10−3 < ∆ < 1/8 λ (4.10) If the segments are too large a loss of accuracy in the numerical computation appears. This constraint can be compared to the coherency constraint that is needed for ISAR imaging that states that the coherency is lost if we have an error of more than π/4 on the phase. On the other hand, if the segments are too small the value of the E-Field at the centers of two neighboring segments are too close and this can create inaccuracies due to quantization issues. Moreover, even if the lower bonud in 4.10 is not reached, too small segments should be avoided to reduce CPU-time consumption. Radius Of Wires NEC2 offers two different methods for the computation of the interaction matrix G. The first method is based on a thin wire condition, i.e. each wire of the model should have a radius R sufficiently smaller in comparison to its length ∆, or R < 1/8 ∆ (4.11) A second method is also implemented in NEC2 based on an extended-thin wire condition, wherein the requirement on the radius R is less limiting but at a high processing time cost. In this thesis, only the thin-wire condition is considered and then the radius R has to follow (4.11). Overlapping Of Wires And Parallel Wires The NEC2 input file contains the wires’ extrema coordinates and the number of segments they are divided into. First, NEC2 determines every junctions between all segments. A junction is created if a wire is sufficiently close to another (less than 10−3 times the shorter segments). If wires are too close to each other or worse still, overlapping, an excessive number of junctions will be created and it will at least produce an overconsumption of 50 Chapter 4 4.4. From CAD Model To NEC2 Interpretable Model CPU time or even worse it will reach the limit of wires per junction (maximum 30 wires per junction). A Rule Of Thumb For Modeling A Surface A common rule of thumb used for modeling surfaces is the “same area rules”, which introduces in a new constraint between the surface area of the mesh and the surface area of the modeled objects [8, 34]. The mesh area surface should be twice the area surface of the object for a more accurate model. Then it gives us a constraint on the radius R of the wires used for the mesh. R= AΩ , πL (4.12) where AΩ is the surface area of the object Ω and L is the total length of the wire mesh. The constraint given by Equation (4.12) is the main constraint on the radius of the wires. Therefore, the radius R has to satisfy both conditions (4.11) and (4.12). 4.4 From CAD Model To NEC2 Interpretable Model NEC2 is a well-known program but the main difficulty lies in finding a good model for the object. In this thesis, we used free CAD models using COLLADA files (extension .dae) available on-line in Google SketchUp’s warehouse. Unfortunately, with a COLLADA model available on-line it is not possible to expect to meet all the previously mentioned conditions and a modification of the CAD model is needed to create a NEC2 interpretable model. For that purpose, the main difficulties that the processing will have to deal with are explained and the solution implemented in our work is briefly described. The processing steps used to provide a NEC2 interpretable model are summarized in Figure 4.4. 51 Chapter 4 4.4. From CAD Model To NEC2 Interpretable Model CAD Model Create a symmetric model Merge vertices sufficiently close Check the meshing size Convert the face model to a wire model Create a junction between components Delete wire inside the structure Suppress overlapping of wires Rotate and move the model NEC2 Interpretable Model Figure 4.4: Block diagram of the processing for obtaining a NEC2c interpretable model from a CAD model. CAD Model And Model Imported To MATLAB COLLADA is an XML-based schema to enable applications to freely exchange information about a 3-D model between different software [35]. The main part of the information 52 Chapter 4 4.4. From CAD Model To NEC2 Interpretable Model in the COLLADA files is out of the scope of our interest, and only a list of vertices and a list of faces are imported from the COLLADA files to MATLAB. In those two lists, a vertex consists of a vector with three Cartesian coordinates and a face consists of three indexes referencing three vertices in the list of vertex. Moreover, a COLLADA model is composed of components, each of which describes a part of the object. Creating A Symmetric Model By providing a symmetric model to NEC2 and giving it the necessary symmetry information, we decreases the processing time and memory requirement needed for the computation of the scattered E-Field of the target. Moreover, the assumption that an airplane is symmetric is practically reasonable. Unfortunately, the COLLADA models obtained on-line are not symmetric and the models have to be modified in order to obtain a symmetric model. The operator has to define three points non-collinear onto the symmetry plane of the model, a symmetry plane is then numerically defined. If a triangle face is cut by the symmetry plane, the triangle face is divided in 4 triangle faces, the first face is defined by one vertex and the line intersection between the initial face and the symmetry plane, the remaining trapezoid is then divided into three faces. Finally, only triangle faces from one side of the airplane are kept. By an affine symmetry, the second half of the model can be reconstructed. The work described in this paragraph is represented in Figure 4.4 by the block Create a symmetric model. Merge Vertices Too Close Together More often than not a vertex is not unique, so two indexes (or more) may refer to the same vertex. The first steps then consists of limiting the number of vertices by deleting all the wires appearing twice in the list. A similar issue is that some vertices can be extremely close, and those vertices have to be merged to reduce the number of vertices and also to avoid overly small wires. A criterion is defined such that if two points are separated by less than the criterion distance then the vertices have to be merged. Moreover, if two 53 Chapter 4 4.4. From CAD Model To NEC2 Interpretable Model vertices that have been merged belongs to the same face then the face has to be deleted. The work described in this paragraph is exemplified in Figure 4.4 by the block Merge vertices sufficiently close. Creating A Sufficiently Dense Mesh Secondly, the COLLADA model is a triangle face model of the object and we need to create a wire mesh model from it. The wire mesh is created from the edges of the triangle face model. The wire mesh has a similar behavior to the metallic face if the wire meshing is sufficiently small. In that purpose, if a surface area of a triangle face is not small enough then the face is divided in 4 similar faces with a ratio 12 , represented in Figure 4.5. 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 −0.2 −0.2 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 −0.2 (a) Original face 0 0.2 0.4 0.6 0.8 1 1.2 (b) Face subdivided 1 0.8 0.6 0.4 0.2 0 −0.2 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 (c) Wire Model extracted Figure 4.5: Example of a face divided in four sub-faces and the wires model derivated from it. 54 Chapter 4 4.4. From CAD Model To NEC2 Interpretable Model The area of a face has to be smaller than: Af ace < Pmin · λ2 , (4.13) where λ is the wavelength, Pmin is a chosen criterion. The work described in this paragraph is represented in Figure 4.4 by the blocks Check the meshing size and Convert the face model to a wire model. Controlling The Junction Of Components The COLLADA models available are composed of components and components may not fit perfectly together, e.g. for providing a better visual effect most models are assembled so that the faces of each components are crossing each other. The electrical junction between two components is not guaranteed by the COLLADA model. Indeed, the vertices provided by different components of a same model may not provide any vertex in common and thus the total structure may be only a juxtaposition of wire structures that are almost but not exactly a whole wire structure. The electrical junction between components is created by a modification of the intersection between two faces from different structures. First, each wire crossing a face is divided in two parts and new wires are added to provide an electrical junction between the two faces, as illustrated in Figure 4.6. Finally, wires inside the structure have to be deleted. The work described in this paragraph is represented in Figure 4.4 by the block Create a junction between components and Delete wire inside the structure. Avoiding Overlapping Of Wires The processing tends to produce overlapping or extremely close parallel wires, which may result in a model that NEC2 is not able to interpret. Therefore, a check on those two conditions has to be implemented. Two wires are considered as parallel if they have a same direction vector, the distance between the extremity of the two wires is indicating 55 Chapter 4 4.4. From CAD Model To NEC2 Interpretable Model Original Wire Wires divide in two New Wires Original Wire 1 1 0.5 0.5 0 0 −0.5 −0.5 1 −1 0 0.2 0.5 0.4 0.6 0.8 1 0 (a) Before the processing 1 −1 0 0.2 0.5 0.4 0.6 0.8 1 0 (b) After the processing Figure 4.6: Example of a face crossed by a wire and the modification of the wires structure induced the wires are sufficiently close to create a problem. If the wires are parallel and too close, different configurations are possible such as one wire is included in the other or the two wires are only overlapping at one vertex. All those issues are analyzed and each wire is divided in sub-wires. Afterwards, the duplicated wires are all deleted and the overlapping is thus avoided. The work described in this paragraph is represented in Figure 4.4 by the block Suppress overlapping of wires. Positioning The Models Finally, the last step consists of a rotation and a translation of the position of the airplane model in the Cartesian coordinates to be able to compare the model with other work published in the literature. Indeed, the variation of few degrees from other works can give a quite different RCS and thus a different radar image. A correctly oriented orthonormal base is attached to the object, then a change of base allows us to define the coordinates of each wires in this new base. The new base is defined such that its center is the middle of the two farther points from the symmetry plan, the first vector of the base is defined from the center of the new base to the nose of the airplanes, the second vector is the normal vector of the symmetry plan and the third vector is the cross product of the two 56 Chapter 4 4.5. Validation Of The Approach And Limitations first ones. of course, all vectors are chosen normalized. Finally a translation vector and a rotation matrix can be defined to perform a change of basis and to obtain the coordinates of the model in the new base. The work described in this paragraph is represented in Figure 4.4 by the block Rotate and move the model. 4.5 4.5.1 Validation Of The Approach And Limitations Verification On A Sphere The meshing obtained by our method is verified and validated thanks to the use of a sphere as a canonical object in order to provide a comparison between our work and the other work published in the literature [8, 17, 36]. The wire model of the sphere gives good results for low frequency but the accuracy decreases with the highest frequency as pointed out by [36] for the case of polyhedral spheres. In our simulation the first local minima at the beginning of the resonance zone are the same as the minima obtained with the Mie’s theory [15] as shown in Figure 4.7 and allows us to validate the behavior of the monostatic RCS in function of the frequency. Therefore, NEC2 and the conformal model obtained appears to be a good simulation method for the RCS in the Rayleigh region and the lower part of the resonance region. RCS in function of the frequency 6 4 2 RCS (dBSm) 0 −2 −4 −6 −8 −10 −12 Polarisation VV by NEC2 Polarisation VV by Mie series 0 10 20 30 40 Frequency (MHz) 50 60 70 Figure 4.7: RCS of a 10-m sphere with 5376 faces. 57 Chapter 4 4.5. Validation Of The Approach And Limitations Moreover, by using a frequency such that ka = 5.3 where k is the wavenumber and a the radius of the sphere, our bistatic RCS is similar to the RCS obtained by [8], as shown in Figure 4.8. RCS in function of the scattered Angle for a fix illumination at 50 MHz 2 10 1 RCS (dBSm) 10 0 10 −1 10 Polarisation VV by NEC2 Polarisation VV by Mie series −2 10 0 50 100 150 200 250 Bistatic Angle (degrees) 300 350 400 Figure 4.8: RCS of a 10-m sphere with 5376 faces when ka = 5.3, i.e at 50 MHz. In this section, we have shown that the RCS of a sphere obtained by electromagnetic simulation based on a wire model that is sufficiently dense or by the Mie’s theory are really close. It allows us to validate the model built from the processing developed in Section 4.4. 4.5.2 Estimation Of The Computation Time And Memory Required As previously mentioned in Section 4.3.6, if NEC2 is used for the simulation of a wire structures composed of N wires, then the electromagnetic problem consists of solving 4.8 E = GI (4.14) where G is the N × N matrix containing the interaction between each wires. I is the amplitude of the basic function associated to each wire and E is the electric field at the center of each field. The G matrix is a complex matrix, which means that 16 bytes are 58 Chapter 4 4.5. Validation Of The Approach And Limitations needed per coefficient of the matrix, and hence the minimum memory size needed for the system is M emory = 16 × N 2 (4.15) For instance, a 40,000-segment model requires at least 25,6 GB of memory for storing the G matrix. Attention should be paid to the limitation of the operating system (OS) used by the computer. Solving of Equation (4.14) is done in two steps, first an LU decomposition of the matrix is done then two equations are solved by the Gauss pivot method applied twice to a triangular matrix. The complexity of the LU decomposition is 2 3 N +O(N 2 ) 3 and an inversion of the system is also a 2N 2 +O(N 2 ) complexity. Figure 4.9 shows the real computation time for a sphere with an increasing number of wires and the estimated computation time by using a second order or third order polynomial curve fitting approximation. 40 Real Time needed Estimated time by a 2nd order polynomial Estimated time by a 3rd order polynomial 35 30 CPU Time needed (H) 25 20 15 10 5 0 −5 0 0.5 1 1.5 2 2.5 Number Of Segments 3 3.5 4 4 x 10 Figure 4.9: CPU time needed in function of the number of segments, with a fixed number of incident and scattered angle. It appears that both approximations are really close and that the time needed is a quadratic function of the number of segments. So the LU decomposition is not the 59 Chapter 4 4.5. Validation Of The Approach And Limitations operation taking the most of time but the allocation of memory and the computation of the coefficient of the square matrix G. Figure 4.10 shows the time needed for a sphere with 1620 segments in function of the number of incident and scattered angles computed. It appears that the number of angles has a linear influence on the computed time needed. Furthermore, the influence of the number of incident angles is higher than the influence of the number of reflected angle. 80 70 TimeCPU Needed 60 50 40 30 Number of scattered angle Number of incident angle 20 0 50 100 150 200 250 300 350 400 Number of angles Figure 4.10: CPU time needed in function of the number of incident and reflected angles. 4.5.3 Remaining Limitations Other limitations have been discovered by users of NEC2. The number of segments is limited to N = 46340, because memory allocation is not possible for a larger number of segments. It corresponds to an error when the allocation of memory is more than 32 GB. An analysis of the problem indicates that the problem comes from the type of a pointer in the NEC2 software. Indeed a long int is used for the pointer of the G matrix elements and when more than N segments are used N 2 > 231 complex values are needed for the G matrix which is more than the value supported by the long int type. We do not provide a correction to the NEC2 program not to create a loss of stability of the program. 60 Chapter 4 4.6 4.6. Simulation Of Radar Cross Section Of Airplanes Simulation Of Radar Cross Section Of Airplanes The processing flow presented previously is applied to different airplanes and their RCS is computed. The airplanes considered are: • General Dynamics F-16 Fighting Falcon, a 14.8 meters fighter aircraft, represented in Figure 4.11a. • Cessna C550 Bravo, a 14.4 meters private jet,represented in Figure 4.11b. 6 6 4 2 Z 4 0 2 Z −2 0 −10 −2 −5 5 −5 0 5 0 5 0 5 −5 0 −5 Y X Y X (a) General Dynamics F-16 Fighting Falcon (b) Cessna C550 Bravo Figure 4.11: Airplane CAD model used for PBR imaging. 4.6.1 RCS At Different Frequencies In this section, the influence of the frequency on the bistatic RCS of the airplane is pointed out for the F16 and the Cessna Bravo C550 as shown in Figure 4.12, the maximum of the RCS is provided in the top-left corner of each representation. The number of lobes depends mainly on the frequency considered, at low frequency (20 Mhz) the bistatic RCS has only two lobes, but at higher frequency the number of lobes increases. Moreover, it can be observed that the Babinet’s rule can be applied over the range of frequencies considered and a diffraction phenomenon appears [15]. Indeed, 61 Chapter 4 4.6. Simulation Of Radar Cross Section Of Airplanes max =29.1426 dB max =31.006 dB 90 90 30 120 60 60 20 20 150 150 30 30 10 10 180 0 210 f=20MHz f=40MHz f=89.7MHZ 330 240 30 120 300 270 (a) Cessna Bravo C550 180 0 210 f=20MHz f=40MHz f=89.7MHZ 330 240 300 270 (b) F16 Figure 4.12: Influence of the frequency on the bistatic RCS. the back-lobe amplitude of RCS is inversely proportional to its spread and to the ratio between the size of the airplane and the wavelength considered which is coherent with the theory of diffraction. Finally, the RCS of the airplane model is symmetric since the airplane model is symmetric and the transmitter is on the symmetry axis. 4.6.2 Variation Of RCS In Function Of An Orientation Error Of The Airplanes In this section, the influence of an orientation error, in both elevation and azimuth, on the bistatic RCS of the airplane is pointed out. The position of the transmitters and the receiver are supposed exact but the orientation, direction of the airplanes’ nose from the center of the wing, is slightly modify by few degrees in azimuth (Figure 4.13) and in elevation (Figure 4.14). Different points can be emphasized on the RCS obtained for an azimuth mistake. First, the Babinet’s rule is respected for all configuration and then the maximum of the bistatic RCS is obtained when the transmitter and the receiver are symmetric from the center of the target. The value of the maximum is almost fixed from one azimuth 62 Chapter 4 4.6. Simulation Of Radar Cross Section Of Airplanes max =30.9484 dB max =27.2121 dB 90 90 40 120 60 60 30 20 20 150 30 120 150 30 30 10 10 180 0 210 330 2 degree less 240 Reference Elevation 2 degree more 300 270 (a) Cessna Bravo C550 180 0 210 3 degree less Reference Elevation 3 degree more 330 240 300 270 (b) F16 Figure 4.13: Influence of an azimuth error on the bistatic RCS. orientation to another which is coherent since the value of the surface diffracted varies a little. Second, the symmetry of the model is respected when the azimuth of refence is used and the symettry is lost when a 2 degrees mistake is done on the azimuth. Moreover, the two RCS curves for 2 degrees and - 2 degrees mistake are symmetric of each other, which seems to be normal since the model is symmetric. Finally, it appears that the RCS of the Cessna Bravo C550 is less influenced by a mistake on the azimuth, for instance the bistatic RCS of the F16 at 45◦ has a quite different dynamic for each reference of azimuth. Different points can also be emphasized on the RCS obtained for an elevation mistake. Firstly, the Babinet’s rule is also respected for all configuration and then the maximum of the bistatic RCS is obtained when the transmitter and the receiver are symmetric from the center of the target. The value of the maximum of the RCS is varying a bit more than when the azimuth orientation is modified, which can be explained by the fact that the surface diffracted is varying more with the elevation than with the azimuth. Second, the symmetry of the model is always respected. Moreover, the two RCS curves for 2 degrees and - 2 degrees mistake are symmetric of each other, which seems to be normal since the elvation doesn’t change the fact that the transmitter is onto the symmetry plan. Finally, 63 Chapter 4 4.7. Simulation Of PBR Images Using Low Frequency Signals max =31.3744 dB max =27.4368 dB 90 90 40 120 60 30 120 60 30 20 20 150 150 30 30 10 10 180 0 210 330 3 degrees less 240 Reference Elevation 3 degrees more 300 270 180 0 210 3 degrees less Reference Elevation 3 degrees more 330 240 (a) Cessna Bravo C550 300 270 (b) F16 Figure 4.14: Influence of an elevation mistake on the bistatic RCS. the overall influence of an elevation mistake does not seem to change the dynamic but only the value of the RCS obtained. A last general remark can be done over the influence of an orientation mistake, it does not change totally the RCS of the airplane. This property is important for two main reasons, the first reason is that it proves that the wire mesh has a behavior close to a PEC solid object contrary to a wire grid not enough dense [36]. The second reasons is that a airplane position mistake and thus a airplane orientation mistake does not prevent us to build PBR images. 4.7 Simulation Of PBR Images Using Low Frequency Signals 4.7.1 Simulation Of Passive Bistatic Radar Image PBR images are built from the CRCS obtained in Section 4.6. A monostatic radar image of an F16 and of a Cessna Bravo C550 is built from a 360 degree variation of the aspect angle and by using the frequencies available in Singapore. Figure 4.15 shows the two radar 64 Chapter 4 4.7. Simulation Of PBR Images Using Low Frequency Signals images with or without the shape of the airplanes. The two radar images are different by the position of their maximum. Different remarks on the PBR images obtained have to be expressed. First, the pixel square dimension used is 10 cm while the wavelength of the signal used is close to 3 meters, thus the separation of two pixels by a third pixel with a lower intensity doesn’t means that we have two different bright-points. Second, the use of a too large aspect angle variation has to be interpreted carefully since a different part of the airplane is hidden at different aspect angle, a shadowing effect appears and deteriorates the images. However, the monostatic radar image of the two airplanes are different and the shape of the radar image is close to the dimension of the airplanes considered. The purpose of our work is to build PBR images. In a first step, a constant 20 degrees bistatic angle and a 120 degrees variation of the aspect angle between 230 and 350 degrees are considered, this configurations was considered in [8], the PBR images obtained are then represented in Figure 4.16. The shape of the airplanes is not drawn onto the figure in order no to hide a part of the PBR images. The two PBR images are quite different. Indeed, the Cessna Bravo C550 seems to have a larger number of bright point. Moreover, the spread of the bright-point is more important for the Cessna Bravo. The difference of shape between the two airplanes should be sufficient for being able to differentiate their radar images. 4.7.2 Simulation Of Passive bistatic Radar Image Using Actual Airplanes Trajectory Finally, the use of actual airplanes trajectory for filling the Fourier space is considered for the PBR image is represented in Figure 4.17. The range of aspect angle variation is close to 90 degrees and the bistatic angle is ranging from few degrees to 20 degrees. Figure 4.18 shows the PBR images of a F16 and a Cessna Bravo C550 obtained from the actual trajectory just described previously. The shape of the airplane was added to 65 4.7. Simulation Of PBR Images Using Low Frequency Signals 30 0 30 0 20 −5 20 −5 10 −10 10 −10 0 −15 0 −15 −10 −20 −10 −20 −20 −25 −20 −25 −30 −30 −30 −30 −30 −20 −10 0 10 x−axis, meters 20 30 y−axis, meters y−axis, meters Chapter 4 −20 −10 30 −30 30 0 20 −5 10 −10 0 −15 −10 −20 −20 −25 −30 −30 (c) Cessna Bravo C550 20 (b) F16 y−axis, meters (a) Cessna Bravo C550 0 10 x−axis, meters −20 −10 0 10 x−axis, meters 20 30 (d) F16 Figure 4.15: Monostatic radar images two different airplanes with or without their shape using a 360 degrees range of angles. show that the exact position of the airplanes. The two PBR images, represented in Figure 4.18, are relatively similar for the F16 and Cessna Bravo C550. The difference between the two radar images is mainly a difference of spreading of the bright point intensity. Finally, the difference of PBR image resolution between Figures 4.16 and 4.18 corresponds to the difference between the simulation using simulated or actual constraints. 66 −30 4.8. Conclusion 30 0 30 0 20 −5 20 −5 10 −10 10 −10 0 −15 0 −15 −10 −20 −10 −20 −20 −25 −20 −25 −30 −30 −30 −30 −30 −20 −10 0 10 x−axis, meters 20 30 y−axis, meters y−axis, meters Chapter 4 −20 −10 (a) Cessna Bravo C550 0 10 x−axis, meters 20 30 (b) F16 Figure 4.16: PBR images of two different airplanes with a 20 degree constant bistatic angle and an aspect angle ranging from 230 to 350 degrees. 8 1.5 x 10 1 fy−axis (Hz) 0.5 0 −0.5 −1 −1.5 −1.5 −1 −0.5 0 fx−axis (Hz) 0.5 1 1.5 8 x 10 Figure 4.17: Fourier space considered for the PBR imaging. 4.8 Conclusion In this Chapter, we built a NEC2 interpretable model of small airplanes from CAD models available on-line. The CAD-model was modified to build a wires mesh model respecting different conditions given by NEC2 constraints and physical constraints. Afterward, NEC2 was used for the computation of the E-Field reflected off the object from the wire models and the CRCS of the airplanes were extracted. The RCS of two different 67 −30 Chapter 4 4.8. Conclusion (a) Cessna Bravo C550 (b) F16 Figure 4.18: Influence of an elevation mistake on the bistatic RCS. airplanes, an F16 and a Cessna, with similar size were presented, and the influence of different parameters were emphasized. Finally, PBR images of the two airplanes were built from the CRCS and were presented. The PBR images obtained from a monostatic configuration or from a constant bistatic configuration show that the PBR images can be used for the identification of the airplane. However, the PBR images obtained from actual trajectories seems less easy to interpret and discrimination between the two airplanes is not a priori evident. Unfortunately, the simulation of PBR images for larger airplanes was not possible because of a limitation regarding the number of wires usable into NEC2. 68 Chapter 5 Passive Bistatic Radar Using Real Data 5.1 Introduction In the previous Chapter, we discussed the principles behind PBR images and a simulated PBR system was built. In this chapter, a PBR system using the radio FM broadcasting signals around Singapore is presented. In Section 5.2, the design of the passive bistatic radar built is presented. The PBR system is built from an already existing one and the differences between the original and the proposed PBR are pointed out. In Section 5.3, the experimental results are presented. Range Doppler map obtained by the PBR system are discussed, the tracking of the airplanes in RD map initialized by the ADSB data is performed, and the RCS extracted from them are presented. Finally, in Section 5.3.3 , a constructive critic about our work is performed to explains the reasons why PBR images were not successfully generated. 69 Chapter 5 5.2 5.2. Design Of The Experiment Design Of The Experiment 5.2.1 General Description Of The Real Data Collection And Processing The purpose of the thesis is to build PBR images of airplanes using FM broadcasting signals for identification purposes. In this section, we present the processing chain used for the construction of PBR images from real data. Figure 5.1 shows the full processing flow used. It should be emphasized that the work presented here was done in collaboration with the Temasek Laboratory at NTU (TL@NTU) and the RF processing is out of the scope of our work. Moreover, it has to be emphasized that the extraction of the RCS is reused from previous work performed at TL@NTU [37]. Signals RF processing Extract RCS Build PBR image PBR Images Main work performed Figure 5.1: Block diagram of the processing chain for experimental data. As underlined earlier, the extraction of the RCS is an interface with the real data or the simulated data. Moreover, the radar image processing remains unchanged in this chapter and only few comments on it are expressed in this chapter. Therefore, the extraction of the RCS from the real data is discussed in the following sections and it is presented Figure 5.2. Section 5.2.2 presents the blocks ADC and Filter. Sections 5.2.3 presents the blocks Adaptive interference cancellation, matched filter, matched filters, track the targets, compute E-Fiel powers, and Compute RCS. Sections 5.2.4 presents the blocks Synchronize FM data and ADSB Data and Filter ADSB Data. The processing was performed at TL@NTU [38]. Improvements provided by the present work highlighted by the dashed box in Figure 5.2. The synchronization has 70 Chapter 5 FM Data 5.2. Design Of The Experiment ADC Filter Adaptive interference cancellation ADSB Data Matched filter Matched filters Synchronize FM and ADSB data Estimate position Track the targets of targets Compute EField intensity Filter ADSB Data Compute RCS RCS Figure 5.2: Block diagram of the extraction of RCS from real data. The improvement provided by our work is emphasized by the yellow background been modified, the ADSB data are filtered to provide a more accurate estimation of the airplane position, the tracking is performed on interpolated positions, the computation of the RCS is taking into account the gain of the antenna, and finally the processing is modified to be run on parallel cores. 5.2.2 Acquisition Of Measured And Reference Signals Two signals are measured by our PBR system, the first being the reference signal received by the antenna directed towards the FM station and the second signal being the measured signal received by the antenna directed towards the airplanes that we wish to track. The FM signals are digitized by an analog-to-digital converter (ADC). The signal is then centered, filtered by a pass-band filter near the frequency of interest and decimated. The 71 Chapter 5 5.2. Design Of The Experiment processing is parallelized for each frequency in order to reduce the processing time. 5.2.3 Generation Of RD Map And Extraction Of RCS In this section, we explains how the RCS is extracted from the FM signals. In this section, the power refers to as the complex power, i.e the phase is also considered. Using notation presented in Figure 3.5, the direct path signal power PRT received is PRT = PT GRT GT R λ2 4πL2 (5.1) where L is the baseline distance and GRT and GT R are antenna gain of the receiver and transmitter. The ratio between the direct path signal power in (5.1) and the reflected signal power given in (1.7) gives us the value of the RCS [2] σ= 2 2 4πRR RT GT R GRT PRT L2 GT S GRS PRS (5.2) The last equation emphasizes the need for good knowledge of the antenna gain and the position of the airplanes for computing the RCS of the airplanes which is discussed in Section 5.2.4. This computation of the RCS corresponds to the block compute RCS in Figure 5.2. The computation of the power of the reflected signal and direct path signal is obtained from Range-Doppler (RD) map. An RD map is a representation of a two dimensional matched filter between a reference signal and an unknown signal. The two dimensions used are the frequency shift and delay shift applied to the reference signal. In a radar application, the frequency shift is referred to as the Doppler shift and the delay shift is referred to as the range shift. The matched filter operation is given by the following equation [39] +∞ s(t)s∗ref (t − τ )ej2πf t dt M (τ, f ) = (5.3) −∞ 72 Chapter 5 5.2. Design Of The Experiment where τ is a delay, f is a frequency shift, s(t) is the measured signal and sref (t) is the reference signal. Both signals contain a strong direct path signal but it is delayed and slightly reduced for the unknown signal because of the position of the antenna and their orientation. The integration should be done on an infinite time, but practically the integration is done over a limited time called coherent integration time (CIT). Three RD maps are build: • RDMap1 corresponds to the matched filter between the reference signal and itself, referred to as ambiguity function of the reference signal performed by the block Matched filters in Figure 5.2. • RDMap2 corresponds to the matched filter between the reference signal and the measured signal, performed by theblock Matched filters in Figure 5.2. • RDMap3 corresponds to the matched filter between the reference signal and the measured signal after an adaptive interference cancellation described in [40], performed by the block Matched filter in Figure 5.2. The direct path signal power PRT is the maximum of the RDmap1 obtained in (0, 0). The reflected signal power of a target at a bistatic range rB and with a Doppler shift fd corresponds to the value of RDmap2 in (rB , fd ) corrected by the value of the ambiguity function (RDMap1) in (rB , fd ) [38] and divided by the power of the direct path in the measured signal. The power of the direct path in the measured signal is obtained by multiplying the direct path signal power PRT by the ratio of the maximum of the RDMap1 and RDMap2. This computation of the E-field powers corresponds to the block Compute E-Field intensity in Figure 5.2. Since there are a strong clutter and the direct path signal is quite strong in the measured signal, the targets cannot be detected in RDMap2. An adaptive interference cancellation is performed onto the unknown signal to build RDMap3, block Adaptive interference cancellation in Figure 5.2. The adaptive cancellation modifies the measured 73 Chapter 5 5.2. Design Of The Experiment signal to maximize the signal to clutter ratio and so modify the echo signal. The phase and amplitude may have been changed by the processing but RDMap3 can be used for tracking the target. The ADSB Data are used to provide a first estimation of the position (r˜B , f˜d ) of the target, the global maximum of RDMap3 on a window around the estimated position (r˜B , f˜d ) gives us the exact position (rB , fd ) of the target, referred to as tracked position in this thesis. This tracking corresponds to the block Track the targets in Figure 5.2. 5.2.4 Synchronization And Filtering Of The ADSB Data The estimation of the position is done by using ADSB data. The ADSB data transmitted by an airplane contains the aircraft identifier, its encoded position, and ground velocity. An error on the position is due to the encoding and has been pointed out in [41]. The bistatic range RB (t) at a time t is the bistatic distance between the transmitter and the receiver RB (t) = RR (t) + RT (t) − L (5.4) where RT (t) is the range between the transmitter and the airplane at the instant t, RR (t) the range between the receiver and the airplane at that instant t, and L the baseline distance between the receiver and transmitter. The Doppler shift fd (t) is defined by fd (t) = fc RB (tt) − RB (t − ∆t) fc d RB (t) ≈ c dt c ∆t (5.5) where ∆t corresponds to the time difference between two ADSB packets, fc to the centered frequency, and c to the light velocity. The bistatic and aspect angles are defined as β(t) = ∠ SR(t), ST (t) , (5.6) 74 Chapter 5 5.2. Design Of The Experiment α(t) = ∠ V , SR(t) ST (t) + RR (t) RT (t) ≈∠ RS(t) − RS(t − ∆t) SR(t) ST (t) , + ∆t RR (t) RT (t) , (5.7) where ∠(u, v) is an operator giving the angle between u and v, S the scatterer, R is the receiver, T the transmitter and V the airplane velocity. If those formula are directly applied to the ADSB data, because of the encoding error of the airplane position, the aspect angle and Doppler shift are totally wrong. Indeed the range difference between two consecutive points may have up to 200-meters error and the time difference ∆t between two ADSB packets is less than 0.5 seconds so the difference of position between two consecutive points, around 200 meters, is less than the potential error due to the encoding. 20 140 10 130 Aspect angle smoothed Aspect angle observed 120 aspect angle (degree) Doppler shift (Hz) 0 −10 −20 −30 110 100 90 −40 Dopler shift smoothed Doppler shift observed −50 −60 80 70 0 50 100 150 200 time (ADSB index number) 250 (a) Estimation of the Doppler shift 300 0 50 100 150 200 time (ADSB index number) 250 (b) Estimation of the Aspect angle α Figure 5.3: Example of ADSB data smoothed by a polynomial function of degree 6 and its influence on the aspect angle and Doppler shift at the different instant of a trajectory Unfortunately, the bistatic range and the Doppler shift are needed for the extraction of the RCS as was pointed out in Equation (5.2). The data has to be filtered to provide a correct aspect angle and a correct Doppler shift. The airplanes trajectories studied are simple airliners trajectories and thus can be modeled by a polynomial function of low degree. Figure 5.3 shows the influence of the position correction on the aspect angle and on the Doppler shift at different instant of the trajectory. The filtered positions are then 75 300 Chapter 5 5.3. Experimental Results used for extracting the RCS. 5.3 5.3.1 Experimental Results Range Doppler Map Obtained An example of RD maps obtained with or without using an adaptive interference cancellation is presented in Figure 5.4. Figure 5.4a represents the matched filter between the reference signal and the measured signal (RDMap2). (a) RDMap1 (b) RDMap2 Figure 5.4: RD map obtained by using FM signals and the station at 93.8 MHz. If the direct path and the clutter are not canceled then the signals reflected off the targets are hidden in the RD map because their power are too low in comparison of the power of the reflected path or the clutter return power. RDMap1 is not represented since its representation is close to RDMap2. In Figure 5.4b, the matched filter between the reference signal and the unknown signal after adaptive interference cancellation is represented and cursors have been added to indicate the position of an airplane according to the ADSB data. The two cursors corresponding to the closest positions, bistatic range of 23km and 40km, are close to a peak into the RD map, those peaks correspond to 76 Chapter 5 5.3. Experimental Results reflected path signals. The peak value does not gives us a correct information on the power reflected by the scattering points since the unknown signal was modified to RDMap 3 but gives us an exact position of those targets onto RDMap1 and RDMap2. Those three RD maps are used in the following for the computation of the direct path signal power, the reflected signal power and thus the RCS. 5.3.2 RCS Extraction Of Commercial Airliner By Using Real Data Figure 5.5 represents RDMap3, cursors are added to show the estimated positions with the ADSB data and the tracked positions obtained by finding global maximum of RDMap3 in a window centered on the position estimated from the ADSB data. 85 150 80 Doppler frequency (Hz) 100 75 50 70 0 65 −50 60 −100 −150 −200 0 55 Estimated Position from ADSB Tracked position from RDMap3 20 40 60 80 Bistatic range (Km) 50 100 120 dB Figure 5.5: Example of target tracking on RDMap3. We call a correct tracking of a target when the position of the target from one RD map to the following RD maps is sufficiently smoothed and the tracked position is close enough to the position estimated from the ADSB data. For instance, in Figure 5.5, only the target with a bistatic range of 43 km is correctly tracked. The tracking of this airplane is visually checked on each RDMap3, the tracking appears to be correct for 95% of the 77 Chapter 5 5.3. Experimental Results 200 RDMap3 checked. A comparison between the estimated positions and the tracked positions for one target is provided in Figure 5.6. The tracked bistatic range and Doppler shift give us an information on the pixel position of the RD map which contains the targets. Since the range cell size is 1,5km and the Doppler cell size is 2Hz, the variation over 1,5km or 2Hz does not indicate an error on the target tracking but the variation can be due to a target situated between two pixels in RDMap3 and that the bistatic range and Doppler shift obtained from tracking on RDMap3 are step functions. 4 −15 5.4 x 10 −20 5.2 Bistatic Range (in meter) Doppler Shift (in Hz) −25 −30 −35 −40 5 4.8 4.6 −45 −55 4.4 Estimated from ADSB Data Tracked from RDMap3 −50 0 20 40 60 CIT Number (a) Doppler shift 80 Estimated from ADSB Data Tracked from RDMap3 100 4.2 0 20 40 60 CIT Number 80 (b) Bistatic range Figure 5.6: Example of Doppler shift and bistatic range estimated from ADSB data and tracked from RDMap3. If Figures 5.6a and 5.6b are analyzed together, it can be seen that the tracking is not inaccurate for a few values since the variation of Doppler shift and bistatic range after tracking remain smoothed and close to their value estimated by the ADSB data. Inaccuracies on the tracking presented in Figure 5.6 appears at the 8th , 18th , and 44th CIT. Figure 5.6b shows that a bistatic range offset exists between the estimated and tracked bistatic range. Figure 5.7 shows the ratio between the value of the peak in RDMap3 and the average value of RDMap3. It help us to point out the reason why fews values are not tracked 78 100 Chapter 5 5.3. Experimental Results correctly. Indeed, the power ratio represented is smaller for positions not correctly tracked than for correctly tracked position. Moreover, Figure 5.7 also shows that this ratio remains low for all RDMap3s. 13 12 Power Ratio (in dB) 11 10 9 8 7 6 5 4 0 20 40 60 CIT Number 80 100 Figure 5.7: Representation of the ratio between the peak value corresponding to the reflected path and the noise level on RDMap3 An example of power received from the direct path and the reflected path is given in Figure 5.8a and the computed RCS is given in Figure 5.8b. The power received from the direct path is quite constant, while the power received from the reflected path varies. Two main possible reasons exist, the reflected signal is too low to be able to separate it from the clutter and the direct path signal of the RCS of the airplanes is changing abruptly from a CIT to another. Finally, the RCS σ, expressed in dBm, is represented in a polar representation (α, σ) in Figure 5.9a where α denotes the aspect angle and the corresponding bistatic angle is shown in Figure 5.9b. The polar representation is presented to provide a comparison with the Chapter 4. Indeed, we have discussed in Chapter 4 of the number of lobe in a polar representation (α, σ) and pointed out that it depends on the ratio between the airplane size and the wavelength. The airplanes considered are larger for the real data than the F16 used for simulation, so the number of lobe should be smaller. The polar 79 Chapter 5 5.3. Experimental Results 120 60 110 55 100 45 80 RCS (in dBm) Signal Power (in dBW) 50 90 70 60 35 30 50 25 40 Direct Path Signal Refelected Path Signal 30 20 40 0 20 40 60 CIT Number 80 20 15 100 0 20 (a) Power received 40 60 CIT Number 80 100 (b) RCS Figure 5.8: Example of power received and RCS computed. representation of the RCS represented in Figure 5.9a has a too large number of lobe to be a realistic RCS of the airplane. As a consequence, it can be concluded that the PBR system built is not able to separate the reflected path from the clutter and the direct path signal. max =54.7791 dB 90 Frequency =93.8 MHz 20.7 60 20.6 30 120 20 30 10 180 0 210 330 240 300 270 (a) RCS in function of the aspect angle Bistatic angle (in degree) 20.5 150 20.4 20.3 20.2 20.1 20 19.9 19.8 0 20 40 60 CIT Number 80 (b) Bistatic angle Figure 5.9: Polar representation of the RCS of a target in function of the aspect angle α and its bistatic angle 80 100 Chapter 5 5.3.3 5.4. Conclusion Discussion On The Passive Bistatic Radar System Built The orientation of the antenna should have been more thought. Indeed, the two antennas have been directed to the transmitter and to the trajectories followed by airplanes landing and taking off at Changi Airport, and the antenna’s linear polarization chosen were vertical. Unfortunately, the two antennas in this configurations have an omni-directional radiation pattern in azimuth. As a consequence, the reference signal contains the direct path signal and the reflected path and the unknown signal measured by the other antenna contains also both signals. Therefore, the adaptive interference cancellation performed on the unknown signal cancels both the direct path signal and the reflected path signal. The matched filter cannot be used for computing the power reflected off the targets. A change of the polarization of the two antennas will provide a more directional radiation pattern and thus a better attenuation of the contribution of the reflected path into the reference signal and a better attenuation of the contribution of the direct path in the measured signal. As a result, the adaptive interference cancellation will less attenuate the contribution of the reflected path into the measured signal. Moreover, the direct path signal and the clutter is canceled thank to an adaptive interference cancellation filter. The influence of the adaptive interference cancellation on the amplitude and phase of the reflected signal should be analyzed and taken into account for computing the power of the signal reflected off the target. 5.4 Conclusion In this Chapter, we built a passive bistatic radar (PBR) system using the FM broadcasting signals. The PBR system was reused from a work performed at TL@NTU. However, important improvements were provided to the system. First, the PBR system was parallelized in order to perform the processing on all the frequencies at the same time. Moreover, the ADSB data were smoothed by approximating the airplanes trajectories by low degree polynomial function. The ADSB data synchronization were automatically 81 Chapter 5 5.4. Conclusion synchronized without the intervention of the user. Finally, the tracking of the targets on RD map were improved by interpolating the ADSB data from one packet to another and a better management of the tracking windows was implemented. And finally, the reasons why the RCS of a target were not generated was discussed and a solution was proposed. 82 Chapter 6 Conclusion 6.1 Summary Of The Thesis In this thesis, we discussed the construction of passive bistatic radar (PBR) images of air targets based on FM broadcasting signals as an illuminator of opportunity for identification and classification purposes. The thesis is designed to show that a PBR system is able to provide interpretable PBR images, i.e. PBR images with a resolution significantly smaller than the size of the air targets. The PBR system built is based on the assumption that the target has already been detected and tracked. Since the PBR system is not detecting and tracking the air targets, we consider civilian airplanes providing automatic dependent surveillance-broadcast (ADSB) data provided by the airplanes for obtaining the airplanes’ position. The configuration considered in this thesis is the actual Singaporean configuration, with the position of the receiver and transmitters of the PBR system known. The basic characteristic of the transmitter such as the frequency used, its polarization are also assumed known. On the other hand, the system is passive and thus the FM signals are unknown. First, the construction of PBR images from the complex radar cross section (CRCS) by applying tomographic principles was discussed and implemented. The first part of the 83 Chapter 6 6.1. Summary Of The Thesis work then studied the detection range of the system and the resolution that our system will achieve. Afterwards, we defined the concepts of resolution and of interpretable image. The analysis of the PBR system characteristic is performed for the actual Singaporean configuration based on ADSB data provided by civil airplanes. Examples of PBR images obtained by using bright-points model are generated to underline the definition introduced earlier. Since the bright-point model is proven to give correct results close to the theoretical principles shown previously, a more complex model is investigated to show that the PBR images can be build for airplanes. The purpose of our work is to show that we are able to build PBR images for identification purposes and a bright-point model does not provide a realistic model for airplanes. Therefore, the realization of electromagnetic simulation based on CAD model freely available on-line is investigated. In comparison with more classic radar systemc, the FM frequency are considered as low frequencies. At low frequency, a common approach is to use the method of the moments to simulate the RCS of an object and one of the most common tools is the Numerical Electromagnetics Code (NEC2). The main difficulty is then to build an interpretable model for the software. For that purpose, we create a MATLAB script able to build a wire model interpretable by NEC2 from any COLLADA model. However, although our program is able to build a NEC2 interpretable model for any airplane, NEC2 is limited by its internal constraints and commercial airliners are currently too large for NEC2 to compute of the reflected field. Since we are able to simulate the CRCS of small airplanes such as private jet or fighter jet, PBR images of such aircraft are presented and the influence of the bistatic configurations on the radar images is shown. The PBR images obtained by our simulated system provides slight differences that can be used for discriminating the two airplanes. The resolution of the PBR system and the dimension of the airplanes are too close to provide clearly different radar images. 84 Chapter 6 6.2. Future Work Finally, a PBR system using real data is designed. A receiver is located at the Nanyang Technological University (NTU) for the collection of real data. An ADSB system is used for providing the real-time position of commercial airplanes. The recorded data are then processed to extract the CRCS of airplanes. Unfortunately, the passive radar system built does not provide a sufficient signal to noise ratio for the reflected signal off the target and the RCS extracted is not reliable. On the other hand, the system used show that the synchronization between the ADSB data and the FM data is working and that the ADSB data can be used for tracking commercial airplanes for the PBR imaging system. 6.2 Future Work Various ways ti extend this work should be considered. Four extensions are presented here : • Overcoming NEC2 limitations. • Improving the extraction of the CRCS from real data measurements. • Using of multiple FM station transmitters. • Considering another signal. 6.2.1 Overcoming NEC2 limitations In this thesis, we used NEC2 for simulating the electrical field reflected off air target models. Limitations of NEC2 were pointed out such as the required processing time or the segments limits. The use of more parallel processing would provide a more efficient simulation tool and changing the type of some pointer could increase the memory allocation limit. 85 6.2.2 Improving the extraction of the CRCS from real data measurements The CRCS was extracted from two received signals. The amplitude and phase of those two signals have been processed to find the CRCS of the airplanes. Unfortunately, we were not able to extract from it the correct CRCS of the airplane and to monitor its phase. The adaptive interference cancellation applied to the measured signal for building the RD map is maximizing the signal-to-clutter ratio but does not provide the real power scattered by the target and a better understanding of the influence of the adaptive interference cancellation on the phase and the amplitude of the scattered signals could provide a better estimation of the CRCS. 6.2.3 Use of multiple FM station transmitters and receivers We studied two transmitters that are not co-located for the design of our PBR system. Each transmitter is provided a different incident angle on the target and thus a different kind of information. The harnessing of this sort of illuminator diversity for building PBR images should be investigated. 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Contribution Of The Thesis The main contributions of the thesis are : • The feasibility study of a passive bistatic radar system using the radio broadcasting FM signals for imaging airplanes applied to the Singaporean configuration • The use of low frequency signals to build radar image in a constrained environment based on the principles of tomography from simulated data • The construction of a conformal... Principles Applied To Bistatic Radar Imaging Second, a bistatic configuration is considered in order to apply the tomography principles to passive bistatic radar imaging Figure 2.4 shows the bistatic configuration used for the mathematical description of the tomography principles applied to the bistatic radar imaging, where ω denotes an elementary element of the object, O the center of the object A Cartesian... FM band signals is too low for practical detection and estimation applications However, despite the low image resolution, radio broadcasting FM signals appears to be a good candidate for imaging airplanes thanks to the widespread use of the technology 4 Chapter 1 1.2 Radar and the typical large size of the FM cells In [8], Daoult et al investigated the construction of passive radar images of synthetic... from the signal of a single FM station In this thesis, the construction of passive radar images using CAD-modeled and real airplanes flying actual trajectories 1.2.4 Radar Imaging The radar image of a target is the distribution of its elementary scattering coefficients A radar image is generally presented as a two dimension map where each pixel intensity/color represents the amplitude of the elementary... ratio SR-CRCS Square root of the complex radar cross-section TL@NTU Temasek Laboratory at Nanyang Technological University TL@NTU Worldwide Interoperability for Microwave Access VAC Visual approach chart XML Extensible markup language xii Chapter 1 Introduction The main goal of our work is to build radar images of aircraft using passive bistatic radar signals The use of the FM band for that purpose... of a scattered field of small airplanes using NEC2 • The realization of a tracking system based on both FM data and ADSB data • The processing of the FM data to find the complex RCS of airplanes 6 Chapter 1 1.5 1.5 Organisation Of The Thesis Organisation Of The Thesis The thesis is organized as follows Chapter 2 presents the electromagnetic and radar background needed for the understanding of the radar. .. generation It presents the principles of tomography used for the construction of radar images Chapter 3 presents the feasibility study of the passive bistatic radar system designed in this thesis The chapter discusses the constraints introduced by a true bistatic configuration and their influence on the quality of the radar images obtained by our passive bistatic radar Chapter 4 presents the electromagnetic... receiver-object, and 3 Chapter 1 1.2 Radar Figure 1.2: The bistatic configuration it is derived from Equation (1.7) 1.2.3 Passive Radar A passive radar is a radar system which takes advantage of an illuminator of opportunity to replace the transmitter in a radar system Such systems make use of existing radiated signals already available and so have discretion properties for the radar itself, and do not require... model Chapter 5 presents the design of the passive bistatic radar system built to extract the radar cross section of airplanes The limitations of the system built are underlined and solutions for overcoming them are presented Chapter 6 summarizes the work performed in this thesis and provides ideas for future developments 7 Chapter 2 Principles Of Passive Bistatic Radar Imaging 2.1 Introduction In this... and then for the bistatic configuration The development performed in this Chapter is then used in Chapter 3, 4 and 5 for the construction of radar images The diagram in Figure 2.1 represents the passive bistatic radar considered and it underlines the focus put on the radar imaging part in this Chapter 8 Chapter 2 2.2 Radar Cross-Section And Radar Image Definition Environment parameters FM Data Extract