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High Resolution Radar Cross Section Imaging Based on Complex Target Backscattering Simulation Jiehao Zhu, Jianjiang Zhou, Weijie Xia College of Information Science and Technology, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, P.R. China [email protected] Abstract— Pixel Method which is enlightened from the Graphic Electromagnetic Computing(GRECO) is introduced in this paper and realized by OpenGL and VC programming. Using simulation data, the wideband features of the target can be obtained for radar automatic target recognition(RATR). Some of the calculated features including RCS, range profile, and SAR image which are also refered to zero-dimensional image, onedimensional image, and two-dimensional image of the target are discussed in detail. Results show that the task of complex target backscattering simulation is effective for initial research and development(R&D) of radar automatic target recognition. I. INTRODUCTION There are two main kind of methods for computing Radar Cross Section(RCS) of complex targets in high frequency region at present, including accurate mathematical method and approximate high-frequency method. Accurate mathematical method contain MoM, FDTD, and FIT etc. The characteristic of accurate mathematical method is that for complex target with any shape and material, the result is precise, but limited to the memory and calculation speed of computer. Approximate high-frequency method include GO, PO, GTD, and PTD etc, and can be realized by component method [1], panel method [2], shooting and bouncing rays method [3], and pixel method [4] etc. Approximate high-frequency method own advantages of clear physical concepts and explicit expressions. Radar automatic target recognition R&D requires a mass of experiments. These experiments are not only expensive, but hard to control. Task of simulation replacing of experiments is now widely adopted in initial RATR R&D. By computing the complex target backscattering for specific radar system, wideband features can be obtained. They are abundant in recognizable information, including range profiles, total radar cross sections, range-polarization profiles, range-frequency profiles, and two-dimensional images [5] etc. High resolution signatures play an important role in radar automatic target recognition community. In this paper, pixel method which is enlightened from the GRECO [6] is applied to compute the complex target backscattering by OpenGL and VC programming. Compared with the GRECO, pixel method is based on the given precise CAD modelling, so it is not constrained to the number of screen pixels and provide more precision. Using simulation data, some of the significant imaging signatures are discussed in detail. In addition, the computing results are compared with the measured data, which proves the availability of the task. In sectionĊ, the pixel method is introduced and studied. In sectionċ,Č, andč, the RCS feature of the target, the relative motion effect on the range profile of the target, and the precise imaging of the target in Cartesian coordinate system are discussed in detail respectively. Finally, we conclude with summary in sectionĎ. II. BACKSCATTERING SIMULATION OF COMPLEX TARGET A. Scattering Calculation of the Surface According to the physical optics technique, backscattering of a perfectly conducting surface can be approximate in high frequency by the expression: jk0 Z 0 e jk0 R (1) Es sˆ u sˆ u 2nˆ u H i e jk0 r sˆ dxdy ³ s 4S R where k0 is the wave number of the incident wave, ŝ is the unit vector from the surface to the observer, n̂ is the normal to the surface, r is the position vector of the surface, and R is the distance between the surface and the observer. When applied to complex target, the surface integral is difficult. After discretization of surfaces to pixels, the backscattering of target can be deduced according to GRECO [6]: sin k0 l tan T 2 jk0 z jk0 e jk0 R Es e (2) ¦ 2S R pixels k0 l tan T where l is the actual length corresponding to the pixel, T is the angle between the normal to the surface and the direction of incidence, and z is the distance from the pixel to the observer projected on the incidence direction. Z-Buffer technique can be applied to pixel method to realize exact blanking for the calculation surface acquisition. B. Diffraction Calculation of the Edge Equivalent edge currents method [7] is adopted to calculate the edge diffraction. It is realized by line integral: jk0 e jk0 R ª Z0 Ie sˆ u sˆ u tˆ I m sˆ u tˆº¼e jk0 r sˆ dl (3) Ed 4S R ³c ¬ where tˆ is the tangent unit vector, I e and I m are the electric and magnetic equivalent currents, respectively. Similar to the surface integral, the line integral can be calculated by the sum of discrete sub-lines. The definition of I e and I m is: Ie 2 E i tˆ De (4) jk0 Z 0 sin 2 E ' ______________________________________ 978-1-4244-2193-0/08/$25.00 ©2008 IEEE Im 2 H i tˆ Dm (5) jk0Y0 sin 2 E ' respectively, where E ' is the angle between the edge and the direction of incidence, and De ˈ Dm are scalar diffraction coefficient given by the PTD. When applied to monostatic radar, eq.(3) can be decomposed to specific polarization results [8]. III. RCS OF COMPLEX TARGET The definition of RCS is: V lim 4S R R of 2 Es 2 Ei 2 (6) where E s is the scattering field intensity. Figure 1. is the CAD model of one satellite, Figure 2. is the comparison between the computing results and the measured data. Parameters are given: the bottom radius and the height of the satellite approximate 0.3m and 0.8m respectively, and the radar frequency is 9.0GHz with HH polarization. The computing results are in close agreement with the measured data. Acquisition of high resolution information along the range direction requires wideband signals. Range profile is the IDFT of the wideband frequency responses. Backscattering of moving target can be obtained by calculating the precise distance between radar and target at different time. Relative motion of the target makes the phase of the backscattering contain extra linear and high-order components. The extra linear component leads to range profile shift, and on the other hand, the high-order component leads to range profile decline and widening. The extra phase component make both the resolution and sensitivity of range profile get worse. These effects seriously affect the stability of the features extracted from the range profile, and make the recognition more difficult. Figure 3. is the simulation range profile of the B-52 aircraft at one specific flight attitude, the carrier frequency is 10GHz, the bandwidth is 128MHz, the step frequency is 1MHz, the PRF is 20kHz, and the radial velocity is 50m/s. Figure 4. is the range profile which has the same parameters but with velocity compensation. Fig. 3 Range profile of the moving target Fig. 1 CAD model of the satellite Fig. 4 Range profile with velocity compensation Fig. 2 Comparison between computing results and measured data IV. RANGE PROFILE OF COMPLEX TARGET When radar working at optical region, the scattering characteristic can be described by scattering centers model. V. PRECISE IMAGING OF COMPLEX TARGET In spotlight SAR imaging, when the phase of echoes is compensated, the sampling data in frequency space are arranged in a sector region, as show in Figure 5. T 0 and 'T stands for center azimuth and azimuth range, f0 and B stands for carrier frequency and bandwidth respectively. 0.1m×0.1m resolution SAR images of one kind of aircraft using PFA method and sampling in Cartesian coordinate are presented in Figure 6. and Figure 7. respectively. The blurs at wing tips in Figure 6. are caused by the interpolation errors when using PFA method, and the sampling in Cartesian coordinate method perform better imaging quality. Fig. 5 Format of sampling data in frequency space For the sake of improving cross range resolution, the synthetic aperture needs to be lengthened, and the corresponding angle of the sampling data in frequency space also increased. At the same time, lengthening the synthetic aperture leads to scatter’s motion through range cells(MTRC). Performing the Fourier transformation direct to the echoes leads to blurred images. The reason is that the echoes are sampled in polar coordinates, but the Fourier transformation is fit for Cartesian coordinate only. To solve this problem, one can interpolate the sampling data to the Cartesian coordinate, then perform the Fourier transformation to interpolation data. This is the well known Polar Format Algorithm(PFA). However, the interpolation errors also lead to blurred images. The essential approach to solve this problem is to direct sample the echoes in Cartesian coordinate [9], and one can perform the Fourier transformation immediately to the sampling data to obtain the high quality imaging. It is impossible to control the sampling data arranged in Cartesian coordinate, that is the corresponding frequency and azimuth are changed with unequal spacing, in actual application, but possible to control in simulation. The frequency and azimuth determined in Cartesian coordinate are given: xij2 yij2 fij T ij 1/ 2 § yij · arctan ¨ ¸ ¨x ¸ © ij ¹ yij f i cos T 0 tan T 0 sin T 0 b j tan T 0 1 tan 2 T 0 xij tan T 0 b j B i 1 B 2 M 1 j 1 b j b0 b0 N 1 i 1, 2, , M j 1, 2, , N fi f0 Fig. 7 Cartesian coordinate sampling imaging (7) (8) where xij Fig. 6 PFA imaging (9) (10) (11) (12) VI. CONCLUSIONS In this paper, Pixel Method is introduced to compute the backscattering of complex target. Using simulation data, the RCS feature of the target, the relative motion effect on the range profile of the target, and the precise imaging of the target in Cartesian coordinate system are discussed in detail. The results show that the task of target backscattering simulation is effective for initial research and development of the radar automatic target recognition. ACKNOWLEDGMENT This work is supported by the Academician Foundation of the 14th Research Institute of CETC. REFERENCES [1] Yulia V. 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