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
zhujh@nuaa.edu.cn
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.
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