3258 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 57, NO. 10, OCTOBER 2009
Range Profile Analysis of the 2-D Target Above
a Rough Surface Based on the Electromagnetic
Numerical Simulation
Si-Yuan He, Fang-Shun Deng, Hai-Tao Chen, Wen-Xian Yu, Wei-Dong Hu, and Guo-Qiang Zhu
Abstract—In this paper, 1-D range profiles of a 2-D perfect
electric conductor (PEC) target above a 2-D PEC rough surface
are investigated with numerical solutions for the electric field
integral equations (EFIEs) of the combined scattering model. The
backscattering is computed accurately by the reradiation of the in-
duced surface currents on the target and the rough surface. Using
a stepped frequency waveform (SFW), 1-D high-resolution range
profiles (HRRPs) of the target above a rough surface are obtained
by performing the inverse discrete Fourier transform (IDFT) on
the wideband backscattered field. Plots of range profiles show that
the multiple interactions between the target and the bottom sur-
face lead to a series of equivalent range profiles, especially when
the bottom surface is smooth. Range locations of the equivalent
range profiles are in good agreement with the results expected
from the ray theory. The range profiles could be understood and
analyzed based on the knowledge of the scattering mechanisms.
Thus, the connection between the numerically simulated range
profiles and the scattering mechanisms is established.
Index Terms—Range profile, target/rough surface scattering, in-
teraction scattering.
I. INTRODUCTION
T
HE combined target/rough surface model has numerous
applications in long-range radar surveillance, oceanic re-
mote sensing, target identification, and target tracking [1]–[3].
Radar imaging of the target/rough surface can be helpful to un-
derstand the scattering properties of the combined scattering
model. Radar signatures, for example, the range profiles and
scattering centers [4] can be used for detection and recognition
of the target in a rough surface background. In the past, several
high-frequency approaches have been used to obtain the scat-
tering data for radar target imaging, such as the physical op-
tics (PO) approximation [5] and the ray-tracing technique [6].
Manuscript received October 16, 2008; revised December 28, 2008. First pub-
lished July 28, 2009; current version published October 07, 2009. This work was
supported by the National Natural Science Foundation of China under Grant
60671040 and the Chinese National High Technology Research Plan (863 Plan)
under Grant 2007AA12Z172.
S.-Y. He, F.-S. Deng, and G.-Q. Zhu are with the School of Electronic In-
formation, Wuhan University, Wuhan 430079, China (e-mail: siyuanhi@gmail.
com).
H.-T. Chen is with the Antenna Laboratory, Wuhan Maritime Communication
Research Institute, Wuhan 70005, China.
W.-X. Yu is with the School of Electronic, Information and Electrical Engi-
neering, Shanghai Jiao Tong University, Shanghai 200240, China.
W.-D. Hu is with the ATR Laboratory, National University of Defense Tech-
nology, Hunan 410073, China.
Digital Object Identifier 10.1109/TAP.2009.2028632
Numerical solutions have been applied in the imaging analysis
for a loaded straight wire [7] and the identification of the scat-
tering centers of several canonical targets [8]. Due to the ad-
vent of modern computers and the development of efficient nu-
merical methods in recent years, radar images of a single real-
ization rough surface with numerical models are made possible
[9]. However, radar imaging including the presence of a target
above a rough surface is a great challenge since the scattering is
complicated by multiple interactions between the target and the
rough surface [1]. Numerical simulation for the target/rough sur-
face imaging by traditional method of moments (MOM) is im-
practical because of extremely large memory requirements and
long computational time caused by the large electrical size of the
composite model [2]. Using pulse-current expansion and point
matching, a dense discretization of 30 pulse functions per wave-
length was suggested in [8] to obtain the wideband scattered
fields with acceptable phase errors for radar imaging. Computa-
tional efficiency for the target/rough surface imaging is further
challenged by the need for the wideband data at multiple fre-
quencies and a large number of realizations due to the statistical
nature of the random rough surface for the Monte Carlo simu-
lation [11].
In this paper, the range profile analysis for a 2-D perfectly
electric conductor (PEC) target above a 2-D rough surface was
successfully implemented with the numerical scattering model
and the Fourier-based method. Using the MOM method with the
ultraviolet (UV) matrix decomposition technique, the induced
surface currents on the target and the rough surface are obtained
accurately and efficiently by solving the electric field integral
equations (EFIEs). The details of the UV multilevel partitioning
method (with a complexity of
) for the 2-D rough sur-
face scattering are described in [12]. In our previous research,
the UV technique has been applied in the MOM and PO hybrid
method [13]. By performing an inverse discrete Fourier trans-
form (IDFT) [4] on the wideband backscattered field, the 1-D
high-resolution range profiles (HRRPs) [14] of a 2-D PEC target
above the rough surface are achieved via a stepped frequency
waveform (SFW), which is produced by linearly sampling the
desired bandwidth
at specific frequencies [15]. The range
profiles provide information about the position and scattering
strength of the composite model’s scattering centers along the
range direction. Plots of range profiles show that the interaction
scattering between the target and the bottom surface leads to a
series of equivalent range profiles, especially when the bottom
surface is smooth. Numerical results could be understood and
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