IEEE SENSORS JOURNAL, VOL. 15, NO. 4, APRIL 2015 2157
A Novel Motion Compensating Method
for MIMO-SAR Imaging Based
on Compressed Sensing
Fu-Fei Gu, Qun Zhang, Senior Member, IEEE, Long Chi, Yong-An Chen, and Song Li
Abstract—Multiple-input multiple-output-synthetic aperture
radar (MIMO-SAR) can realize high-resolution imaging by
its predominance of parallel sampling. However, the motion
compensation and large data amount are the inevitable problems
to be solved. In this paper, a novel motion compensating method
for MIMO-SAR imaging with the under-sampled echo signal is
put forward. First, the echo signal model of MIMO-SAR system
with motion error is analyzed and a compensating method with
the Nyquist-sampled echo data is proposed. Using the technique
of two-step compensation, the motion error is compensated and
the imaging result is obtained. Second, to compensate the motion
error with the under-sampled echo signal, based on the above
compensating method, the transform operator and the CS-based
imaging scheme are constructed, which could implement the first-
step compensation, range compression, and range cell migration
correction simultaneously. At last, the imaging result is obtained
by the second-step compensation and azimuth compression. Using
the proposed method, just a small amount of imaging data is
required for MIMO-SAR imaging. Finally, the effectiveness of
the proposed method is proved by the imaging simulations.
Index Terms—MIMO-SAR, motion compensation, two-step
compensation, compressed sensing, transform operator.
I. INTRODUCTION
M
ULTIPLE input multiple output- synthetic aper-
ture radar (MIMO-SAR) can obtain abundant space
resources and frequency resources by using the multi-channel
and multi-carrier (multi-waveform) technologies. MIMO-SAR
can not only resolve the contradiction between high azimuth
resolution and wide swath without bringing more burdens on
the system hardware, but also improve the capability of detect-
ing and locating slow speed targets on the ground. So it has
great prospects in both military and civilian purposes [1]–[4].
However, for MIMO-SAR system, the platform motion is
the solution but also the problem. The problem arises from
trajectory deviations, instability of attitude, and forwarding
velocities, which can cast additional phase modulation in the
Manuscript received September 17, 2014; revised November 3, 2014;
accepted November 11, 2014. Date of publication November 20, 2014;
date of current version February 5, 2015. This work was supported by the
National Natural Science Foundation of China under Grant 61102109 and
Grant 61471386. The associate editor coordinating the review of this paper
and approving it for publication was Dr. Shoushun Chen.
F.-F. Gu, Q. Zhang, L. Chi, and Y.-A. Chen are with the Institute of Informa-
tion and Navigation, Air Force Engineering University, Xi’an 710077, China
(e-mail: gffpan@126.com; zhangqunnus@gmail.com; 50669319@qq.com;
15353744009@qq.com).
S. Li is with the Institute of Missile Defense, Air Force Engineering
University, Xi’an 710077, China (e-mail: li_song77@163.com).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSEN.2014.2371451
echo signal. The problem causes not only serious blurring but
also geometric distortion in the SAR imagery. In this paper,
the problem of phase error caused by trajectory deviations is
discussed. Meanwhile, the amount of raw data will increase
sharply along with the improving of image precision. Due
to the characteristics of multi-channel, the raw data amount
of MIMO-SAR is several times than that of single-channel
SAR. The highly huge data amount makes severe demands
on the storage capacity of MIMO-SAR system as well as the
capacity of signal channel for data transmission. Therefore,
compensating motion error and reducing the echo data amount
are the inevitable problems to be solved for MIMO-SAR
imaging.
The paper [5] puts forward an extend range migration algo-
rithm (RMA) to compensate the motion error for MIMO-SAR
imaging. However, this method is based on interpolation
processing, which is quite time-consuming. Firstly, in this
paper, a new motion compensating method for MIMO-SAR
imaging is put forward. The technique of two-step compen-
sation is utilized to compensate the motion error. And the
main processing is based on matrix multiplication. Thus, it can
work faster than the method of paper [5]. However, the above
method is based on the Nyqusit-sampled echo signal. In order
to reduce the amount of echo data, based on the proposed
compensating method, a novel motion compensating method
for MIMO-SAR imaging with Compressed Sensing (CS)
theory is proposed. CS theory is introduced in [6] and [7],
which indicates that one can stably and accurately reconstruct
nearly sparse signals from dramatically under-sampled data
in an incoherent domain. With this prominent advantage,
the CS theory has been used in wide-ranging applications.
Meanwhile, the idea of CS has also been used in some
radar systems, such as conventional radar system [8], imaging
radar system [9]–[12] and MIMO radar system [13], [14].
A waveform designing method is put forward to reduce
the correlations between different target responses in [13].
In the case that the targets are sparsely located in the angle-
Doppler space, an approach proposed in [14] achieves superior
resolution of MIMO radar with far fewer required samples than
that of traditional approaches. It has the advantage of energy
savings. However, there are few reference works available
devoted specifically to MIMO-SAR imaging combining with
CS theory.
In this paper, a novel motion compensating method for
MIMO-SAR imaging with the under-sampled data is put
forward. Firstly, the technique of two-step compensation is
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