A Novel Measurement Matrix Optimization Method
for Radar Sparse Imaging with OFDM-LFM Signals
Yijun Chen, Xiaoyou Yang, Ziqiang Ma, Qun Zhang
Institute of Information and Navigation, Air Force
Engineering University
Collaborative Innovation Center of Information Sensing and
Understanding
Xi’an, People’s Republic of China
Email: chenyijun519@126.com
Guozheng Wang
Institute of Science, Air Force Engineering University
Xi’an, People’s Republic of China
Abstract—Compressed Sensing (CS) has been widely used in
radar imaging field to reduce the data amount. The measurement
matrix has direct effect on the degree of dimension reduction and
the quality of target image. However, the measurement matrix is
usually chosen as random Gaussian matrix or local Fourier
matrix, and the influence from target characteristics to the
measurement matrix optimization has not been considered. In
this paper, focuses on the OFDM-LFM signals, a novel
measurement matrix optimization method for radar sparse
imaging is proposed. In this method, genetic algorithm is used to
implement the measurement matrix optimization by equaling the
measurement matrix to the chromosome. And then the satisfied
imaging result can be achieved with minimal measurement
dimension by using the obtained optimal measurement matrix.
Some simulation results illustrate the effectiveness of the
proposed method.
Index Terms—OFDM-LFM signals, measurement matrix
optimization, genetic algorithm.
I. INTRODUCTION
With the development of radar signal processing
technology, the requirement of imaging resolution has been
increased significantly. The high sampling rate based on
Nyquist sampling theory and the large data amount poses great
challenge to the hardware designation and the memory space of
signal processing system. However, the compressed sensing
(CS) theory can recover a sparse or compressible signal from
far fewer measurements than what the Nyquist sampling theory
claimed with high probability, by exploiting the signal sparsity
[1-3]. Therefore, the compressed sensing (CS) theory has been
widely used in radar imaging field, which can reduce the
required measurements drastically [4-7]. The CS theory is
introduced into high resolution range profile synthesis through
sparse frequency waveforms and the full-resolution image is
reconstructed. A sparse imaging algorithm based on CS is
proposed to estimate the locations of the scattering centers
from a very limited number of measurements [8].
However, in most ISAR imaging method based on
compressed sensing, the measurement matrix is usually chosen
as random Gaussian matrix or local Fourier matrix, and the
observation dimension is determined by experience. The
existing methods have not considered the influence from target
characteristics to the measurement matrix optimization. Hence,
we intend to find a measurement matrix optimization method
based on target characteristics. The genetic algorithm is a kind
of evolutionary algorithm, and the optimal solution or the
suboptimal solution will be obtained after iterations [9]. The
measurement matrix optimization can be treated as an
optimization problem of the measurement matrix dimension
and structure. Therefore the measurement matrix optimization
can be implemented based on the genetic algorithm.
As is known, the orthogonal frequency division
multiplexing-linear frequency modulation (OFDM-LFM)
signal has been applied in radar imaging as a kind of broad-
bandwidth radar signal [10]. Therefore, a measurement matrix
optimization method for sparse ISAR imaging with OFDM-
LFM signals based on genetic algorithm is proposed in this
paper. With this method, the measurement matrix dimension
and structure optimization can be implemented under a given
image quality requirement. Meanwhile, the SBL algorithm is
chosen for signal reconstruction. Also, the noise variance
estimation is obtained by signal subspace decomposition, and
the estimated value is applied to SBL algorithm, which can
avoid the iterative calculation of noise variance during the
signal reconstruction. As a result, the computation of SBL
algorithm can be reduced effectively.
This paper is organized as follows. A measurement matrix
optimization method based on genetic algorithm is proposed in
Section 2. The improved sparse Bayesian learning algorithm is
illustrated in Section 3. Simulations are presented in Section 4
to validate the effectiveness of the proposed method, and some
conclusions are made in the last section.
II. M
EASUREMENT MATRIX OPTIMIZATION BASED ON
GENETIC ALGORITHM
Assuming the radar is located at the point
O in the (,)XY
coordinates. For simplicity, the target area can be divided into
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2015 IEEE