Sparse Imaging Using Improved OMP Technique in
FD-MIMO Radar for Target off the Grid
Tianyun Wang, Changchang Liu, Li Ding, Hongchao Lu, Weidong Chen
Department of Electronic Engineering and Information Science
University of Science and Technology of China, Hefei, Anhui, P.R. China
Email: {wangty, cccliu, lilyding, luhc}@mail.ustc.edu.cn, wdchen@ustc.edu.cn
Abstract—The frequency diverse multiple-input multiple-
output (FD-MIMO) radar has the potential to achieve high
range and angle resolution by combining multiple frequency
signals into a wideband signal. Moreover, higher resolution
can be obtained by exploiting the sparsity of the target based
on compressed sensing (CS) theory. However, traditional CS-
based imaging methods would be severely affected when off-
grid scatterers exist. To overcome the problem stated above, this
paper proposes a sparse imaging method to deal with off-grid
target in FD-MIMO radar using improved orthogonal matching
pursuit (OMP) technique both in the range and angle dimension.
Firstly, the off-grid simultaneous OMP (OG-SOMP) method is
proposed for range compression, then for angle compression, the
off-grid OMP (OG-OMP) method is implemented to each non-
zero range profile. Simulation results are provided to demonstrate
the performance improvement of the proposed method.
I. INTRODUCTION
Multiple-input multiple-output (MIMO) radar utilizes space
diversity to achieve high degree of freedom and high angle
resolution. Moreover , MIMO radar with frequency diversity
(FD-MIMO) system has been a hot research in recent years,
since its range resolution can be further improved by simulta-
neously fusing the echoes coming from different transmitters
to form a wideband signal [1][2].
Based on compressed sensing (CS) theory, higher resolution
can be obtained by exploiting the sparsity of the target. In
literature, the application of CS-based methods [3][4] such as
orthogonal matching pursuit (OMP) and basis pursuit (BP) in
MIMO radar imaging has been widely investigated. However
these methods are based on the assumption that all scatterers
in the scene are located exactly on the pre-discretized grid
otherwise their inversion performance would be severely af-
fected [5]. Since the target space is continuous, the off-grid
problem is likely to exist no matter how densely we grid the
imaging scene. Further, using a denser grid cannot improve
the performance by the theory of CS, and even may cause
invalidation of restricted isometry property (RIP) condition [6].
Therefore, in this paper we investigate more practical scenario
with off-grid target in FD-MIMO radar.
The off-grid problem in CS has recently attracted much
attention. Most existing methods are based on the following
iterative alternating algorithm, i.e. firstly solve the lasso or
The work in this paper is supported by the National Natural Science
Foundation of China under Grant No. 61172155.
re-weighted lasso problem for fixed mismatch matrix, then
derive mismatch matrix by solving a constrained least squares
(LS) problem [7][8]. Compared with lasso, matching pursuit
greedily finds the support and greatly reduces the dimension of
the CS problem. Inspired by idea of continuous basis pursuit
method proposed in [9] and AMP-CTLS method proposed
in [10], we introduce an improved OMP technique to deal
with off-grid target in FD-MIMO radar imaging system, which
has a self-update perturbation mechanism on basis vectors
by exploiting the off-grid error estimation within grid bound
restriction at each iteration. To reduce computation complexity,
we reconstruct the range and angle dimension separately.
Firstly, considering the common sparse support shared in range
profile for each virtual channel, the off-grid simultaneous OMP
(OG-SOMP) method is proposed for range compression, then
for angle compression, the off-grid OMP (OG-OMP) method
is operated to each non-zero range profile.
Notation: (·)
T
, (·)
∗
, (·)
H
, (·)
′
denote the transpose, the con-
jugate, the conjugate transpose, and the derivative operation,
respectively. A
†
= (A
H
A)
−1
A
H
, and diag(x) is a matrix with
its diagonal entries being entries of a vector x.
II. MODEL ESTABLISHMENT
Consider a narrowband MIMO radar imaging system with
M transmitters and N receivers as shown in Fig. 1. More-
over, we assume the transmitted signals are linear frequency
modulated (LFM) waveforms with equal chirp rate and occupy
different frequency bands for practical consideration [2].
Denote p
m
(t) (for m = 1, 2, ..., M) to represent the m
th
transmitted signal
p
m
(t) = rect
t
T
s
e
−j2π
(
f
m
t+
1
2
γt
2
)
(1)
where γ is the chirp rate, f
m
is the carrier frequency, T
s
is
the pulse duration, and rect(·) is the rectangular window with
duration T
s
.
Since the target is usually sparsely distributed in the high-
frequency limit, we suppose there are K scatterers in the imag-
ing scene, whose radial ranges, impinging angles and complex
reflection coefficients are R
k
, θ
k
, σ
k
(for k = 1, 2, · · · , K). It
is worth noting that R
k
, θ
k
indicate arbitrary location of the
k
th
scatterer here.
Assuming that the bandwidth of each LFM signal B = γT
s
is narrow and that the imaging scene is small, by denoting