针对共阵MIMO雷达的EM稀疏成像方法：处理相位同步失配
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本文主要探讨了在具有共定位天线的多输入多输出(MIMO)雷达系统中，面对相位同步失配这一关键问题下的稀疏成像方法。以往的研究往往侧重于MIMO雷达的性能提升，但对直接影响成像质量的相位同步问题关注不足。作者Li Ding、Weidong Chen和Wenyi Zhang针对此问题，在假设每个传播路径上的相位同步误差是独立同分布的均匀随机变量的前提下，结合了目标的稀疏特性与期望最大化(Expectation Maximization, EM)算法。
EM算法在此背景下被用来开发一种针对随机相位失配的稀疏成像算法。该算法利用目标的稀疏性优势，通过迭代过程来估计目标的幅度和相位信息，即使在存在相位同步误差的情况下也能提高成像精度。这种方法的优势在于它能够处理非理想条件下的数据，通过优化目标函数，逐步逼近实际场景中的最佳解。
文章的核心内容可能包括以下几个部分：
1. 背景介绍：阐述了共定位MIMO雷达在使用相干处理时的潜在优势，以及由于相位同步问题对其性能提升的限制。
2. 问题提出：明确了研究焦点——在相位同步失配的条件下，如何实现高效的稀疏成像。
3. 理论模型：建立了基于相位同步误差的随机分布假设，这为后续算法设计提供了数学基础。
4. 方法设计：详细介绍了EM算法如何结合目标的稀疏性，通过迭代更新来估计和补偿相位失配对图像质量的影响。
5. 算法性能评估：可能包括仿真结果分析，展示了算法在实际应用中的成像效果，以及与传统方法的对比，证明其在复杂环境中的优势。
6. 结论与未来工作：总结研究成果，并指出未来可能的研究方向，如进一步提高算法鲁棒性或扩展到其他类型的同步失配情况。
这篇研究论文对于理解并解决共定位MIMO雷达在实际部署中的相位同步挑战具有重要意义，对于提升此类雷达系统的性能和可靠性具有直接的应用价值。
EM-BASED SPARSE IMAGING FOR COLOCATED MIMO RADAR UNDER PHASE
SYNCHRONIZATION MISMATCH
Li Ding, Weidong Chen, Wenyi Zhang
Department of Electronic Engineering and Information Science
University of Science and Technology of China, Hefei, Anhui, P.R. China
Email: lilyding@mail.ustc.edu.cn, {wdchen, wenyizha}@ustc.edu.cn
ABSTRACT
Multiple-input multiple-output (MIMO) radar with colocated
antennas is expected to achieve good imaging performance
via coherent processing. However, a crucial factor to this
process−phase synchronization, which directly determines
the performance gain, has rarely been studied in previous
works. Hence in this paper, given the sparsity of the target, we
address the problem of imaging for colocated MIMO radar
under the phase synchronization mismatch. Based on the
model assumption that the phase synchronization mismatch
in each propagation path is an independent and identically
distributed uniform random variable, we combine the sparsity
of the target and expectation maximization (EM) method to
develop an EM-based sparse imaging algorithm against such
random phase mismatch. The effectiveness of the proposed
algorithm is demonstrated by numerical simulations.
Index Terms— Expectation maximization, MIMO radar,
phase synchronization mismatch, sparse imaging
1. INTRODUCTION
Together with the sparse priority of target, Multiple-input-
multiple-output (MIMO) radar with colocated antennas has
been shown to be of great ability to provide high-resolution
imaging in the wavenumber domain [1] [2] [3].
This good reconstruction performance is mainly brought
by coherent processing. However, the phase synchronization−
a crucial factor to coherent processing− is hard to realize per-
fectly and thus always an inevitable problem. Its imperfect
implementation evidently could lead to performance degrada-
tion. As to phase synchronization mismatch in MIMO radar,
its influence on detection has been studied in [4], on localiza-
tion in [5][6], and further on tracking in [7], but relatively less
attention has been paid on colocated MIMO radar imaging.
Hence, under the premise of sparse target, we investigate the
problem of colocated MIMO radar imaging associated with
random phase synchronization mismatch. In this case, the
The work in this paper is supported by National Natural Science Foun-
dation of China under Grant No. 61172155.
reconstruction is not straightforward because of the random-
ness of phase mismatch, and the conventional sparse recovery
techniques [8], such as the Lasso algorithm, would become
inefficient. So we resort to the combination of expectation
maximization (EM) method [9] and sparsity of target to de-
velop an EM-based sparse imaging algorithm. In addition to
the sparse priority, our algorithm also takes advantage of EM
method to efficiently exploit the statistical property of signal
and provides high reconstruction performance by iteratively
alternating between the expectation stage and maximization
stage.
Notations: (·)
∗
, (·)
T
and (·)
H
denote the conjugate, the
transpose and the conjugate transpose operation respectively.
diag(·) indicates diagonalization while blkdiag(·) is the block
diagonalization. sinh(·), cosh(·) and coth(·) mean the hyper-
bolic sin, the hyperbolic cosine and the hyperbolic cotangent
function, respectively.
2. SIGNAL MODEL
Consider a two dimensional (2-D) colocated MIMO radar
with M transmitters and N receivers in wavenumber domain
[1] . Define (R
T x
m
, ϕ
T x
m
) (for m = 1, · · · , M ) and (R
Rx
n
, ϕ
Rx
n
)
(for n = 1, · · · , N) as the positions in the polar coordinate
of the m-th transmitter and the n receiver, respectively. The
center of imaging scene of interest is regarded as the origin of
the coordinate and we suppose that there are only L scatter-
ers. Exploiting the far-field approximation and orthogonality
separation, we can obtain the echo with the phase synchro-
nization mismatch ψ
nm
at the n-th receiver corresponding to
the m-th transmitter as
y
nm
(f) =
L
l=1
σ (r
l
) e
j2πK
nm
(f )·r
l
e
−jψ
nm
+ z
nm
(f) (1)
where σ(r
l
) denotes the complex reflectivity of the l-th scat-
terer with the location r
l
= (x
l
, y
l
) (for l = 1, · · · , L).
z
nm
(f) is the additive noise. K
nm
(f) indicates the sampling
of 2-D wavenumber domain, given as (K
x
nm
, K
y
nm
),
K
x
nm
(f) =
f+f
m
c
cos ϕ
T x
m
+ cos ϕ
Rx
n
K
y
nm
(f) =
f+f
m
c
sin ϕ
T x
m
+ sin ϕ
Rx
n
(2)
4106978-1-4799-0356-6/13/$31.00 ©2013 IEEE ICASSP 2013
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