非均匀MIMO雷达系统DOD与DOA联合估计方法
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"双基地非均匀多输入多输出雷达系统的DOD和DOA估计"
这篇研究论文专注于双基地非均匀多输入多输出（MIMO）雷达系统的方向-of-departure (DOD) 和方向-of-arrival (DOA) 的联合估计问题。在现代雷达系统中，MIMO技术因其在提高探测性能、分辨能力和抗干扰能力方面的优势而备受关注。非均匀阵列配置则可以进一步提升系统性能，因为它允许更灵活地设计天线布局以适应特定的环境或任务需求。
论文提出了一种新颖的基于非均匀阵列配置的估计方法，该方法利用多普勒频率的变化（即多普勒多样性）来构建虚拟MIMO阵列。这种方法的关键在于，通过利用多普勒效应产生的信号差异，可以创建一个等效的更大规模的虚拟阵列，从而增强参数可识别性。理论证明表明，与传统的估计方法相比，提出的算法在参数可识别性和估计精度上都有显著的提升。
文章的结构通常包括以下几个部分：
II. 文献回顾：论文可能首先回顾了现有的DOD和DOA估计方法，特别是针对MIMO雷达系统的相关工作，强调现有方法的局限性和改进的空间。
III. 非均匀MIMO阵列配置：详细介绍了非均匀阵列的概念，解释其如何通过调整阵元间距和相位中心来提供更丰富的角度分辨率和抗干扰能力。
IV. 提出的方法：详细阐述了利用多普勒多样性的虚拟MIMO阵列构造过程，以及如何利用这个虚拟阵列进行DOD和DOA的联合估计。
V. 参数可识别性分析：这部分可能包含了对所提方法的参数可识别性的理论分析，证明即使在非均匀阵列条件下，也能保证参数的唯一解。
VI. 性能分析：通过数学证明或仿真结果展示新方法在估计性能上的优越性，如均方误差（MSE）和概率密度函数（PDF）等。
VII. 数值模拟：提供了具体的数值模拟案例，以实际验证所提算法的有效性，并与其他方法进行对比。
VIII. 结论：总结研究成果，讨论可能的应用场景和未来的研究方向。
IX. 参考文献：列出论文引用的所有相关文献，为读者提供了深入研究的起点。
这篇论文对于理解MIMO雷达系统中的DOD和DOA估计具有重要意义，对于雷达系统设计者和信号处理专家来说是一份有价值的参考材料。它不仅提出了一种新的估计策略，而且通过理论和实证分析展示了其在参数识别和性能优化方面的优势。
1796 IEEE COMMUNICATIONS LETTERS, VOL. 16, NO. 11, NOVEMBER 2012
DOD and DOA Estimation in
Bistatic Non-Uniform Multiple-Input Multiple-Output Radar Systems
Bobin Yao, Student Member, IEEE, Wenjie Wang, Member, IEEE,andQinyeYin
Abstract—This letter investigates the joint estimation of the
direction of departure (DOD) and direction of arrival (DOA)
for multi-input multi-output (MIMO) radar systems. A novel
estimation method based on non-uniform array configuration is
proposed and the practical identifiability of the corresponding
parameter is analyzed. The key idea is to use the Doppler
diversity to construct a virtual MIMO array. Through the
theoretical proof, we demonstrate that the proposed method can
provide much stronger parameter identifiability than the con-
ventional ones, and also can improve the parameter estimation
performance. Numerical simulations verify the effectiveness of
the proposed algorithm.
Index Terms—Multiple-input multiple-output radar, non-
unform array, parameter identifiability, angle estimation.
I. INTRODUCTION
J
OINT estimation of direction of departure (DOD) and
direction of arrival (DOA), as an important method for
exploiting the opportunistic space-division multiple access
(OSDMA) in wireless communication system [1] or moving
target localization in multiple-input multiple-output (MIMO)
radar system [2], [3], [ 4], [5], has been attracted lots of
attention. Two-dimension multiple signal classification (MU-
SIC) algorithm [3] and its reduced dimension version [4]
were exploited separately, both of which have almost the
same performance. The rotational invariance technique have
been studied in [5], however the performance is inferior
to the MUSIC based algorithms. Moreover, the parameter
identifiability also needs to be discussed elaborately, which
is a natural pre-requisite for a well-posed estimation problem.
The authors in [6] proved that the maximum number of targets
that can be uniquely identified by co-located uniform MIMO
radar (i.e., uniform linear arr a y is utilized on both transmit
and receive ends) is up to M times as that of the conventio nal
uniform phased radar, where M is the number of transmit
antennas. It also shows in [7] that the bistatic uniform MIMO
radar with single pulse in a coherent process interval provides
a identifiability upper bound 0.34M (N +1),whereN is the
number of receive antennas.
To further impr ove the parameter identifiability and the
estimation performance, we utilize a bistatic non-uniform
MIMO array in this letter. The non-uniform means that the
Manuscript received July 25, 2012. The associate editor coordinating the
review of this letter and approving it for publication was H. Wymeersch.
The authors are with the MOE Key Lab for Intelligent Networks and
Network Security, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, P. R.
China (e-mail: yaobobin@gmail.com).
This work was partially supported by the NSFC (No. 60971113, 61172093),
the Ph.D. Programs Foundation of Ministry of Education of China (No.
200806980020) and the Foundation for Innov a tive Research Groups of the
NSFC (No. 60921003).
Digital Object Identifier 10.1109/LCOMM.2012.091212.121605
antenna locations normalized by half carrier wavelength are
not a series of consecutive integers. The typical examples
are the minimum redundancy (MR) array [8], nested array
[9] and coprime array [10]. We herein develop a novel joint
DOD and DOA estimation algorithm, the kernel of which is
to use the Doppler diversity to construct a large virtual MIMO
array with more degree of freedom (DOF). The proposed
scheme is proved to be possessed of much stronger parameter
identifiability and much better estimation performance than the
conventional uniform MIMO arr ay. Meanwhile, it is also with
lower computational complexity and requires no parameter
pairing.
Notation: (·)
∗
, (·)
T
, (·)
H
, (·)
†
denote the complex conju-
gate, transpose, Hermitian transpose, pseudo-inverse, respec-
tively. Symbol “⊗” denotes Kronecker product and “” stands
for Khatri-Rao product (column-wise Kronecker product). I
M
is a M × M identity matrix and 0 symbolizes zero matrix.
A
(m)
is a submatrix o f A formed by its last m rows.
II. N
ON-UNIFORM MIMO RADAR FOR TARGET
LOCAL IZATION
A. Data Model
Consider a b istatic MIMO radar system with M -antenna
transmit array and N-antenna receive array, both o f which
are in non-uniform configuration. It is also assumed that there
are K targets, and the output baseband signal of the matched
filters at the receive array can be written as [4] [5] [7]
y(t)=[b(φ
1
) ⊗ a(θ
1
), ··· , b(φ
K
) ⊗ a(θ
K
)]h(t)+z(t) (1)
where the transmit steering vector a(θ
k
) and the receive
steering vector b(φ
k
),fork =1, 2, ··· ,K, are assumed to
be unchanged during a coherent processing interval (CPI),
and θ
k
,φ
k
are the DOD and DOA of the kth target, re-
spectively. The vector h(t)=[γ
1
(t), ··· ,γ
K
(t)]
T
relies
on the Doppler frequency f
dk
and the radar cross section
(RCS) coefficient β
k
, i.e., γ
k
(t)=β
k
e
j2πf
dk
(t−1)
.Note
that a(θ
k
)=[e
jπl
1
sin θ
k
, ··· ,e
jπl
M
sin θ
k
]
T
and b(φ
k
)=
[e
jπl
1
sin φ
k
, ··· ,e
jπl
N
sin φ
k
]
T
are mutilated Vandemonde vec-
tors, where l is the antenna location normalized by half carrier
wavelength. z(t) is the additive zero-mean Gaussian noise
with covariance σ
2
n
.
Defining A =[a(θ
1
), ··· , a(θ
K
)] ∈ C
M×K
, B =
[b(φ
1
), ··· , b(φ
K
)] ∈ C
N×K
, and after collecting Q consec-
utive pulses, (1) can be rewritten by the following compact
form
Y =(B A)H + Z (2)
where Y =[y(1), ··· , y(Q)], H =[h(1), ··· , h(Q)] and
Z =[z(1), ··· , z(Q)].
1089-7798/12$31.00
c
2012 IEEE
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