Joint 2-D Angle and Doppler Frequency Estimation
for Bistatic Co-Prime MIMO Radar
Wei Xiong
*
†
, Gong Zhang
*
, Zhenni Peng
Ы
*
Key Laboratory of Radar Imaging and Microwave photonics, Ministry of Education
Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
†
Leihua Electronic Technology Research Institute, Aviation Industry Corporation of China, Wuxi, 214063, China
Ы
Key Laboratory of Advanced Technology for Small and Medium-sized UAV, Ministry of Industry and Information Technology
Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Email:wxiong_nuaa@sina.com; gzhang@nuaa.edu.cn; pengzhenni@nuaa.edu.cn
Abstract—A joint two-dimensional (2-D) angle and Doppler
frequency estimation algorithm has been investigated for the
bistatic multiple-input multiple-output (MIMO) radar with co-
prime arrays (CPAs). The key idea is to extend the snapshot
uniform sampling to the co-prime sampling and further obtain
more virtual snapshots to improve the Doppler frequency
estimation. Meanwhile, the covariance matrices of target
parameter vectors, which are extracted via the trilinear
decomposition (TD), are rearranged as Vandermonde structures
to estimate the parameters. In view of more virtual elements and
virtual snapshots, our proposed algorithm can achieve better
estimation performance than the conventional methods for the
bistatic MIMO radar with uniform linear arrays (ULAs) and the
same algorithm except for the uniform sampling for the bistatic
co-prime MIMO radar. Numerical simulations verify the
effectiveness of the proposed algorithm.
Keywords—bistatic MIMO radar; co-prime array; co-prime
sampling; angle-frequency estimation
I.
I
NTRODUCTION
Recently, there has been increasing investigation on bistatic
co-prime multiple-input multiple-output (MIMO) radar
because of its potential in exploiting redundancy, spanning
large apertures with a few elements, and increasing the degrees
of freedom (DOF) [1-7]. A co-prime array (CPA) consists of
two uniform linear subarrays, average inter-element spacing
normalized by the half wavelength of which is not a series of
consecutive integers but co-prime pairs. Compared with the
uniform linear array (ULA), the fewer elements and more
remarkable advantages of CPA represent a strong research
motivation. Based on the spanning large apertures, the range
and Doppler resolution of bistatic MIMO radar with CPAs can
be higher. It was shown that by using
()
M
N+
'
elements, this
structure can achieve
()
M
N
'
DOF [2], which means that more
targets can be detected with fewer elements. Meanwhile, the
increased DOF provided by CPA can be utilized to improve the
angle estimation [2-4]. Zhao et al. [2] fully utilized the
exhibited DOF of a CPA and proposed a sparsity-based
recovery method to improving the estimation accuracy of
direction of arrival (DOA). Weng and Petar [3] investigated a
search-free DOA estimation algorithm that projected the
estimated points in a two-dimensional (2-D) plane onto one-
dimensional line segments, corresponding to the entire angular
domain. However, the algorithm also suffers from high
computation complexity, especially for the 2-D angle
estimation of multiple targets simultaneously. Yao et al. [4]
considered a bistatic MIMO radar system with non-uniform
array configuration, and used the Doppler diversity to construct
a virtual MIMO array to further estimate direction of departure
(DOD) and DOA. Unfortunately, it fails to obtain frequency
estimation owing to the loss of targets’ time-domain
information in the anto-correlation processing.
Employing the tricks of co-prime sampling and trilinear
decomposition (TD) [8], [9], we put forward an efficient hybrid
scheme for the joint 2-D angle and Doppler frequency
estimation in bistatic co-prime MIMO radar. Complex parallel
factor analysis (COMFAC) algorithm is used to speed up the
convergence of TD. The kernel of our algorithm is to extend
the snapshot uniform sampling to the co-prime sampling,
which can obtain more virtual snapshots to improve the
Doppler frequency estimation. Firstly, the transmit array
manifold, receive array manifold and Doppler information
matrix are extracted via the TD of the receiver’s output vector.
Then, their covariance matrices are selected, and reconstructed
as the corresponding virtual Vandermonde matrices for the
angle-frequency joint estimation. Further, we analysis the
uniqueness and complexity of the proposed algorithm. Finally,
in the simulation, the estimation performance is verified with
different co-prime pairs for the element configuration and co-
prime sampling, and we also compare the proposed algorithm
with the estimation of signal parameter via rotational
invariance technique (ESPRIT) [10], [11] and TD for bistatic
MIMO radar ULAs, and the same algorithm except for the
uniform sampling for the bistatic MIMO radar CPAs.
Simulation results demonstrate that the proposed algorithm has
better estimation performance without parameter ambiguous.
The proposed algorithm is also suitable for other non-uniform
array, such as the minimum redundancy array and co-prime
rectangular array.
Notation:
()
T
<
,
()
H
<
and
()
+
<
are the transpose, conjugate-
transpose and pseudo-inverse operations, respectively.
⊕
This work was supported by the National Natural Science Foundation o
f
China (61471191, 61501233, 61671241, 61501228 and 61701046),
Aeronautical Science Foundation of China (20152052026), the Funding o
f
Jiangsu Innovation Program for Graduate Education (KYZZ16_0169), Base
Research foundation (NS2015040) and also funded by the Fundamenta
l
Research Funds for the Central University (3082017NP2017421).
978-1-5386-4167-5/18/$31.00 ©2018 IEEE 0618
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