基于对称和共轭MIMO的DOA估计新配置：Symmetric Sum Coarray与Co-prime设计

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本文是一篇发表在《电子通信学报》(International Journal of Electron Communications, AEÜ)上的研究论文，标题为"基于对称求和共轭阵的共质多输入多输出(MIMO)配置对于方向到达估计"。该研究关注于在射频信号处理领域中的一个重要问题——方向到达估计(Directional Arrival Estimation, DOA)，特别是在无线通信和雷达系统中，准确的方向定位是至关重要的。论文提出了一种新颖的不对称共质MIMO配置，其中发射机配备了M/4个传感器，每个传感器之间的间隔为N个单位，而接收机则有N/2个传感器，间距为M个单位。这种设计的独特之处在于，它将发射机和接收机分别划分成两个子阵列，从而能够充分利用共轭阵列技术。在接收信号模型的基础上，作者利用了四个不同的求和共轭阵列(Symmetric Sum Coarray, SSC)来增强信号处理性能。通过将这些子数组的信号合并，可以提高空间分辨率和信噪比，从而提高了DOA估计的精度。此外，文中还探讨了开发出的对称求和共轭阵的差异共轭阵列(Difference Sum Symmetric Coarray, DSSC)，这是一种通过矢量化方法进一步提升方向估计能力的技术。文章的关键点包括： 1. 共质MIMO配置：共质配置有助于减少同步和时钟相位误差的影响，这对于多个天线之间的协作至关重要。 2. 对称求和共轭阵：利用信号的空间冗余，提供了额外的角度信息，有助于提高DOA估计的分辨率。 3. 空间度量：通过计算不同子阵列间的信号差分，可以得到更多的角度估计，增加了自由度（Degrees of Freedom, DoF），有助于减少噪声的影响。 4. 矢量化技术：在DSSC中，矢量化处理使得处理复杂度降低，同时保持了高精度的DOA估计。总结来说，这篇论文不仅提出了一个创新的MIMO架构，还展示了如何通过共轭阵列技术优化DOA估计，并可能为无线通信和雷达系统的实时性能优化提供新的解决方案。这是一项重要的理论贡献，对于实际工程应用具有潜在的深远影响。

Contents lists available at ScienceDirect

Int. J. Electron. Commun. (AEÜ)

journal homepage: www.elsevier.com/locate/aeue

Regular paper

Symmetric sum coarray based co-prime MIMO conﬁguration for direction of

arrival estimation

☆

Junpeng Shi

a,b

, Guoping Hu

⁎

, Xiaofei Zhang

⁎

, Yu Xiao

Air and Missile Defense College, Air Force Engineering University, 710051 Xi’an, China

Electronic Information Engineering College, Nanjing University of Aeronautics and Astronautics, 210000 Nanjing, China

ARTICLE INFO

Keywords:

Co-prime multiple input multiple output

Direction of arrival estimation

Symmetric sum coarray

Degrees of freedom

ABSTRACT

This paper proposes a symmetric co-prime multiple input multiple output (MIMO) conﬁguration for direction of

arrival (DOA) estimation, where the transmitter has

−M

sensors with spacing of N units and the receiver has

−N2

sensors with spacing of M units. By separating the transmitter and receiver into two subarrays respectively,

the symmetric sum coarray (SSC) exploits four sum coarrays based on the received signal model, and the dif-

ference coarray of SSC (DSSC) is developed by vectorizing the sample covariance matrix. The analytical ex-

pressions for the coarray aperture, the maximum consecutive integers and the attainable number of unique lags

are derived carefully. Compared with the existing conﬁgurations, SSC and DSSC can obtain larger number of

degrees of freedom (DOFs). Then, the DOA estimation of mutually coherent and uncorrelated targets is employed

for illustration. Simulation results demonstrate the eﬀectiveness of proposed conﬁguration.

1. Introduction

Recently, multiple input multiple output (MIMO) conﬁguration has

been widely used for array signal processing and cellular communica-

tions [1], such as direction ﬁnding [2] and coordinated multipoint

(CoMP) techniques [3–5]. To be special, due to the high estimation

accuracy and resolution, direction of arrival (DOA) estimation has re-

ceived great attentions. Nevertheless, the conventional MIMO radars

mainly focus on the uniform linear arrays (ULAs) with inter-elements

spacing of less than or equal to half wavelength. In this case, if both the

transmitter and receiver are composed of N sensors, the upper bounds

of degrees of freedom (DOFs) for monostatic and bistatic MIMO radars

are

−N2

and

respectively.

To obtain larger DOFs, sparse array structures with MIMO radars

have been exploited from the coarray viewpoint. To be special, com-

pared with minimum redundancy array (MRA) [6,7] and nested array

[8], the co-prime array (CPA) [9,10] can avoid the complicated com-

putational search and also address the mutual coupling issue [11,12].In

[13], a novel co-prime array adaptive beamforming algorithm was

proposed for taking full advantage of co-prime property. The authors in

[14] generate a compressive sensing-based co-prime array for eﬃcient

DOA estimation with increased DOFs. Besides, some latest oﬀ-grid

methods have also been proposed for DOA estimation with CPAs. Ref.

[15] proposed a covariance matrix reconstruction approach by

formulating a low-rank matrix reconstruction problem with nuclear

norm. In [16] , a perturbed sparse Bayesian learning (SBL) -based al-

gorithm was developed to solve the inherent limitation of the pre-

deﬁned spatial discrete grids. In [17], SBL framework was developed

for wide-band DOA estimation with low complexity.

Recently, the co-prime MIMO radars have been proposed to increase

the DOFs using diﬀerent array geometries [18–21]. Li et al. [18] em-

ployed the unitary ESPRIT to acquire the unique DOAs by ﬁnding the

common results from transmit and receive arrays. Based on the gen-

eralized diﬀerence co-array of the sum co-array (DCSC), a generalized

co-prime MIMO radar [19] was proposed to obtain more DOFs. The

authors in [20] applied the ﬂexible CPA conﬁguration on the trans-

mitter and receiver for resolving more targets. Besides Zheng et al. [21]

also exploited the joint DOA and direction of departure (DOD) esti-

mation for bistatic MIMO radars with CPA.

However, since the resulting coarray structure of co-prime MIMO

conﬁguration contains more subarrays than the prototype CPAs in

[9,10],itisdiﬃcult to obtain the precise analytical expressions of the

achievable DOFs. For example, the methods in [18,20,21] only present

the number of unique lags without theoretical derivation. Besides, most

of the aforementioned studies only focus on the vectorization of sample

covariance matrix and few have considered the coarray structure of the

received signals. Therefore, this paper considers the co-array structure

of the proposed co-prime MIMO conﬁguration, where the symmetric

https://doi.org/10.1016/j.aeue.2018.07.022

Received 24 October 2017; Accepted 21 July 2018

☆

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61601504, 61501504 and 61601167).

⁎

Corresponding authors.

E-mail addresses: hgp6068@163.com (G. Hu), zhangxiaofei@nuaa.edu.cn (X. Zhang).

Int. J. Electron. Commun. (AEÜ) 94 (2018) 339–347

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