Direction of arrival (DOA) estimation problem for multiple-input multiple-output (MIMO) radar with unknown mutual coupling is studied, and an algorithm for the DOA estimation based on root multiple signal classification (MUSIC) is proposed. Firstly, according to the Toeplitz structure of the mutual coupling matrix, output data of some specified sensors are selected to eliminate the influence of the mutual coupling. Then the reduced-dimension transformation is applied to make the computation burden lower as well as obtain a Vandermonde structure of the direction matrix. Finally, Root-MUSIC can be adopted for the angle estimation. The angle estimation performance of the proposed algorithm is better than that of estimation of signal parameters via rotational invariance techniques (ESPRIT)-like algorithm and MUSIC-like algorithm. Furthermore, the proposed algorithm has lower complexity than them. The simulation results verify the effectiveness of the algorithm, and the theoretical estimation error of the algorithm is also derived.

Multiple-input multiple-output (MIMO) radars have attracted a lot of attention recently for their potential advantages over conventional phased-array radars [

Although MUSIC-like algorithm can achieve high resolution angle estimation with unknown mutual coupling, the high computational peak searches will make it ineffective. As a faster method, ESPRIT-like can obtain the close-form solution of the angle estimation, but it only exploits the relationship between the subarrays, which will lead to a performance loss.

Our goal is to develop an effective method for angle estimation in MIMO radar with unknown mutual coupling. So, in this paper, we propose a Root-MUSIC based method, which is fast and can deal with the mutual coupling problem, which often occurrs in practical situation. The nonauxiliary sensors are also used to eliminate the influence of mutual coupling. Then a transformation is utilized to reduce the dimension of the data, meanwhile a direction matrix with Vandermonde structure can be obtained. Finally, Root-MUSIC, which is a root-finding form of the MUSIC peak searching, can be adopted for the angle estimation. The angle estimation performance of the proposed algorithm is better than that of ESPRIT-like algorithm and MUSIC-like algorithm. Furthermore, it may also have lower complexity.

As shown in Figure

Array structure of monostatic MIMO radar.

By collecting

According to [

The length of the new steering vector

The covariance matrix in (

According to the MUSIC peak search function [

The

The major steps of the proposed algorithm for DOA estimation in MIMO-radar are shown as follows.

Construct the new output via (

Estimate the covariance matrix of the data through

Perform eigen-value decomposition of

Construct the MUSIC function and use root finding technique to obtain the angle estimation

The proposed algorithm has lower complexity than ESPRIT-like algorithm and MUSIC-like algorithm for it requires no peak searches and has lower dimension. Figure

Complexity comparison against the number of antennas (

The decomposition of

According to [

The advantages of the proposed algorithm can be summarized as follows.

It works well with unknown mutual coupling. According to (

It requires no peak search and has lower complexity, which has been shown in Figure

It has better angle estimation performance than MUSIC-like algorithm and ESPRIT-like algorithm. Part of the reason of this advantage can be refered to “Remark

Although MUSIC-like algorithm [

According to [

Define root mean square error (RMSE) as

Figure

Angle estimation result of the proposed algorithm (

The angle estimation performance comparison between the proposed algorithm, ESPRIT-like algorithm, and MUSIC-like algorithm is shown in Figure

Angle estimation performance comparison (

Figures

Angle estimation performance with different

Angle estimation performance with different

Figure

Angle estimation performance with different

To further demonstrate the advantages of the proposed algorithm, another set of parameters is chosen to test the algorithms. Assume that the angles are

Angle estimation performance comparison (different configuration).

In this paper, a DOA estimation algorithm based on Root-MUSIC has been proposed for monostatic MIMO radar with unknown mutual coupling. The proposed algorithm has low complexity and works fast, requires neither peak searches nor iterations, and can work well with practical unknown mutual coupling. So it can support practical online processing. Furthermore, the proposed algorithm has better angle estimation performance then the ESPRIT-like algorithm and MUSIC-like algorithm, which have higher complexity. Many thanks are due to the reviewer’s comments; our future work is to test the algorithms with real world data, and try to convert the theories into practical applications.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by the China NSF Grants (61371169, 61071164), the Jiangsu Planned Projects for Postdoctoral Research Funds (1201039C), the China Postdoctoral Science Foundation (2012M521099, 2013M541661), the Open project of key laboratory of underwater acoustic communication and marine information technology (Xiamen University), the Hubei Key Laboratory of Intelligent Wire1ess Communications (IWC2012002), the Open project of Key Laboratory of modern acoustic of Ministry of Education (Nanjing University), the Aeronautical Science Foundation of China (20120152001), Funding of Jiangsu Innovation Program for Graduate Education (CXZZ13_0165), Funding for Outstanding Doctoral Dissertation in NUAA (BCXJ13-09), the Qing Lan Project, priority academic program development of Jiangsu high education institutions, and the Fundamental Research Funds for the Central Universities (NS2013024, kfjj130114).