Guiyu Wang， Shun’an Zhong， Xiangnan Li， Xiaohua Wang and Shiwei Ren

（School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China)）

Abstract: The concept of difference and sum (diff-sum) coarray has attracted a lot of attentions in the estimation of direction-of-arrival (DOA) for the past few years, due to its high degrees-of-freedom (DOFs). A vectorized conjugate augmented MUSIC (VCA-MUSIC) algorithm is applied to generate an equivalent signal model which contains the virtual sensor positions of both the difference and sum of the physical sensors in the two-dimensional (2D) arrays, by utilizing both the spatial and temporal information. Besides, an augmented 2D coprime array configuration is presented with the basis on the concept of difference and sum coarray. By compressing the inter-element spacing of one subarray and introducing the proper separation between the two subarrays of 2D coprime array, the redundancy between the difference coarray and the sum one can be reduced so that more virtual sensors in both coarrays can make contributions to the DOFs. As a result, a much larger consecutive area in the diff-sum coarray can be achieved, which can significantly increase the DOFs. Numerical simulations verify the superiority of the proposed array configuration.

Key words: degrees of freedom (DOFs)；direction-of-arrival (DOA) estimation；planar coprime array；virtual array

Two-dimensional (2D) direction-of-arrival(DOA) estimation has useful applications in the fields of radar, navigation and communications,etc. Most conventional estimation methods are based on uniform rectangular arrays (URAs)[1?2].Such array configurations usually suffer from significant mutual coupling. Moreover, the great amounts of sensors bring high hardware cost and computational complexity. Thus, it is important to design sparser array configurations to overcome the disadvantages of URAs.

In the past decade, numbers of one-dimensional (1D) linear sparse arrays have been proposed based on the concept of difference co-arrays including the famous nested array[3]and coprime array[4?5]. A series of improved array configurations are also proposed to further enhance the degrees of freedom (DOFs) or reduce the mutual coupling effects, including super nested arrays[6?7], augmented nested arrays[8], coprime arrays with compressed inter-element spacing (CACIS) and co-prime arrays with displaced subarrays (CADiS)[9]. Inspired by the above 1D sparse arrays, some planar sparse configurations have been introduced based on the 2D virtual array concept. By improving the classic open-box arrays (OBAs)[10], some 2D sparse arrays including partially open box arrays, half open box arrays and hourglass arrays[11]are proposed. Half H array (HHA) and ladder array (LA) are proposed to further increase the accuracy of 2D DOA estimation[12]. On the other hand, the concept of 1D linear sparse arrays is extended to 2D situation. 2D nested arrays[13?14]and a coprime planar array geometry[15]are proposed.However, the above array configurations are designed based on the concept of difference coarray.In fact, the sum coarray can be jointly utilized with the difference coarray to generate a larger virtual coarray and increase DOFs significantly.

In this paper, the vectorized conjugate augmented MUSIC (VCA-MUSIC) algorithm[16?17]is applied to the 2D DOA estimation. Based on this algorithm, the diff-sum coarray concept is expanded to 2D cases and an improved planar sparse array configuration named coprime array with two separated subarrays (CATSS) is proposed. As sensors of the two subarrays are arranged to be bilaterally symmetrical and separation between two subarrays is set properly, a central hole-free URA with large amount of virtual elements can be generated in the diff-sum coarray of CATSS.

The rest of this paper is organized as follows.In Section 1, the signal model and the diff-sum coarray concept are overviewed by introducing the 2D VCA-MUSIC algorithm. The array structure of CATSS is introduced in Section 2 and some related property of the array geometry is also introduced. Simulations provided in Section 3 compare the root mean square error (RMSE)of our configuration with other conventional 2D arrays. The superiority of the proposed geometry is demonstrated. Section 4 concludes the paper.

1 Signal Model Based on the 2D VCA-MUSIC Algorithm

2 Coprime Array with Two Separated Subarrays (CATSS)

3 Simulation Results

4 Conclusion

Appendix 1 Proof of Proposition 1

Appendix 2 Proof of Proposition 2