Co-prime Array Interpolation for DOA Estimation Using Deep Matrix Iterative Network

Co-prime arrays achieve a significant number of virtual arrays in the same physical sensors by difference co-arrays. There are however, many existing methods that do not utilize all the information that the coprime array receives due to the difference co-array having defects that cause empty holes in the virtual arrays. For the purpose of estimation of the direction of arrival (DOA), we present in this paper an algorithm for co-prime array interpolation based on Deep Learning. The proposed interpolation algorithm employs the covariance matrix of the interpolated virtual array to construct a self-supervision loss function based on the Hermitian semi-definite Toeplitz condition. And build a novel net structure to learn the mapping of the loss function described above. Firstly, we build a matrix iterative network (MIN) by the idea of array interpolation such that all the information of the virtual array can be utilized. Subsequently, we fill in zero elements in each empty hole of virtual arrays, put it into the MIN and receive the interpolated covariance matrix. By exploiting MIN, we recover the covariance matrix for DOA estimation. The simulation performance and experimental result have verified the superiority of the proposed algorithm.