Sparse nested linear array for direction of arrival estimation

In this paper, we provide an approach to perform direction of arrival (DOA) estimation with the hole free part of difference coarray, including the physical sparse uniform linear array (ULA) itself. The sparse two-level nested linear array (NLA), whose inter-element spacings are all enlarged by the identical rate compared with the conventional two-level NLA, is selected as the example to present our work due to the typicalness, under-determinedness and the relatively obvious mutual coupling effect. The difference coarray of the sparse two-level NLA is a sparse ULA and the existing methods can not be exploited for it. We derive the sparse uniform linear array discrete Fourier transform (SULA-DFT) algorithm based on the original DFT method to extend its application from only conventional ULA to sparse ULA to solve this problem. With the SULA-DFT, reliable estimation for positive angle within a limited range under a constraint condition between angle and sparsity of array is able to be obtained directly without any ambiguous angle. Compared with the conventional two-level NLA and many other state of the art configurations, the sparse two-level NLA is able to get least mutual coupling effect and largest array aperture and the SULA-DFT often obtain better estimation accuracy with the sparse two-level NLA. On the whole, sparse two-level NLA with more sparsity gets better estimation accuracy. The numerical simulations verify the superiority of the SULA-DFT with the sparse two-level NLA. (C) 2019 Elsevier B.V. All rights reserved.