Low-rank tensor recovery for 2-D DOA estimation using cylindrical nested conformal array

Abstract

In recent years, nested conformal arrays have received considerable attention because they are capable of providing extended array aperture and increased degrees of freedom compared to uniform conformal arrays. In this article, we suggest a low-rank tensor recovery algorithm for two-dimensional (2-D) direction-of-arrival (DOA) estimation with cylindrical nested conformal array (CNCA). First of all, we derive the tensor form coarray output of the CNCA and use the coarray output to construct a third-order augmented tensor. Subsequently, we reconstruct a noise-free third-order augmented tensor by formulating a tensor nuclear norm (TNN) minimization problem. With the reconstructed tensor, we finally derive the closed-form expressions of 2-D DOA estimates. Compared with the existing approaches, the proposed approach achieves better performance by exploiting the multidimensional structure inherent in the coarray output signal. Numerical results illustrate the advantage of the proposed method over several existing techniques.