Extended transformed nested arrays for DOA estimation of non-circular sources

Recently, direction of arrival (DOA) estimation for non-circular (NC) sources has attracted great attention in array signal processing since NC signals can provide more information to generate the virtual difference and sum (diff-sum) coarray. In this paper, we propose a generalized vectorized noncircular MUSIC (GVNCM) method, which can solve the underdetermined DOA estimation problem when the difference coarray and the sum coarray are discontinuous. Based on the GVNCM algorithm, an extended transformed nested array strategy is proposed by splitting the dense subarray of transformed nested array (TNA) into several parts and shifting them to the right to reduce the redundant elements between the difference coarray and the sum coarray. Following this strategy, two novel array configurations are developed. The analytical expressions of the new structures and the consecutive range of their diff-sum coarrays are provided. The two proposed arrays can achieve higher degrees of freedom and maximum number of detectable signals compared with TNA. In order to evaluate the underdetermined DOA estimation performance of NC signals, we derive the corresponding expression of Cramér-Rao bound. The effectiveness of the proposed arrays is verified through numerical simulations.