2-D DOA estimation via correlation matrix reconstruction for nested L-shaped array

For a nested L-shaped array (N-LsA) composed of two orthogonal nested subarrays, the self-difference co-array of each nested subarray is hole-free, whereas cross-difference co-arrays between subarrays have holes. Due to the existence of holes, virtual cross-correlation matrices with increased degree of freedoms (DOFs) can not be constructed from cross-difference co-arrays, which will degrade the performance of direction of arrival (DOA) estimation. To overcome this problem, a high resolution two-dimensional (2-D) DOA estimation algorithm is exploited for N-LsA in this paper. Specifically, by using oblique projection operators, filled cross-difference co-arrays can be achieved by filling the holes, and virtual cross-correlation matrix will be obtained. Then the virtual correlation matrix of the N-LsA, which consists of virtual cross-correlation matrices and virtual autocorrelation matrices given by filled self-difference co-arrays, is reconstructed for 2-D DOA estimation. Additionally, the proposed algorithm contains an automatic angle-pairing procedure and can handle underdetermined DOA estimation. The estimation error, Cramér-Rao bound and computational complexity are derived. Simulation results show that the proposed algorithm offers substantial performance improvement over the existing algorithms.