Cumulants-Based Toeplitz Matrices Reconstruction Method for 2-D Coherent DOA Estimation

In this paper, a new high-resolution approach called fourth-order cumulants-based Toeplitz matrices reconstruction (FOC-TMR) method, is presented for two-dimensional (2-D) direction-of-arrival (DOA) estimation of incident narrowband coherent signals. The angle estimation problem is addressed by arranging the cumulants elements of received signals from two parallel uniform linear arrays (ULAs) to two Toeplitz matrices. In Gaussian noise cases, it is shown that the ranks of the two Toeplitz matrices equal the number of the incoming waves and are independent of their coherency. Therefore, with eigen decomposition of the Toeplitz-based generalized DOA matrix, the closed-form, automatically paired 2-D angle parameters can be estimated properly from its large eigenvalues and corresponding eigenvectors, respectively. In the condition of two closely spaced coherent signals in both 2-D angles, simulation results show that, in comparison with the fourth-order cumulants-based forward spatial smoothing (FOC-FSS) method, the proposed algorithm has lower computational complexity and yields better estimation performance in terms of maximum probability of success (MPS), maximum root mean square error (MRMSE) of incoming signals in both white noise and color Gaussian noise situations, especially, in low signal-to-noise ratio (SNR) and small number of snapshots conditions.