Noncircular Tensor Toeplitz Covariance Decomposition for Coherent DOA Estimation

Direction-of-arrival (DOA) estimation of coherent noncircular (NC) sources is challenging because source coherence causes covariance rank deficiency, whereas many existing decorrelation methods do not fully exploit the additional pseudo-covariance information of NC signals. To address this problem, this letter proposes an NC tensor Toeplitz covariance decomposition (NC-TTCD) method for coherent DOA estimation. The covariance and pseudo-covariance matrices of the received data are first combined to construct a set of NC covariance-like matrices. For each matrix, a group of Toeplitz matrices is generated from selected rows, and their forward and backward Hermitian products are stacked into a third-order tensor. A Tucker2 higher-order orthogonal iteration is then employed to estimate the signal subspace, followed by a gridless least-squares DOA estimator. Simulation results show that the proposed NC-TTCD method provides improved DOA estimation accuracy and resolution over conventional TTCD, forward-backward partial Toeplitz matrix reconstruction (FB-PTMR), and block diagonal spatial smoothing reduced dimensional multiple signal classification (BSS-RD-MUSIC) methods, especially at low-to-moderate signal-to-noise ratios.