Enhanced Unitary Root SAMV with Toeplitz Covariance Completion and Subspace Projection for Coprime Array DOA Estimation

To address the issues of incomplete virtual array utilization and direction of arrival (DOA) estimation performance degradation under noise interference in coprime array processing, this paper proposes the Toeplitz Assisted Subspace Projection enhanced Unitary Root Sparse Asymptotic Minimum Variance (TASP-URootSAMV) algorithm. First, trace regularized Toeplitz covariance completion is employed to fill aperture holes in the virtual domain by exploiting shift invariance structure, reconstructing the interpolated covariance matrix through convex optimization and Wiener prediction. Second, eigenspace projection is performed to suppress background noise through Toeplitz-averaged covariance estimation and signal/noise subspace separation. Third, unitary root SAMV is applied to perform grid-initialized off-grid DOA refinement through iterative polynomial rooting, thereby mitigating grid-induced modeling errors and reducing sensitivity to the initial angular grid. Algorithm performance is evaluated through two complementary experiments. Spatial spectrum and root mean square error (RMSE) analysis indicate that, at T=200 snapshots and SNR=−10 dB, the proposed method reduces the RMSE by 47.86–56.47% compared with the considered algorithms, with accuracy close to the Cramér–Rao bound (CRB) in the tested cases. Additionally, the algorithm maintains distinguishable spectral peaks for the tested source numbers. Grid-spacing analysis indicates relatively stable performance over the tested initialization-grid intervals, whereas the performance of the grid-dependent comparison method degrades as the grid spacing increases. The convergence experiments also show limited sensitivity to the tested initialization settings and comparable computational efficiency. Under the adopted simulation assumptions, these results indicate improved estimation accuracy under the tested noisy conditions.