DOA Estimation with Coprime Arrays Using Toeplitz and Hankel-Based Structured Covariance Reconstruction

Coprime arrays are attractive for direction-of-arrival (DOA) estimation because they can generate a large virtual aperture from a limited number of physical sensors. Their performance, however, deteriorates markedly when coherent sources coexist with unknown nonuniform sensor noise. To cope with this difficulty, this paper develops a structured DOA estimation scheme that integrates difference-coarray lag averaging, Toeplitz positive semidefinite covariance reconstruction, Hankel-based low-rank refinement, and forward–backward spatial smoothing. The sample covariance of the physical coprime array is first mapped into the coarray domain, where repeated lags are averaged, and missing lags are treated by a mask, rather than by zero padding. A Hermitian Toeplitz positive semidefinite virtual covariance matrix is then recovered in the lag domain with redundancy-aware weighting. To further enhance robustness under source coherence, the reconstructed covariance sequence is refined through a Hankel-structured low-rank restoration step. The recovered virtual covariance is finally processed by forward–backward spatial smoothing, and DOAs are obtained from the MUSIC spectrum. Simulation results under coherent-source and unknown nonuniform-noise scenarios show that the proposed method yields a lower estimation error than representative baselines, preserves clear spectral separation in multi-source cases, and maintains reliable two-source resolution under different angular separations. Additional experiments further examine RMSE trends with respect to SNR, snapshots, source number, and computational costs.