High-Precision DOA Estimation for Cyclostationary Signals Using an Augmented Extended Coprime Array and Atomic Norm Minimization

Direction-of-arrival (DOA) estimation of cyclostationary signals is an important problem in array signal processing, especially in sensor-limited and underdetermined scenarios. Sparse arrays and cyclostationary statistics can improve virtual degrees of freedom and target selectivity, but incomplete difference coarray information caused by missing lags may degrade virtual covariance reconstruction and reduce the reliability of DOA estimation in closely spaced, coherent, and interference-contaminated environments. To address this issue, this paper proposes a cyclostationary DOA estimation method based on an augmented extended coprime array (AECA), SVT-based hole recovery, and weighted atomic norm minimization (ANM). The proposed method first constructs the cyclic correlation matrix at the target cyclic frequency and maps it into the AECA-based virtual coarray domain. Redundant lag observations are then aggregated, and an iterative hole recovery procedure is applied to obtain an initial structured virtual covariance matrix. On this basis, a weighted ANM-based covariance refinement model is introduced, where directly observed lags and SVT-recovered hole entries are assigned different confidence levels. The final DOA estimates are obtained using MUSIC on the refined virtual covariance matrix. Simulation results under the considered underdetermined, closely spaced, coherent-source, and interference-contaminated scenarios show that the proposed method achieves lower RMSE and clearer spectral responses than the selected baseline methods. Additional ablation, parameter sensitivity, cyclic frequency mismatch, non-Gaussian noise, and runtime analyses further clarify the contribution, robustness range, and computational cost of the proposed framework.