Integrated Approach for Efficient Adaptive Underdetermined DOA Estimation: Coarray LMS with Covariance Matrix Error Removal

—Underdetermined direction of arrival (U-DOA) estimation relies on the higher degrees of freedom provided by the difference coarray of a non-uniform linear array. The coarray domain signal is obtained by vectorizing the array covariance matrix, which is estimated using array signals from multiple snapshots. However, in low snapshot scenarios, errors arise in the covariance matrix due to non-zero off-diagonal elements in the signal and noise covariance matrices, degrading U-DOA estimation performance. This work proposes an integrated approach combining a novel covariance matrix error removal technique with the adaptive Coarray LMS and subspace-based Coarray MUSIC U-DOA estimation methods. Our method uses a matrix decomposition based approach to estimate a sparse, full-rank covariance matrix while removing low-rank residual errors caused by low snapshots. Unlike conventional methods, we treat the sparse matrix as the desired covariance matrix, addressing low-snapshot underdetermined scenarios. Additionally, we introduce a novel computationally efficient gridless approach to obtain the DOA spectrum by analyzing weights in the Fourier domain. Simulations validate the improved U-DOA estimation performance of the proposed method in low snapshot scenarios.