Sparsity-Based Underdetermined DOA Estimator via Toeplitz Matrix Reconstruction for Sparse Array

In this paper, we provide a novel idea to achieve underdetermined direction of arrival (DOA) estimation for sparse array by introducing covariance matrix reconstruction into sparsity-based algorithms. Based on the Toeplitz property of covariance matrix of uniform linear array, the covariance vector sparsely representation (CVSR) model is established and DOAs can be retrieved through sparse reconstruction. Moreover, Toeplitz covariance matrix estimation can be transformed as convex optimization problem with less constraints and solved by proposed original covariance matrix reconstruction (OCMR). Finally, CVSR achieve more accurate DOA estimation based on accurate Toeplitz covariance matrix estimation by OCMR. By implementing simulation experiments, we demonstrate that CVSR can outperform existing sparsity-based DOA estimators in terms of estimation accuracy and efficiency which also demonstrates the effectiveness of the novel idea about combinations of covariance matrix reconstruction and sparsity-based algorithms.