A Sparse Array DOA Estimation Approach via Atomic Norm Minimization

Sparse arrays can achieve high degree of freedom Direction of Arrival (DOA) estimation by constructing equivalent virtual difference co-array. Due to the existence of holes, however, most existing algorithms only use an equivalent uniform array of the continuous part of the virtual difference co-array for some sparse arrays such as coprime arrays and nested arrays, which cannot fully utilize all the information received by the original sparse array, resulting in the loss of DOA estimation performance. This paper proposes a DOA estimation algorithm based on atomic norm minimization and covariance matrix reconstruction. The proposed algorithm first utilizes singular value thresholding to process the received signal from the sparse array, resulting in a rough reconstruction as a prior. Next, it constructs a covariance matrix for the equivalent virtual linear array by solving the atomic norm minimization problem. Finally, the MUSIC algorithm is employed for DOA estimation. The simulation results demonstrate the performance advantages of the algorithm on sparse arrays, particularly for its high precision and strong noise resistance in multi-target scenarios.