Toeplitz Matrix Reconstruction of Interpolated Coprime Virtual Array for DOA Estimation

A coprime array enables an increased number of degrees-of-freedom by deriving a non-uniform virtual array. However, existing work such as spatial smoothing fails to utilize all of the information provided by the coprime array, which results in performance loss. In this paper, we propose a novel coprime virtual array interpolation-based direction-of-arrival (DOA) estimation algorithm by Toeplitz matrix reconstruction. After investigating the challenges caused by the non-uniformity, we introduce the idea of array interpolation to construct a uniform linear virtual array, such that the information contained in the coprime virtual array can be fully utilized. According to the statistics of non-uniform coprime virtual array signal, we formulate a convex optimization problem for DOA estimation by reconstructing the covariance matrix of the equivalent received signals of the interpolated coprime virtual array under the Toeplitz constraint. Simulation results demonstrate the effectiveness of the proposed algorithm.