Vandermonde decomposition of coprime coarray covariance matrix for DOA estimation

In this paper, we propose a novel Vandermonde decomposition-based direction-of-arrival (DOA) estimation algorithm by using a coprime array, where increased number of degrees-of-freedom (DOFs) can be achieved in an off-grid manner. Specifically, the equivalent statistics corresponding to an augmented virtual uniform linear array are first derived from the coprime array received signals, and the resulting coprime coarray covariance matrix is capable to increase the DOFs. While the obtained coprime coarray covariance matrix follows a positive semi-definite Hermitian Toeplitz structure, Vandermonde decomposition can be incorporated to perform unique decomposition in the virtual domain. By matching the Vandermonde decomposition result and its theoretical version, closed-form solutions are formulated for estimating the DOA and power of each source. Simulation results demonstrate the effectiveness of the proposed DOA estimation algorithm.