In the existing DOA estimation methods based on coprime array,discarding the non-uniform virtual elements in the difference coarray leads to the decrease of the number of the resolvable sources.In order to solve the problem,a DOA estimation method based on matrix completion was proposed.Firstly,according to the correspondence between the difference coarray and the wave path difference,a Toeplitz array covariance matrix was constructed,of which some elements are zero.Additionally,the DOA estimation model was established based on matrix completion and it was proved that the proposed model satisfied null space property.Secondly,according to the low rank matrix completion theory,the DOA estimation was transformed into the minimization of the nuclear norm,and then the Toeplitz matrix was recovered to the full covariance matrix by the fixed-point iterative algorithm.Finally,the DOA estimation was transformed into the determination of polynomial roots by singular value decomposition on the Toeplitz matrix.Simulation results showed the effectiveness and superiority of the proposed method.The experimental results showed that it can effectively fill the holes of the difference coarray,increase the available DOFs and the number of the resolvable signals.Meanwhile,it can eliminate the influence of the basis mismatch on the estimation performance in traditional sparse reconstruction methods due to the discretization in angel domain.Compared with the existing methods,the proposed method improved the DOA estimation accuracy and resolution.
