Convex relaxation approaches to maximum likelihood DOA estimation in ULA´s and UCA´s with unknown mutual coupling

Direction of arrival (DOA) estimation using sensor array super-resolution techniques are known to suffer from array modeling errors including array element displacements, mutual coupling, and array gain/phase perturbations. In this paper, we consider maximum likelihood (ML) DOA estimation for multiple sources in the presence of unknown mutual coupling, and propose convex semidefinite relaxation approaches to this nonlinear and non-convex problem for uniform linear arrays (ULA´s) and uniform circular arrays (UCA´s), respectively. Simulation results show that the proposed method are effective to practical applications.