Making use of the Toeplitz structure of the mutual coupling matrix of the Uniform Linear Array (ULA), estimating the direction-of-arrival (DOA) of the sources as well as the mutual coupling coefficients of the array can be formulated as a linear inverse problem, where the solution is given by the Kronecker product of the vectors with respect to the DOAs and the mutual coupling coefficients. Through mathematical manipulation, these solution vectors can be decoupled. Estimation of the DOAs is cast into the framework of sparse solution finding. To derive the solution, an alternating minimization technique is presented. The proposed method is firstly developed based on the noise free observation covariance matrix, and can be generalized to directly using the snapshots. Using the proposed method, DOA estimation is feasible even in single snapshot case. The performance of the proposed methods with covariance matrix, single snapshot and multiple snapshots are illustrated by computer simulations. Their ability to resolve closely spaced targets and the applicability to correlated sources have also been demonstrated.
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