Direction-of-arrival estimation in nonuniform noise via low-rank matrix decomposition

The problem of direction-of-arrival (DOA) estimation in the presence of unknown nonuniform noise is addressed and a new approach based on low-rank matrix decomposition is developed. Unlike existing methods such as nonuniform maximum likelihood and iterative least squares subspace estimation algorithms, it is proposed in this paper to determine the noise-free covariance matrix and noise covariance matrix through rank minimization. To deal with the nonconvexity of the resulting optimization problem, nuclear norm minimization is employed as convex relaxation. Furthermore, in order to take the array covariance matrix estimation errors into account, the equality constraint in this problem is appropriately modified by a norm constraint in a generalized least squares sense. Once the noise-free covariance matrix and noise covariance matrix have been determined, traditional high-resolution DOA estimation algorithms for the uniform noise model can be applied. Numerical examples are provided to illustrate the performance of the proposed method.