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A full multi-dimensional characterization of the angle of arrival (AoA) has immediate applications to the efficient operation of modern wireless communication systems. In this work, we develop a compressed sensing based method to extract multi-dimensional AoA information exploiting the sparse nature of the signal received by a sensor array. The proposed solution, based on the atomic 0 norm, enables accurate gridless resolution of the AoA in systems with arbitrary 3D antenna arrays. Our approach allows characterizing the maximum number of distinct sources (or scatters) that can be identified for a given number of antennas and array geometry. Both noiseless and noisy measurement scenarios are addressed, deriving and evaluating the resolvability of the AoA propagation parameters through a multi-level Toeplitz matrix rank-minimization problem. To facilitate the implementation of the proposed solution, we also present a least squares approach regularized by a convex relaxation of the rank-minimization problem and characterize its conditions for resolvability.
3d antenna array; atomic norm; multi-dimensional aoa; multi-level vandermonde decomposition