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A full multi--dimensional characterization of the angle of arrival (AoA) hasimmediate applications to the efficient operation of modern wirelesscommunication systems. In this work, we develop a compressed sensing basedmethod to extract multi-dimensional AoA information exploiting the sparsenature of the signal received by a sensor array. The proposed solution, basedon the atomic $\ell_0$ norm, enables accurate gridless resolution of the AoA insystems with arbitrary 3D antenna arrays. Our approach allows characterizingthe maximum number of distinct sources (or scatters) that can be identified fora given number of antennas and array geometry. Both noiseless and noisymeasurement scenarios are addressed, deriving and evaluating the resolvabilityof the AoA propagation parameters through a multi--level Toeplitz matrixrank--minimization problem. To facilitate the implementation of the proposedsolution, we also present a least squares approach regularized by a convexrelaxation of the rank-minimization problem and characterize its conditions forresolvability.

Gridless Multidimensional Angle of Arrival Estimation for Arbitrary 3D Antenna Arrays