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

TL;DR

This paper introduces a gridless, compressed sensing-based method for accurate multi-dimensional AoA estimation in arbitrary 3D antenna arrays, applicable in noisy and noiseless scenarios, with theoretical guarantees on source resolvability.

Contribution

It develops a novel atomic  norm approach for gridless AoA estimation in 3D arrays, addressing arbitrary geometries and providing resolvability conditions.

Findings

Accurately estimates AoA in arbitrary 3D antenna arrays.

Provides theoretical bounds on the number of resolvable sources.

Offers a practical least squares implementation with convex relaxation.

Abstract

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 $\ell_0$ 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.