Low-complexity optimization for Two-Dimensional Direction-of-arrival Estimation via Decoupled Atomic Norm Minimization

TL;DR

This paper introduces a low-complexity, decoupled atomic norm minimization method for 2D DOA estimation that significantly reduces computational costs while maintaining super-resolution and robustness, benefiting large-scale antenna systems.

Contribution

It proposes a novel decoupled ANM formulation using semi-definite programming, enabling efficient 2D angle estimation with automatic pairing and reduced complexity.

Findings

Reduces computational complexity by several orders of magnitude.

Maintains super-resolution and robustness to noise and source correlation.

Effective for large-scale antenna systems like massive MIMO.

Abstract

This paper presents an efficient optimization technique for super-resolution two-dimensional (2D) direction of arrival (DOA) estimation by introducing a new formulation of atomic norm minimization (ANM). ANM allows gridless angle estimation for correlated sources even when the number of snapshots is far less than the antenna size, yet it incurs huge computational cost in 2D processing. This paper introduces a novel formulation of ANM via semi-definite programming, which expresses the original high-dimensional problem by two decoupled Toeplitz matrices in one dimension, followed by 1D angle estimation with automatic angle pairing. Compared with the state-of-the-art 2D ANM, the proposed technique reduces the computational complexity by several orders of magnitude with respect to the antenna size, while retaining the benefits of ANM in terms of super-resolution performance with use of a small number of measurements, and robustness to source correlation and noise. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO and radio astronomy.