Efficient Two-Dimensional Line Spectrum Estimation Based on Decoupled Atomic Norm Minimization

TL;DR

This paper introduces a decoupled atomic norm minimization method for efficient 2-D line spectrum estimation, significantly reducing computational costs while maintaining high accuracy and robustness, especially for large-scale applications.

Contribution

The paper develops a novel decoupled 2-D ANM approach using SDP that reduces complexity and enables practical large-scale 2-D spectrum estimation.

Findings

Reduces computational complexity by several orders of magnitude.

Retains super-resolution and robustness to source correlation.

Effective for large-scale antenna systems like massive MIMO and radar.

Abstract

This paper presents an efficient optimization technique for gridless {2-D} line spectrum estimation, named decoupled atomic norm minimization (D-ANM). The framework of atomic norm minimization (ANM) is considered, which has been successfully applied in 1-D problems to allow super-resolution frequency estimation for correlated sources even when the number of snapshots is highly limited. The state-of-the-art 2-D ANM approach vectorizes the 2-D measurements to their 1-D equivalence, which incurs huge computational cost and may become too costly for practical applications. We develop a novel decoupled approach of 2-D ANM via semi-definite programming (SDP), which introduces a new matrix-form atom set to naturally decouple the joint observations in both dimensions without loss of optimality. Accordingly, the original large-scale 2-D problem is equivalently reformulated via two decoupled one-level Toeplitz matrices, which can be solved by simple 1-D frequency estimation with pairing. Compared with the conventional vectorized approach, the proposed D-ANM technique reduces the computational complexity by several orders of magnitude with respect to the problem size. It also retains the benefits of ANM in terms of precise signal recovery, small number of required measurements, and robustness to source correlation. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO, radar signal processing and radio astronomy.