DOA Estimation via Optimal Weighted Low-Rank Matrix Completion

TL;DR

This paper introduces a weighted low-rank matrix completion approach for DOA estimation from a single snapshot, improving accuracy and reducing sample complexity for sparse, non-uniform sensor arrays.

Contribution

It proposes a novel weighted lifted-structured low-rank matrix recovery framework that enhances DOA estimation accuracy with fewer samples compared to existing methods.

Findings

Achieves near-optimal sample complexity for array interpolation.

Significantly outperforms non-weighted and atomic norm methods in accuracy.

Reduces normalized mean-squared error by approximately 10 dB at low noise.

Abstract

This paper presents a novel method for estimating the direction of arrival (DOA) for a non-uniform and sparse linear sensor array using the weighted lifted structure low-rank matrix completion. The proposed method uses a single snapshot sample in which a single array of data is observed. The method is rooted in a weighted lifted-structured low-rank matrix recovery framework. The method involves four key steps: (i) lifting the antenna samples to form a low-rank stature, then (ii) designing left and right weight matrices to reflect the sample informativeness, (iii) estimating a noise-free uniform array output through completion of the weighted lifted samples, and (iv) obtaining the DOAs from the restored uniform linear array samples. We study the complexity of steps (i) to (iii) above, where we analyze the required sample for the array interpolation of step (iii) for DOA estimation. We demonstrate that the proposed choice of weight matrices achieves a near-optimal sample complexity. This complexity aligns with the problem's degree of freedom, equivalent to the number of DOAs adjusted for logarithmic factors. Numerical evaluations show the proposed method's superiority against the non-weighted counterpart and atomic norm minimization-based methods. Notably, our proposed method significantly improves, with approximately a 10 dB reduction in normalized mean-squared error over the non-weighted method at low-noise conditions.