Super-resolution Multi-signal Direction-of-Arrival Estimation by Hankel-structured Sensing and Decomposition

TL;DR

This paper introduces a novel super-resolution DoA estimation framework using Hankel-structured sensing and matrix decomposition, effective under various noise conditions and suitable for hardware-constrained systems.

Contribution

It develops a new super-resolution DoA estimation method with optimality guarantees under different noise models, suitable for hardware-limited autonomous sensing.

Findings

The $L_2$-norm estimator is maximum-likelihood optimal in Gaussian noise.

The $L_1$-norm estimator is maximum-likelihood optimal in Laplace noise.

The proposed methods outperform recent approaches in resolution and SNR requirements.

Abstract

Motivated by sensing modalities in modern autonomous systems that involve hardware-constrained spatial sampling over large arrays with limited coherence time, we develop a novel framework for rapid super-resolution multi-signal direction-of-arrival (DoA) estimation based on Hankel-structured sensing and data matrix decomposition of arbitrary rank, under both the $L_2$ and $L_1$-norm formulation. The resulting $L_2$-norm estimator is shown to be maximum-likelihood optimal in white Gaussian noise. The $L_1$-norm estimator is shown to be maximum-likelihood optimal in independent, identically distributed (i.i.d.) isotropic Laplace noise, offering broad robustness to impulsive interference and corrupted measurements commonly encountered in practice. Extensive simulations demonstrate that the proposed methods exhibit powerful super-resolution capabilities, requiring significantly lower SNR and achieving substantially higher resolution probability than recent competing approaches.