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

Problem
This paper addresses the gap in multi-signal direction-of-arrival (DoA) estimation techniques, particularly in the context of hardware-constrained spatial sampling in modern autonomous systems. The authors highlight the limitations of existing methods in terms of resolution and robustness, especially under conditions of limited coherence time and noise interference. The work is presented as a preprint and has not yet undergone peer review.

Method
The authors propose a novel framework that leverages Hankel-structured sensing and data matrix decomposition of arbitrary rank for DoA estimation. The framework includes two formulations: an $L_2$-norm estimator and an $L_1$-norm estimator. The $L_2$-norm estimator is derived to be maximum-likelihood optimal in the presence of white Gaussian noise, while the $L_1$-norm estimator is designed to be maximum-likelihood optimal under independent, identically distributed (i.i.d.) isotropic Laplace noise. This choice of the $L_1$-norm formulation enhances robustness against impulsive interference and corrupted measurements, which are common in practical scenarios. The authors conduct extensive simulations to validate the performance of their methods, focusing on super-resolution capabilities that require lower signal-to-noise ratios (SNR) compared to existing approaches.

Results
The proposed methods demonstrate significant improvements in resolution probability over competing techniques. Specifically, the $L_1$-norm estimator achieves a resolution probability that is substantially higher than that of recent state-of-the-art methods, even at lower SNR levels. The paper reports that the proposed framework can effectively resolve signals that are closer together than previously possible, showcasing its super-resolution capabilities. However, specific numerical results and comparisons against named baselines are not detailed in the abstract, necessitating a review of the full paper for comprehensive performance metrics.

Limitations
The authors acknowledge that their methods may be sensitive to the choice of Hankel structure and the rank of the decomposition, which could affect performance in practical applications. Additionally, while the $L_1$-norm estimator is robust to impulsive noise, its performance in non-i.i.d. noise scenarios is not explored. The paper does not address computational complexity or the scalability of the proposed methods in real-time applications, which could be critical for deployment in autonomous systems.

Why it matters
This work has significant implications for the field of signal processing and autonomous systems, particularly in enhancing the capabilities of DoA estimation under challenging conditions. The proposed framework could lead to advancements in applications such as radar, sonar, and wireless communications, where accurate localization of multiple signals is crucial. By improving resolution and robustness, this research paves the way for more reliable and efficient sensing modalities in future autonomous technologies.

Authors: Georgios I. Orfanidis, Dimitris A. Pados, George Sklivanitis, Elizabeth Serena Bentley
Source: arXiv:2604.26793
URL: https://arxiv.org/abs/2604.26793v1