An Interactive Graphical Tool to Check the Coarray Continuity of Two-Fold Redundant Sparse Arrays (TFRSAs) Under Single Sensor Failures

TL;DR

This paper introduces a MATLAB-based graphical tool to verify the true two-fold redundancy of sparse arrays, ensuring reliable DOA estimation even under sensor failures, crucial for critical applications.

Contribution

The paper presents the first formal framework and GUI for checking hidden dependencies in TFRSAs, aiding array designers in validating array configurations.

Findings

The GUI accurately detects hidden dependencies in TFRSAs.

Numerical examples demonstrate the tool's effectiveness across scenarios.

The tool helps prevent array configurations that could cause failure in critical systems.

Abstract

Two-fold redundant sparse arrays possess inbuilt redundancy to tackle single-element failures. This property enables them to perform accurate direction of arrival (DOA) estimation even during single sensor faults. However, recent literature suggests that some TFRSAs suffer from hidden dependencies whereby a single sensor fault at peculiar positions within the array cause discontinuities (holes) in the difference coarray (DCA). This violates the very idea of providing two-fold redundancy. Such hidden dependencies could prove catastrophic in many critical applications such as defense, autonomous driving, and biomedical imaging. Despite this issue, no formal tools or techniques exist to ascertain whether a given array configuration is truly twofold redundant or not. To address this gap, we provide a comprehensive framework and a first-ever graphical user interface (GUI). The GUI has been built using the features in MATLAB app designer and tested with known examples available in sparse array literature. Several numerical examples have been discussed to check the tool's response in each scenario. We conclude that the GUI is functionally accurate and can be an indispensable tool for sparse array designers in making informed choices about array configurations prior to real deployment.