Computational and Numerical Properties of a Broadband Subspace-Based Likelihood Ratio Test

TL;DR

This paper analyzes a polynomial subspace projection method combined with a likelihood ratio test for detecting weak transient signals in broadband array data, highlighting its computational, numerical, and detection advantages.

Contribution

It provides a theoretical analysis of how polynomial subspace projection improves likelihood ratio test performance in broadband signal detection.

Findings

Whitens crucial parts of signals, enabling shorter temporal windows

Reduces computational complexity and improves numerical stability

Demonstrates effectiveness through simulations and examples

Abstract

This paper investigates the performance of a likelihood ratio test in combination with a polynomial subspace projection approach to detect weak transient signals in broadband array data. Based on previous empirical evidence that a likelihood ratio test is advantageously applied in a lower-dimensional subspace, we present analysis that highlights how the polynomial subspace projection whitens a crucial part of the signals, enabling a detector to operate with a shortened temporal window. This reduction in temporal correlation, together with a spatial compaction of the data, also leads to both computational and numerical advantages over a likelihood ratio test that is directly applied to the array data. The results of our analysis are illustrated by examples and simulations.