Detection of a rank-one signal with limited training data

TL;DR

This paper develops new detection methods for rank-one signals in Gaussian noise that perform well even with limited training data, improving upon previous methods designed for abundant data.

Contribution

It re-derives the GLRT and 2S-GLRT detectors for limited training data, showing they are effective and outperform existing methods in low-sample scenarios.

Findings

Detectors work effectively with low sample support.

In abundant data environments, the re-derived GLRT matches previous methods.

Re-derived 2S-GLRT outperforms previous 2S-GLRT in detection performance.

Abstract

In this paper, we reconsider the problem of detecting a matrix-valued rank-one signal in unknown Gaussian noise, which was previously addressed for the case of sufficient training data. We relax the above assumption to the case of limited training data. We re-derive the corresponding generalized likelihood ratio test (GLRT) and two-step GLRT (2S--GLRT) based on certain unitary transformation on the test data. It is shown that the re-derived detectors can work with low sample support. Moreover, in sample-abundant environments the re-derived GLRT is the same as the previously proposed GLRT and the re-derived 2S--GLRT has better detection performance than the previously proposed 2S--GLRT. Numerical examples are provided to demonstrate the effectiveness of the re-derived detectors.