Large system analysis of a GLRT for detection with large sensor arrays in temporally white noise

TL;DR

This paper analyzes the performance of a generalized likelihood ratio test (GLRT) for signal detection in large sensor arrays with white noise, using large system asymptotics to predict test behavior when sensor count and sample size are comparable.

Contribution

It provides a theoretical analysis of the GLRT performance in large sensor array regimes, extending classical results to high-dimensional settings.

Findings

Accurately predicts GLRT performance in large system regimes.

Shows the asymptotic distribution of the test statistic.

Provides insights into detection capabilities with many sensors.

Abstract

This paper addresses the behaviour of a classical multi-antenna GLRT test that allows to detect the presence of a known signal corrupted by a multi-path propagation channel and by an additive white Gaussian noise with unknown spatial covariance matrix. The paper is focused on the case where the number of sensors M is large, and of the same order of magnitude as the sample size N, a context which is modeled by the large system asymptotic regime M goes to infinity, N goes to infinity in such a way that M/N goes to c for c in (0, infinity). The purpose of this paper is to study the behaviour of a GLRT test statistics in this regime, and to show that the corresponding theoretical analysis allows to accurately predict the performance of the test when M and N are of the same order of magnitude.