Blind Non-parametric Statistics for Multichannel Detection Based on Statistical Covariances

TL;DR

This paper introduces non-parametric detection statistics for multichannel signals that are robust to unknown noise variance and system parameters, improving detection reliability in uncertain environments.

Contribution

It proposes novel non-parametric statistics based on covariance matrices that are immune to noise variance uncertainty, addressing limitations of traditional GLRT methods.

Findings

Statistics are invariant to noise variance uncertainty.

Proposed methods outperform GLRT in specific scenarios.

Detection performance is analyzed under various signal correlations.

Abstract

We consider the problem of detecting the presence of a spatially correlated multichannel signal corrupted by additive Gaussian noise (i.i.d across sensors). No prior knowledge is assumed about the system parameters such as the noise variance, number of sources and correlation among signals. It is well known that the GLRT statistics for this composite hypothesis testing problem are asymptotically optimal and sensitive to variation in system model or its parameter. To address these shortcomings we present a few non-parametric statistics which are functions of the elements of Bartlett decomposed sample covariance matrix. They are designed such that the detection performance is immune to the uncertainty in the knowledge of noise variance. The analysis presented verifies the invariability of threshold value and identifies a few specific scenarios where the proposed statistics have better performance compared to GLRT statistics. The sensitivity of the statistic to correlation among streams, number of sources and sample size at low signal to noise ratio are discussed.