On detection of Gaussian stochastic sequences

TL;DR

This paper investigates the minimax detection problem for Gaussian signals in white noise, focusing on when the uncertainty set of signal intensities can be reduced without compromising detection performance.

Contribution

It analyzes conditions under which the set of possible signal intensities can be simplified to a smaller set or a single point without losing detection quality.

Findings

Conditions for replacing the set of intensities with a smaller set.

Criteria for substituting the set with a single point.

Implications for simplifying detection strategies.

Abstract

The problem of minimax detection of Gaussian random signal vector in White Gaussian additive noise is considered. It is supposed that an unknown vector $\boldsymbol{\sigma}$ of the signal vector intensities belong to the given set ${\mathcal E}$. It is investigated when it is possible to replace the set ${\mathcal E}$ by a smaller set ${\mathcal E}_{0}$ without loss of quality (and, in particular, to replace it by a single point $\boldsymbol{\sigma}_{0}$).