A General Euclidean Geometric Representation for the Classical Detection Theory

TL;DR

This paper introduces a universal Euclidean geometric framework for classical detection theory, enabling a unified approach to various communication problems by mapping hypotheses and observations into Euclidean space.

Contribution

It presents a highly general geometric representation that simplifies the analysis of detection problems across different communication scenarios.

Findings

Posterior probability decreases exponentially with squared Euclidean distance.

Framework applies to nearly all communication detection problems.

Provides a unified geometric perspective for detection theory.

Abstract

We propose an Euclidean geometric representation for the classical detection theory. The proposed representation is so generic that can be employed to almost all communication problems. The hypotheses and observations are mapped into R^N in such a way that a posteriori probability of an hypothesis given an observation decreases exponentially with the square of the Euclidean distance between the vectors corresponding to the hypothesis and the observation.