The Divergence and Bhattacharyya Distance Measures in Signal Selection

TLDR

Determining optimum signals by minimizing error probability is difficult, so simpler suboptimal performance measures have been studied. The paper compares the properties of the commonly used divergence measure with a newly proposed Bhattacharyya distance. The authors introduce the Bhattacharyya distance, which is easier to evaluate than the divergence. In the studied problems, the Bhattacharyya distance yields results at least as good as, and often better than, the divergence.

Abstract

Minimization of the error probability to determine optimum signals is often difficult to carry out. Consequently, several suboptimum performance measures that are easier than the error probability to evaluate and manipulate have been studied. In this partly tutorial paper, we compare the properties of an often used measure, the divergence, with a new measure that we have called the Bhattacharyya distance. This new distance measure is often easier to evaluate than the divergence. In the problems we have worked, it gives results that are at least as good as, and are often better, than those given by the divergence.