Calculation of entropy for a sinusoid with beta-distributed phase

Abstract

In this paper, an analytical expression is developed for the differential entropy of a sinusoid with a Beta-distributed phase angle. This particular signal model is prevalent in optical communications, however an expression for the associated differential entropy does not currently exist. The expression we derive is approximate as it relies on a series expansion for one of the key terms needed in the derivation. However, we are able to show that the approximation is accurate (error < 5%) for a wide variety of Beta parameter choices. © 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland.