Closed-Form Bounds for the Rice $Ie$-Function

TL;DR

This paper derives new tight closed-form upper and lower bounds for the Rice Ie-function, which are useful for analytical studies in engineering and natural sciences, especially in digital communications over fading channels.

Contribution

The paper introduces novel closed-form bounds for the Rice Ie-function that are tight and can be used in performance analysis of communication systems.

Findings

Bounds are mathematically tight and accurate within certain parameter ranges.

Derived bounds are expressed in simple closed-form expressions.

Bounds are applicable in analyzing error probabilities in fading channels.

Abstract

This work is devoted in the derivation of novel upper and lower bounds for the Rice $Ie$-function. These bounds are expressed in closed-form and are shown to be quite tight. This is particularly evident by the fact that for a certain range of parameter values, the derived lower bound virtually behaves as a remarkably accurate approximation. As a result, the offered expressions can be considered useful mathematical tools that can be efficiently employed in various analytical studies related to natural sciences and engineering. To this effect, they can be sufficiently applied in the area of digital communications over fading channels for the derivation of explicit representations for vital performance measures such as bit and symbol error probability, among others.