Tighter and Stable Bounds for Marcum Q-Function

TL;DR

This paper introduces new bounds for the Marcum Q-function that are extremely tight and stable across all parameter ranges, outperforming previous bounds and useful for various applications.

Contribution

The paper presents novel bounds for the Marcum Q-function derived through refined Bessel function approximations, improving tightness and stability over existing bounds.

Findings

Bounds are tighter than previous ones across all parameter ranges.

Proposed bounds are stable for both large and small parameter values.

New bounds outperform existing bounds in accuracy and applicability.

Abstract

This paper proposes new bounds for Marcum Q-function, which prove extremely tight and outperform all the bounds previously proposed in the literature. What is more, the proposed bounds are good and stable both for large values and small values of the parameters of the Marcum Q-function, where the previously introduced bounds are bad and even useless under some conditions. The new bounds are derived by refined approximations for the 0th order modified Bessel function in the integration region of the Marcum Q-function. They should be useful since they are always tight no matter the parameters are large or small.