Connections between the Generalized Marcum Q-Function and a class of Hypergeometric Functions

TL;DR

This paper establishes a novel link between the generalized Marcum Q-function and hypergeometric functions, enabling new closed-form expressions for distributions relevant in communication theory.

Contribution

It introduces a new connection between the Marcum Q-function and phi3 hypergeometric function, leading to closed-form characterizations of complex distributions.

Findings

Closed-form expressions for bivariate Nakagami-m distribution

Distribution of minimum eigenvalue of correlated non-central Wishart matrices

Applications to communication-theoretic problems

Abstract

This paper presents a new connection between the generalized Marcum-Q function and the confluent hypergeometric function of two variables, phi3. This result is then applied to the closed-form characterization of the bivariate Nakagami-m distribution and of the distribution of the minimum eigenvalue of correlated non-central Wishart matrices, both important in communication theory. New expressions for the corresponding cumulative distributions are obtained and a number of communication-theoretic problems involving them are pointed out.