A New Twist on the Generalized Marcum Q-Function QM(a, b) with Fractional-Order M and Its Applications

Abstract

A new exponential-type integral for the generalized M-th order Marcum Q-function QM(α,β) is obtained when M is not necessarily an integer. This new representation includes a classical formula due to Helstrom for the special case of positive integer order M and an additional integral correction term that vanishes when M assumes an integer value. The new form has both computational utility (numerous existing computational algorithms for QM(α,β) are limited to integer M) and analytical utility (e.g., performance evaluation of selection diversity receiver in correlated Nakagami-m fading with arbitrary fading severity index, unified analysis of binary and quaternary modulations over generalized fading channels, and development of a Markovian threshold model for block errors in correlated Nakagami-m fading channels). Tight upper and lower bounds for QM(α,β) that holds for any arbitrary real order M≥0.5 are also derived.