Exponential-Type Bounds on the First-Order Marcum Q-Function

This paper presents new bounds on the Marcum Q-function Q₁ (a, b). First, new, simple, arbitrarily tight, exponential lower bounds on the zeroth-order modified Bessel function of the first kind I_o(x) and the Gaussian Q-function Q(x) are derived. Due to their elegant features, these new bounds are fundamental in their own rights. Then, when they are applied to the Marcum Q-function that is expressed as a function of l_o(x) and Q(x), various new exponential-type lower and upper bounds are developed.