WLC10-1: Generic Exponential Bounds and Erfc-Bounds on the Marcum Q-Function via the Geometric Approach

The first-order Marcum Q-function, Q(a,b), can be interpreted geometrically as the probability that a complex, Gaussian random variable Z with real mean a, takes on values outside of a circular region C_O,b of radius b centered at the origin O. Bounds can thus be easily obtained by computing the probability of Z lying outside of some geometrical shapes whose boundaries tightly enclose, or are tightly enclosed by the boundary of C_O,b. In this paper, the bounding shapes are chosen to be a set of sectors or angular sectors of annuli to generate generic exponential bounds, and to be a set of rectangles to generate generic erfc-bounds. These generic exponential bounds and erfc-bounds involve an arbitrarily large number of exponential functions and erfc functions, respectively, and are shown to approach the exact value of Q(a, b) as the number of terms involved increases.