Stochastic Representations of the Marcum Q-S Function and Associated Radar Detection

This report introduces new research on the generalised Marcum Q-Function, and in particular, the probability of detection of a number of incoherently integrated signals in a Gaussian clutter and noise environment. A new probabilistic association is derived, linking this detection probability with a probability associated with two independent Poisson random variables. Additionally, it is shown that this detection probability is the solution to two stochastic Volterra integral equations. This results in a means of obtaining estimates of this detection probability. Specifically, lower and upper bounds are derived using these representations, and the bounds are compared with known results. As a byproduct of this work a new useful expression for the differences in distributions of independent Poissons random variables is obtained. APPROVED FOR PUBLIC RELEASE