On the difference of two chi-square variates with application to outage probability computation

An expression for the cumulative distribution function evaluated at zero of the difference of two chi-square variates with different number of degrees of freedom is derived and applied to the outage probability computation of cellular mobile radio systems in fading channels. In particular, a generic result is developed for this probability which takes on several forms, the simplest of which, is a single integral with finite limits and an integrand composed of elementary (exponential and trigonometric) functions. The results are applicable to cellular systems that are subject to independent identically distributed (i.i.d.) interfering signals and that employ maximal-ratio combining reception over i.i.d. diversity paths. Various fading channel models are assumed for the desired signal and interferers. For each desired signal/interferer combination, the outage probability is expressed in closed form in terms of a set of parameters that characterize the particular scenario. A tabulation of these various scenarios and their associated parameters for channels of practical interest is included.