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 integran d composed of elementary (exponential and trigonometric) functions. The res ults are applicable to cellular systems that are subject to independent ide ntically distributed (i.i.d.) interfering signals and that employ maximal-r atio combining reception over i.i.d. diversity paths. Various fading channe l models are assumed for the desired signal and interferers. For each desir ed signal/interferer combination, the outage probability is expressed in cl osed form in terms of a set of parameters that characterize the particular scenario. A tabulation of these various scenarios and their associated para meters for channels of practical interest is included.