Exact capture probability analysis of GSC receivers over i.n.d. Rayleigh fading channels

A closed-form expression of the capture probability of generalized selection combining (GSC) RAKE receivers was introduced in [1]. The idea behind this new performance metric is to quantify how the remaining set of uncombined paths affects the overall performance both in terms of loss in power and increase in interference levels. In this previous work, the assumption was made that the fading is both independent and identically distributed from path to path. However, the average strength of each path is different in reality. In order to derive a closed-form expression of the capture probability over independent and non-identically distributed (i.n.d.) fading channels, we need to derive the joint statistics of ordered non-identical exponential variates. With this motivation in mind, we first provide in this paper some new order statistics results in terms of both moment generating function (MGF) and probability density function (PDF) expressions under an i.n.d. assumption and then derive a new exact closed-form expression for the capture probability GSC RAKE receivers in this more realistic scenario.