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Order statistics find applications in various areas of communications andsignal processing. In this paper, we introduce an unified analytical frameworkto determine the joint statistics of partial sums of ordered random variables(RVs). With the proposed approach, we can systematically derive the jointstatistics of any partial sums of ordered statistics, in terms of the momentgenerating function (MGF) and the probability density function (PDF). OurMGF-based approach applies not only when all the K ordered RVs are involved butalso when only the Ks (Ks < K) best RVs are considered. In addition, we presentthe closed-form expressions for the exponential RV special case. These resultsapply to the performance analysis of various wireless communication systemsover fading channels.

An MGF-based Unified Framework to Determine the Joint Statistics of Partial Sums of Ordered Random Variables