On the sum of ordered random variables and its applications to physical‐layer security of communication over η‐μ fading channels with generalized selection combining

Abstract

AbstractOrder statistics have attracted the interest of the research community since they find numerous applications in several areas of communications and signal processing fields. This paper introduces an approximate yet accurate approach to determine the statistics of the sum of ordered independent but not necessarily identically distributed η‐μ random variables, which is an accurate model in a generic non–line‐of‐sight propagation environment. The proposed method is used to assess the secrecy performance of wiretap η‐μ fading channels employing generalized selection combining (GSC) diversity. We consider the case of GSC(L,2L), where L branches with the largest instantaneous signal‐to‐noise‐ratio (SNR) values, from a total of 2L available branches, are selected. By introducing a novel modified cascade combining receiver structure whose output SNR statistics closely approximate that of GSC(L,2L), a simple and accurate closed‐form approximation for the moment generating function of the GSC(L,2L) output SNR is derived. This expression is further employed to evaluate the secrecy outage probability and the secrecy capacity of a wiretap channel consisting of a single‐antenna transmitter, a multiantenna receiver, and a multiantenna eavesdropper. Using the proposed analytical approach, various numerical performance evaluation results accompanied with complementary Monte Carlo simulations are further presented. These results have shown that the proposed approach is accurate over the entire range of SNR values, thus enabling a low‐complexity computation of important performance metrics.