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We present novel general, simple, exact, and closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the ratio of the products of two independentα-μvariates, where all variates have identical values of alpha parameter. Obtained results are applied in analysis of multihop wireless communication systems in different fading transmission environments. The proposed theoretical analysis is also complemented by various graphically presented numerical results.

SUMMARYThe problem concerning short‐term fading and long‐term fading (shadowing) and their deleterious effects on wireless systems performance has been in focus for a long time. In this paper, motivated by the results of propagation measurements in land‐mobile and indoor‐mobile systems, and by the fact that gamma distribution can describe shadowing reliably, Nakagami‐m distribution is used to model the signal envelope and gamma distribution is used to model the average signal power. Receive diversity with maximal‐ratio combining and selection combining is implemented at the microlevel and macrolevel, respectively. The general case is explored, which assumes that microdiversity and macrodiversity are provided through arbitrary number of channels. Because shadowing has larger correlation distance than short‐term fading, correlated macrodiversity channels are studied. This paper investigates the dynamics of the received signal. A novel rapidly converging infinite‐series expression for average level crossing rate and average fade duration are obtained. Numerical results are graphically presented to examine the impact of fading severity, shadowing severity, number of diversity branches at the microlevel, number of base stations and correlation between base stations to the system's performance. Computer simulations are also performed to verify the validity and the accuracy of proposed theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.