Statistics of ratios of random variables arising in analysis of wireless Poisson networks

Abstract

In this paper, the author analyses statistics of some typical ratios of random variables (RVs) occuring in analysis of large-scale wireless networks with node locations modeled by Poisson point processes. In such networks, fading and path-loss effects are the most important factors affecting the signal-to-interference ratio, which, in turn, is the crucial factor affecting various performance metrics. The author obtains formulas for the probability density, cumulative distribution, and moment generating functions for ratios of RVs occurring under typical scenarios in cellular-like networks, in spectrum sharing networks, and in cooperative wireless networks. All obtained results are valid for arbitrary fading models of propagation paths.