The Distribution of Minimum of Ratios of Two Random Variables and Its Application in Analysis of Multi-hop Systems

Abstract

The distributions of random variables are of interest in many areas of science. In this paper, ascertaining on the importance of multi-hop transmission in contemporary wireless communications systems operating over fading channels in the presence of cochannel interference, the probability density functions (PDFs) of minimum of arbitrary number of ratios of Rayleigh, Rician, Nakagami-m, Weibull and α-µ random variables are derived. These expressions can be used to study the outage probability as an important multi-hop system performance measure. Various numerical results complement the proposed mathematical analysis.

Keywords

• Fading
• ratios of random variables
• Rayleigh distribution
• Rician distribution
• Nakagami-m distribution
• Weibull distribution
• α-µ distribution
• multi-hop technique