First and Second Order Characteristics of a Wireless Three-hop Relay Channel with the Presence of Rayleigh Fading

In this paper, a wireless three-hop relay communication system operating in a Rayleigh multipath fading environment is analyzed. The output signal from such a system is a product of signal envelopes from all sections, meaning that it is actually a product of three random variables (RVs) with Rayleigh distribution. We considered here the first-order characteristics: probability density function (PDF), cumulative distribution function and outage probability (OP). Then, the moments and amount of fading (AoF) were derived in the closed forms. The second order characteristics we present include the following: level crossing rate (LCR) and average fade duration (AFD). A few graphs are given to show the impact of the specific parameters of the wireless three-hop relay system.