Performance Analysis of Multi-Hop AF Relaying Systems with a Poisson Field of Interferers in Nakagami-m Fading Channels

In this paper, we investigate the performance of a wireless transmission system that employs amplify-and-forward (AF) relays and operates in an interference-limited environment. We consider a multi-hop network in which the co-channel interferers are scattered according to a spatial Poisson process and the desired and interfering signals at each relay and the destination experience Nakagami-m fading. Exact expressions for the average bit error probability and the average channel capacity of the considered system are obtained as single integrals that can be reliably evaluated numerically. In addition, the diversity and coding gains per hop are obtained. The novel expressions can be used to show the impact of system and interference model parameters such as the number of hops and the transmit power, path loss exponent, and spatial density of interferers, respectively, on the performance of multi-hop systems. Simulation results are further provided to demonstrate the accuracy of the analytical expressions.