Performance Analysis of AF Relays with Maximal Ratio Combining in Nakagami-m Fading Environments

This paper investigates the maximal ratio combining (MRC) performance of an amplify and forward (AF) relay system in Nakagami-m fading environments. The study considers a general scenario with distinct m fading parameters for the following three links, source to relay link, and source to destination link and relay to destination link. We derive new closed form expressions for the statistics of important performance metrics, including the moment generating function, outage probability, higher order moments of equivalent signal to noise ratio (SNR), ergodic capacity, and average symbol error probability (SEP) of common modulation types. In particular, we focus on analytical SEP expressions in the context of an additive white generalized Gaussian noise (AWGGN). As an active area of research, generalized noise receives much attention for its flexible model. However, analytical performance of modulation scheme in generalized noise type has not been found in open literature for AF relaying with MRC despite its practical usefulness. Without the help of analytical solutions, the SEP in generalized noise can only be obtained by a large number of repeated simulation experiments. Therefore, we present the general SEP expression by using special Fox's H function. Simulation results verify the accuracy of our theoretical analysis and show that the diversity order of MRC criterion linearly depends upon Nakagami parameters of three links.