Outage probability of multiuser relay networks in Nakagami-m fading channels

We evaluate the performance of downlink multiuser relay networks (MRNs) equipped with a single amplify-and-forward (AaF) relay. A thorough and exact analysis is conducted to analyze the outage probability of MRNs under dissimilar Nakagami-$m$ fading conditions. More specifically, we derive new closed-form expressions for the outage probability and the probability density function (pdf) of the highest end-to-end signal-to-noise ratio (SNR) associated with the strongest destination with the single user and Rayleigh fading as special cases. In particular, we provide new results for channel-state information (CSI)-based-gain relaying and fixed-gain relaying. We then demonstrate that the achievable diversity order is equal to either the first-hop fading parameter or the product of the second-hop fading parameter and the number of destinations. Furthermore, we derive compact closed-form expressions for the moments of the highest end-to-end SNR, from which other moment-based measures such as the average SNR and the amount of fading are deduced. Our results highlight the performance improvements offered by opportunistic scheduling and reveal the impact of the relay location with unbalanced hops on the overall performance. Various numerical examples illustrate the proposed analysis.