Outage Probability of N-th Best User Selection in Multiuser Two-Way Relay Networks over Nakagami-m Fading

We analyze the outage probability of the multiuser two-way relay network (TWRN) where the N-th best mobile user (MU) out of M MUs and the base station (BS) exchange messages with the aid of an amplify-and-forward relay. In the analysis, we focus on the practical unbalanced Nakagami-m fading between the MUs-relay link and the relay-BS link. We also consider both perfect and outdated channel state information (CSI) between the MUs and the relay. We first derive tight closed-form lower bounds on the outage probability. We then derive compact expressions for the asymptotic outage probability to explicitly characterize the network performance in the high signal-to-noise ratio regime. Based on our asymptotic results, we demonstrate that the diversity order is determined by both Nakagami-m fading parameters, M, and N when perfect CSI is available. When outdated CSI is available, the diversity order is determined by Nakagami-m fading parameters only. In addition, we quantify the contributions of M, N, and the outdated CSI to the outage probability via the array gain.