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Outage probability of outdated relay selection in two-way relay network

In this paper, we consider a two-way relay network (TWRN) consisting of two sources and N amplify-and-forward (AF) relays (N ≥ 1), among which the best relay is chosen to assist the data communication. In a time-varying fading channel, the relay selection may be based on the outdated channel state information (CSI). We study the impact of outdated relay selection on the system performance by deriving a tight lower bound for the outage probability in Rayleigh block-fading channels. We further provide an asymptotic analysis in high signal-to-noise ratio (SNR) region. From the asymptotic results, we can find that the system diversity order degenerates into unity as long as the CSI is outdated. Numerical results demonstrate the tightness of the performance bounds as well as the effects of outdated relay selection on the system performance. Simulation results are also provided to corroborate the theoretical analysis.