Mutual information of amplify-and-forward relaying with partial relay selection

In this paper, we provide asymptotic analysis of the mutual information (MI) of the basic two-hop amplify-and-forward (AF) channel, where the relaying node is selected out of a pool of N potential relay nodes based on instantaneous backward channel state information (CSI). The asymptotic formula obtained by implementing extreme value theory (EVT) adopts a simpler form compared to the exact MI expression, which makes it easier to operate with. Despite its simplicity, the asymptotic expression is quite accurate even with small N, which is confirmed by numerical simulation. We show that the power allocation coefficient obtained by optimizing the asymptotic expression is close to the optimal value obtained from simulation results.