Maximum achievable rate for AF TWRC with optimal power allocation

This paper addresses the maximum achievable rate for amplify-and-forward (AF) one-way relay channel (OWRC) and two-way relay channel (TWRC) with a total transmit power constraint. The achievable rate is maximized for both channels where the optimal power allocation is applied over all the nodes and the closed-form expressions for the maximum achievable rate are derived. It is shown that for TWRCs, the rate is maximized if half of the total power is allocated to the relay node regardless of the channel variations. Furthermore, we conclude that in the case of optimal power allocation, the achievable rate of TWRC is much greater than that of OWRC, which is however generally not true in the case of equal power allocation.