Power sum optimization in two-way amplify and forward relaying

This paper considers a two-way amplify-and-forward (AF) relay network. Two source nodes exchange messages during two time slots via a half-duplex relay node. We aim to minimize system total power by constraining source nodes´ received signal-to-noise ratios (SNR), thus, satisfying the minimum quality of service (QoS). By solving the optimization problem composed for this case, closed form expressions of source and relay node powers are obtained. Furthermore the variation of optimum power allocation versus some parameters which gives information about the channel qualities and the bounds on the SNR received at source nodes is investigated. Numerical results show that optimal power scheme reduces the total power consumption significantly compared to the equal power scheme.