Optimal Power Minimization in Two-way Relay Network with Imperfect Channel State Information

We study a two-way amplify and forward relay network with two transceivers which communicate through a network of nr relays while there is no direct link between the two transceivers. Each relay is equipped with a single antenna for transmitting and receiving. We study the minimization of the total transmit power that is used in all of the network nodes given the condition that the transceiver which calculates the optimal transmitting power has a full knowledge about the channels between itself and the relays and the variance with zero mean of the channels between the relays and the other transceiver. The total average power is minimized subject to a soft constraint which guarantees that the outage probability is below a certain level. The optimal solution is derived in closed form and leads to a single relay selection criterion.