In this paper, the authors consider a two-way relay network system consisting of two users and multiple relays. The communication process is divided into two time slots. At the first time slot, both users send their information to the relays. The relays, at the second time slot, amplify their received signals and forward the resultant signals to both users. the authors minimize the power consumed at the relays while maintaining the average mean-square-error (MSE) of the two transmitted signals under a pre-defined threshold. Furthermore, at each relay, there is a constraint of power consumed at the relay.