In this paper, the author consider a two-way relay network 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 relay. The relays, at the second time slot, amplifie their received signals and forward the resultant signals to both users. The study 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.