Cooperative communication is regarded as a promising technique for improving the reliability of wireless communication links and enhancing the radio coverage simultaneously. Unlike the conventional half-duplex(HD) mode relaying techniques,the full-duplex based two-way relaying(FD-TWR) enables data exchanges between two nodes to be completed within a single time-slot,thus resulting in a significant improvement in the spectrum efficiency. In this paper,the channel model of the FD-TWR is first given out,followed by deriving the critical performance metrics,including the received signal-to-interference-plus-noise ratio(SINR),the upper bound of the ergodic capacity and the closedform solution of the proposed FD-TWR under amplify-and-forward(AF) mode. Furthermore,taking the limit of sum-transmit-power into account,we formulate the objective function of the optimal power allocation of FD-TWR as an extreme-value problem by deriving the optimal transmit power for both the source nodes and the relay node. As long as the self-interference(SI) signal in the FD-TWR nodes can be sufficiently suppressed,the proposed scheme is shown to outperform the conventional HD mode in terms of both the ergodic capacity and the outage probability. In addition,regardless of the practical SI power,the proposedFD-TWR is always capable of achieving its best performance with an aid of the proposed optimal power allocation scheme. Cooperative communication is viewed as a promising technique for improving the reliability of wireless communication links and enhancing the radio coverage simultaneously. Unlike the conventional half-duplex (HD) mode relaying techniques, the full-duplex based two-way relaying (FD- TWR) enables data exchanges between two nodes to be completed within a single time-slot, thereby resulting in a significant improvement in the spectrum efficiency. In this paper, the channel model of the FD-TWR is first given out, followed by deriving the critical performance metrics, including the received signal-to-interference-plus-noise ratio (SINR), the upper bound of the ergodic capacity and the closed form solution of the proposed FD-TWR under amplify- and-forward (AF) mode. the limit of sum-transmit-power into account, we formulate the objective function of the optimal power allocation of FD-TWR as an extreme-value problem by deriving the optimal transmit power for both the source nodes and the r As long as the self-interference (SI) signal in the FD-TWR nodes can be suppressed suppressed, the proposed scheme is shown in outperform the conventional HD mode in terms of both the ergodic capacity and the outage probability. , regardless of the practical SI power, the proposedFD-TWR is always capable of achieving its best performance with an aid of the proposed optimal power allocation scheme.