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Power allocation (PA) is an efficient approach to enhance the system performance of an analog network coding (ANC)-based two-way relay channel (A-TWRC). In previous works, optimal PAs, in the sense of minimizing the outage probability and maximizing the achievable sum rate for A-TWRCs, were studied, respectively. In this paper, by virtue of the Lagrange method, we theoretically prove that optimal PA problems in the sense of minimizing the outage probability and maximizing the achievable sum rate are equivalent to each other. Meanwhile, a unified optimal PA scheme for A-TWRCs is proposed. We show that some previous optimal PA schemes are special cases of the proposed unified scheme under certain conditions. Simulation results show that the proposed unified PA scheme obtains the optimal outage probability and achievable sum-rate performance, whereas previous works approach the proposed unified PA scheme on either outage or achievable sum-rate performance. [ABSTRACT FROM PUBLISHER]