Achievable Sum-Rate of Two-Way AF Relay Networks with Relay Adaptation

In this paper, we establish the achievable sum-rate of a half-duplex single-relay two-way amplify-and-forward network in which the relay uses channel knowledge of the two incoming links to cooperate with the two sources. Specifically, by assuming that the relay can acquire full channel knowledge and that Gaussian codebooks are used at the source nodes, the optimal power adaptation scheme at the relay that maximizes the achievable sum-rate under a long-term average power constraint is derived. While the maximization of the sum-rate is shown to be a convex optimization problem, obtaining optimal solutions are challenging. By using the Karush-Kuhn-Tucker conditions, we first show that finding the optimal relay adaptation scheme is equivalent to finding the root of a quartic polynomial. The closed-form optimal solutions are then obtained. Important insights on the proposed adaptation scheme are also presented and discussed. Numerical results reveal that the derived relay adaptation technique outperforms the conventional fixed-gain and variable-gain amplification coefficients at low signal-to-noise ratio regimes, thanks to the benefit of dynamic power allocation.