Energy Efficiency optimization for two-way relay channels

Energy efficiency (EE) is becoming increasingly important for the green communications, so this paper considers the EE optimization for the wireless two-way relay channel (TWRC) with physical network coding (PNC). Considering the unconstrained EE optimization case without power constraints at first, the framework of nested optimization is employed to obtain the optimal power allocations. After that, the optimal unconstrained solutions are extended to the constrained case. If the optimal unconstrained solutions fall within the maximum power constraints, then they are the optimal solution for the constrained case where each node has a maximum power constraint. Otherwise, we transform it into a single variable optimization problem with quasi-concave objective to drive the constrained optimal solution. Simulations are finally provided to show the effectiveness of our algorithms.