Optimal power allocation for two-way relaying over OFDM using physical-layer network coding

In this paper, a network scenario of two-way relaying over orthogonal frequency division multiplexing （OFDM） is considered, in which two nodes intend to exchange the information via a relay using physical-layer network coding （PLNC）. Assuming that the full channel knowledge is available, an optimization problem, which maximizes the achievable sum rate under a sum-power constraint, is investigated. It is shown that the optimization problem is non-convex, which is difficult to find the global optimum solution in terms of the computational complexity. In consequence, a low-complexity optimal power allocation scheme is proposed for practice implementation. A link capacity diagram is first employed for power allocation on each subcarrier. Subsequently, an equivalent relaxed optimization problem and Karush-Kuhn-Tucker （KKT） conditions are developed for power allocation among each subcarrier. Simulation results demonstrate that the substantial capacity gains are achieved by implementing the proposed schemes efficiently with a low-complexity computational effort.