Two-way OFDM-based Nonlinear Amplify-and-Forward Relaying: Power Allocation

We consider the problem of allocating power among the nodes of a two-way amplify-and-forward OFDM-based relay network employing physical layer network coding. Because of the large peak-to-average power ratios that occur at the relay of such systems, we deem it important to understand the negative effects that nonlinear transmissions might have at the relay. Thus, we assume that the relay is subject to its own independent transmit power constraint, beyond which nonlinear distortion is introduced. We consider two power allocation problems: 1) the transmit power budget of the communicating nodes is independent of the relay's transmit power, 2) the relay's transmit power is included within the total power budget of the network. For the former, a closed form solution is obtained. For the latter, the problem is shown to be non-convex in its standard form. By applying a substitution, we show that it can be converted into a convex problem. Numerical results are provided to demonstrate the efficacy of our methods. Finally, a discussion is included to give further insight into how our power allocation scheme behaves as a function of the network's asynunetry.