Utility Maximization for Two-Way AF Relaying Under Rate Outage Constraints

In this paper, we focus on maximizing the system utility (e.g., the weighted sum-rate, weighted geometric mean rate, and the harmonic mean rate) of a two-way relay network (TWRN) from the outage probability perspective; a TWRN has multiple relay nodes and two terminal nodes. We assume amplify-and-forward relaying with analog network coding protocol and half-duplex transmission with perfect channel state information at the receiver ends and channel distribution information at the transmitter ends. We derive the approximated closed-form for the outage probability of a TWRN; however, the approximated outage constraints lead to a non-convex structure for the considered problem. Based on the successive convex approximation technique, we obtain near optimal solution for the non-convex problem. Moreover, we derive closed-form solutions for the maximization problem for the weighted sum rate maximization problem for a TWRN with a single relay node and two relay nodes under individual power constraints. Our simulation results demonstrate the accuracy of our outage probability approximation model and the advantages of our algorithm over naive methods of full and uniform power allocation.