Two-way relay networks optimized for Rayleigh fading channels

In this paper, we consider a three-node, two-way relay network with digital network coding over fading channels. The aim is to minimize total energy consumption for a given pair of required rates through this network. The uplink is a multiple access channel. In the downlink, we first consider orthogonal time sharing of network coded broadcasting and one way forwarding. We extend this approach to include a superposition strategy for the downlink, in which the network coded message and the remaining bits of the larger message are superimposed. This network coding superposition strategy is shown to always decrease total energy usage. We verify our findings via a series of numerical computations of the total energy consumption of the two strategies.