Physical Layer Differential Network Coding for Two-way Relay Channels

In this work, we consider differential modulation in two-way relay channels (TWRC). In single antenna systems, we propose non-coherent schemes for both amplify-and forward (AF) and decode-and-forward (DF) where the channel state information is not required. These new schemes are counterparts of the traditional non-coherent detection in point to point communications. The difficulty with differential modulation design in TWRC is that the received signal is a mixture of the signals from both source terminals. We derive maximum likelihood (ML) detectors for both AF and DF. The DF protocol can be considered as performing differential network coding at the physical layer. In addition, we propose several suboptimal alternatives including decision feedback and prediction based detectors. All these strategies work well as evidenced by simulation results. We also extend the schemes to the multiple-antenna case and provide design criterion of differential unitary space time modulation.