Optimal Tomlinson-Harashima precoding for physical layer network coding

We consider a two-way relaying system employing physical layer network coding in channels suffering from frequency-selective fading. In order to mitigate the distortions introduced by the channel, Tomlinson-Harashima precoding is applied at the source nodes. We introduce an optimal precoding scheme that provides intersymbol interference free source-to-relay transmission without requiring identical overall channel impulse responses, which is in contrast to previously proposed equalization approaches. The performance of our novel approach is compared against that of a benchmark precoding scheme, motivated by the optimal decision-feedback equalization for physical layer network coding, which creates identical overall channel impulse responses in order to be able to use identical feedback filters for precoding at both source nodes.