Maximum SNR Transmit Filtering for Decision-Feedback Equalization in Physical Layer Network Coding

We consider a two-way relaying system employing physical layer network coding (PNC) in channels suffering from frequency-selective fading. In order to mitigate the distortions introduced by the channel, decision-feedback equalization (DFE) is used at the relay node. We introduce transmit filters that generate identical overall channel impulse responses for the links from both source nodes to the relay node, while achieving the maximum signal-to-noise ratio (SNR) for zero-forcing DFE and minimum mean-squared error DFE at the relay node. The performance gain of our novel approach is compared against a benchmark filtering scheme which also creates identical channel impulse responses to enable decision-feedback equalization at the relay.