Maximum SNR transmit filtering for linear 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, a linear equalizer is used at the relay node. We introduce transmit filters that generate identical overall channel impulse responses for both source nodes, while achieving the maximum signal-to-noise ratio (SNR) for linear zero-forcing (ZF) and minimum mean-squared error (MMSE) equalization 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 linear equalization at the relay.