Nonlinear Equalization Approaches for Physical Layer Network Coding

We consider a two-way relaying system employing physical layer network coding in channels suffering from frequency-selective fading. We study decision-feedback equalization (DFE), a technique based on delayed decision-feedback sequence estimation (DDFSE), and Tomlinson-Harashima precoding (THP) approaches for mitigating the distortions introduced by the channel. For DFE, we introduce transmit filtering schemes that generate identical overall source-to-relay channel impulse responses for both source nodes, while achieving the maximum signal-to-noise ratio after equalization for the zero-forcing and the minimum mean-squared error criterion, respectively. The advocated DDFSE approach also relies on transmit filtering at the source nodes. For the THP scheme, we derive the optimal precoding filters that guarantee an intersymbol interference free source-to-relay transmission. In order to obtain a two-way relaying system, which uses the same equalization techniques in both transmission directions, we design a THP-based compromise precoding scheme for the relay-to-destination transmission. The performance of the proposed techniques is compared with that of benchmark schemes with simpler filtering/precoding, where identical overall source-to-relay channel impulse responses are enforced by straightforward but suboptimum choices for the transmit filters. Our results reveal that the developed schemes enable significant gains compared with the benchmark schemes.