Physical-layer network coding with limited feedback in two-way relay channels

In this study, the authors introduce the limited feedback technique into the physical-layer network coding which is the most spectrally efficient protocol for two-way relay channels, consisting of one relay and two end (source) nodes. In amplify-and-forward strategy, each source node obtains full channel state information (CSI) of the channel between relay and itself from training sequences and partial CSI of the channel between relay and the other node by means of a limited number of feedback bits provided by the relay. In the decode-and-forward strategy, the authors completely remove training sequences and the source nodes provide the partial CSI of the link between relay and themselves from limited feedback bits, the CSI of the other link being useless for this strategy. Tight upper bounds on the bit error probability depending on the number of feedback bits are derived for binary phase shift keying (PSK) and quadrature-PSK modulations for both strategies. It is shown via computer simulations that the bit-error-rate performance of the system with full CSI at all nodes is achieved for both strategies by using a few number of feedback bits. Moreover, the computation complexity is reduced for the proposed scheme with a single antenna at all nodes.