Partial-decode-and-forward strategy with limited feedback for two way relay channels

In two-way relay channels (TWRC), consisted of one relay and two end nodes, it is generally assumed that all nodes have full channel state information (CSI) about the two links. However, one end node can not obtain the CSI of the link between relay and the other end node, without extra protocol complexity. Therefore, it is difficult to implement the strategies such as partial-decode-and-forward (PDF) in physical-layer network coding (PLNC) which is the most spectrally efficient protocol for TWRC. In this paper, we introduce the limited feedback technique into the PDF strategy in PLNC protocol and propose a practical scheme in which the differential phase information between two channels is fed back to the end nodes from relay using a limited number of feedback bits. For binary phase shift keying (BPSK) modulation, tight upper bounds on the bit error probability (BEP) depending on the number of feedback bits are derived. It is shown via computer simulations that the bit-error-rate performance of the system with full CSI at all nodes is achieved using a few number of feedback bits.