Physical-layer network coding with limited feedback based on decoding at relay

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 and decode-and-forward (DF) strategies of PLNC protocol and propose a practical scheme in which the partial CSI is fed back to the end nodes from relay using a limited number of feedback bits. In PDF strategy, each source node obtains full 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 DF strategy, we 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. For binary phase shift keying (BPSK) and quadrature-PSK (QPSK) modulations, tight upper bounds on the bit error probability (BEP) depending on the number of feedback bits are derived for all strategies. It is shown via computer simulations that the bit-error-rate (BER) performance of the system with full CSI at all nodes are achieved for both strategies by using a few number of feedback bits. Moreover, the computation complexity is reduced for the proposed scheme with single antenna at all nodes.