Limited feedback in physical-layer network coding

In physical-layer network coding (PLNC) applied to wireless communications systems where two source communicate with each other by means of a relay between them, in the lack of a direct path, it is assumed so far that all nodes have all channel state information (CSI). Whereas, a source can not know CSI between relay and the other source, without extra protocol complexity. Moreover, a training sequence is needed to learn its own channel with pilot symbols. Therefore, in this paper, for practical implementation of amplify-and-forward (AF) protocol, it is proposed to send limited number of feedback bits from relay to each source, which inform about relative channel state information of the channel between relay and the other source. In another PLNC protocol, decode-and-forward (DF), it is sufficient for each source to learn channel between relay and itself. By limited feedback, there is no need for training sequences to learn channels for sources. For both PLNC protocols mentioned above, decoding complexity is reduced in sources and for the system having single antenna at all nodes, bit error rate (BER) performance of full-CSI schemes is achieved with a few number of feedback bits.