Physical-layer network coding with Alamouti scheme for the TWRC with linear decoder

In this paper, we consider a Rayleigh faded two-way relay channel with two antennas at each user and a single antenna at the relay. Two users adopt the Alamouti scheme to transmit BPSK modulated signals to the relay simultaneously. First, we develop eighteen types of physical-layer network codewords that can be applied in this system. To simplify the operation of the relay, we focus on two simplest types of physical-layer network codewords of the eighteen types. Then a linear decoder is proposed for the relay to detect the selected two types of network coded information of two users. We present the numerical result of the bit error probability of the proposed physical-layer network coding scheme with the linear decoder and discuss the further improvements of the decoder.