Design of linear physical-layer network coding for MIMO two-way relay channels without transmitter CSI

In this paper, we propose a new linear physical-layer network coding scheme for spatial-multiplexing MIMO two-way relay channels (TWRCs), where the transmitters lack the channel state information (CSI). In the uplink, each user transmits independent signal streams from its multiple antennas, and the two users transmit simultaneously. The relay selects a finite-field coefficient matrix based on its receiver CSI. It then jointly computes the associated linear combinations of all messages. In the downlink, the resultant message-combinations are forwarded to the users, which recover their desired messages. We derive an asymptotic expression for the coefficient matrix used by the relay that minimizes the error probability. We show by numerical results that for Rayleigh fading channel, the proposed linear PNC scheme outperforms existing schemes by up to 4.5 dB and that the proposed scheme approaches an interference-free lower bound at a sufficiently high SNR.