Linear Vector Physical-Layer Network Coding for MIMO Two-Way Relay Channels: Design and Performance Analysis

In this paper, we propose a new linear vector physical-layer network coding (NC) scheme for spatial multiplexing multiple-input multiple-output (MIMO) two-way relay channel (TWRC) where the channel state information (CSI) is not available at the transmitters. In this scheme, each user transmits M independent quadrature amplitude modulation signal streams respectively from its M antennas to the relay. Based on the receiver-side CSI, the relay determines a NC generator matrix for linear vector network coding, and reconstructs the associated M linear combinations of all messages. We present an explicit solution for the generator matrix that minimizes the error probability at a high SNR, as well as an efficient algorithm to find the optimized solution. We propose a novel typical error event analysis that exploits a new characterization of the deep fade events for the TWRC. We derive a new closed-form expression for the average error probability of the proposed scheme over a Rayleigh fading MIMO TWRC. Our analysis shows that the proposed scheme achieves the optimal error rate performance at a high SNR. Numerical results show that the proposed scheme significantly outperforms existing schemes, and match well with our analytical results.