On MIMO Linear Physical-Layer Network Coding: Full-Rate Full-Diversity Design and Optimization

This paper considers a multiuser communication network, where a receiver is set to compute functions of the messages from K users. All user nodes and the receiver are equipped with multi-antenna. We propose a space-time (ST) coded multiple-input multiple-output (MIMO) linear physical-layer network coding (LPNC) scheme that promises full-rate and full-diversity, while achieving the maximum coding gain of LPNC. In the proposed framework, the users' messages are encoded by the same linear dispersion ST code and transmitted simultaneously. The receiver exploits the MIMO LPNC mapping in reconstructing an arbitrary number of linearly network-coded (NC) messages. We derive the NC generator matrix that leads to the greatest coding gain and minimized error probability at the receiver. On top of that, we analytically show that the proposed ST coded LPNC scheme guarantees the full-diversity and full-rate transmission. The proposed method applies to a wide range of network configurations. Two case studies on: (1) MIMO two-way relay network and (2) MIMO multiple-access relay network are presented in this paper. For both case studies, numerical results are shown to demonstrate the performance improvement of the proposed scheme over conventional schemes by more than 4 dB, while the full-rate and full-diversity behaviors are in line with our analysis.