Lattice network coding in multiple-antenna two-way relay channels

In this paper, lattice network coding (LNC) is studied in the multiple-antenna (MA) two-way relay channel (TWRC), where each user has a single antenna and the relay has multiple antennas. We propose two relay computation schemes for the MA TWRC with nested lattice codes, namely the receive antenna selection (RAS) scheme and the receive antenna combining (RAC) scheme. In the RAS scheme, the relay calculates the computation rates of all the relay antennas with different channel conditions and then selects a single antenna with the highest computation rate to recover a linear combination of transmitted messages. In the RAC scheme, the signals from all the relay antennas are combined with a scaling factor vector, from which a linear combination of the transmitted messages is recovered. We derive the achievable rate and analyze the error performance of the two scheme. The simulation result shows that the RAC scheme outperforms the RAS scheme significantly.