On sum-rate of two-way relay with multiple antennas using PNC

We present a suboptimal multicast strategy to facilitate the communication in the two-way relay (TWR) channel with multiple antennas using physical layer network coding (PNC). We study the sum-rate of the TWR channel and find an upper bound. Such a system enjoys the benefits of having fewer time slots due to the use of PNC and the additional spatial degree of freedom created by multiple antennas. The same number of antennas is assumed in the relay and two terminals, which makes the multicast problem much more complicated. With the assumption of channel reciprocity and the CSI at the transmitters, we design a suboptimal codebook for the multicast and a criterion for the uplink data rates selection to optimize the sum-rate. The analysis shows that the data rate achieved via this suboptimal multicast scheme is very close to the optimal multicast capacity. We also observe in the optimization process that maximizing the uplink data rates may not increase the sum-rate and instead, they should be adjusted according to the downlink data rate in order to maximize the sum-rate of the TWR channel.