Spectral efficiency of the multipair two-way relay channel with massive arrays

We consider a multipair two-way relay channel where multiple communication pairs share the same time-frequency resource and a common relay node. We assume that all users have a single antenna, while the relay node is equipped with a very large antenna array. We consider two transmission schemes: (I) separate-training zero-forcing (ZF) and (II) a new proposed coupled-training ZF. For both schemes, the channels are estimated at the relay by using training sequences, assuming time-division duplex operation. The relay processes the received signals using ZF. With the separate-training ZF, the channels from all users are estimated separately. By contrast, with the coupledtraining ZF, the relay estimates the sum of the channels from two users of a given communication pair. This reduces the amount of resources spent in the training phase. Self-interference reduction is also proposed for these schemes. When the number of relay antennas grows large, the effects of interpair interference and self-interference can be neglected. The transmit power of each user and of the relay can be made inversely proportional to the square root of the number of relay antennas while maintaining a given quality-of-service. We derive a lower bound on the capacity which enables us to evaluate the spectral efficiency. The coupled-training ZF scheme is preferable for the high-mobility environment, while the separate-training ZF scheme is preferable for the low-mobility environment.