Multi-pair amplify-and-forward relaying with very large antenna arrays

We consider a multi-pair relay channel where multiple sources simultaneously communicate with destinations using a relay. Each source or destination has only a single antenna, while the relay is equipped with a very large antenna array. We investigate the power efficiency of this system when maximum ratio combining/maximal ratio transmission (MRC/MRT) or zero-forcing (ZF) processing is used at the relay. Using a very large array, the transmit power of each source or relay (or both) can be made inversely proportional to the number of relay antennas while maintaining a given quality-of-service. At the same time, the achievable sum rate can be increased by a factor of the number of source-destination pairs. We show that when the number of antennas grows to infinity, the asymptotic achievable rates of MRC/MRT and ZF are the same if we scale the power at the sources. Depending on the large scale fading effect, MRC/MRT can outperform ZF or vice versa if we scale the power at the relay.