Ergodic rate analysis for massive MIMO relay systems with multi-pair users under imperfect CSI

In this paper, we consider a multi-pair relay system with massive antenna arrays deployed at a single relay. We analyze the ergodic achievable rate when MRC/MRT is utilized at relay with the consideration of imperfect channel state information (CSI). An analytical expression of the ergodic rate is derived, based on which, the asymptotic analysis and power scaling law are conducted when the number of antennas N grows large. It is shown that the ergodic rate logarithmically increases over the number of relay antennas. Moreover, the transmit power at the terminals and relay can be scaled down simultaneously maximally by 1/VN in the imperfect CSI and by 1/N in the perfect CSI with the achievable rate unchanged.