Performance Analysis and Scaling Law of MRC/MRT Relaying With CSI Error in Multi-Pair Massive MIMO Systems

This paper provides a comprehensive scaling law and performance analysis for multi-user massive multiple-input-multiple-output (MIMO) relay networks, where the relay is equipped with a massive antenna array and uses maximal-ratio combining/maximal-ratio transmission (MRC/MRT) for low-complexity processing. Imperfect channel state information (CSI) is considered for both source-relay and relay-destination channels. First, a sum-rate lower bound is derived, which manifests the effect of system parameters, including the numbers of relay antennas and users, the CSI quality, and the transmit powers of the sources and the relay. Via a general scaling model on the parameters with respect to the relay antenna number, the asymptotic scaling law of the signal-to-interference-plus-noise-ratio (SINR) is obtained, which shows quantitatively the tradeoff of the network parameters. In addition, a sufficient condition on the parameter scalings for the SINR to be asymptotically deterministic is given, which covers existing results on such analysis as special cases. Then, the scenario where the SINR increases linearly with the relay antenna number is studied. The sufficient and necessary condition on the parameter scaling for this scenario is proved. It is shown that in this case, the interference power is not asymptotically deterministic, and then, the average bit error rate is analyzed.