Power scaling of massive MIMO systems with arbitrary-rank channel means and imperfect CSI

In this paper, we study the achievable uplink rates of massive multiple-input multiple-output (MIMO) systems using maximal-ratio combining (MRC) and zero-forcing (ZF) receivers, assuming imperfect channel state information (CSI). Unlike all previous studies, the fast fading MIMO channel matrix here is modeled to have an arbitrary-rank deterministic component as well as a Rayleigh-distributed random component. In particular, it is found that with a non-zero Ricean K-factor, the approximations and the exact uplink rates converge to the same constant value if the number of base station antennas, M, grows large, while the transmit power of each user is scaled down proportionally to 1/M. However, if the channel is Rayleigh fading, we can only cut the transmit power of each user proportionally to 1/√M. In addition, we show that with increasing Ricean K-factor, the uplink rates will converge to fixed values for both MRC and ZF receivers.