Achievable rates of uplink multiuser massive MIMO systems with estimated channels

We study the performance of uplink transmission in a large-scale (massive) MIMO system, where all the transmitters have single antennas and the receiver (base station) has a large number of antennas. Specifically, we first derive the rates that are possible through minimum mean-squared error (MMSE) channel estimation and three possible linear receivers: maximum ratio combining, zero-forcing, and MMSE. Based on the derived rates, we quantify the amount of energy savings that are possible through increased number of base-station antennas or increased coherence interval. We also analyze achievable degrees of freedom of such a system without assuming channel state information at the receiver, which turns out to be the same as that of a point-to-point MIMO channel. Linear receiver is sufficient when the number of users is less than the number of antennas. Otherwise, nonlinear processing is necessary to achieve the full degrees of freedom.