We consider a correlated multiuser (MU) massive multiple-input multiple-output (MIMO) downlink channel in which many heterogeneous users have different channel qualities (i.e., different path-losses) to a base station (BS) equipped with a large antenna array. Using the theory of extreme values of regularly varying functions, we characterize the scaling laws of the achievable sum-rate of the system, when both numbers of BS antennas and users grow large. We then prove that for a large number of users, a simple user scheduling that chooses the users with the largest instantaneous channel vector norms based on the global channel state information (CSI) can significantly improve the achievable system sum-rate. Finally, since the scheduling method needs the global CSI estimate to operate, we propose an efficient algorithm based on low-rank matrix approximation to estimate the global CSI with a moderate number of training signals. Analysis and numerical simulations show that the proposed scheme provides favourable results in terms of system sum-rate performance and computational complexity.
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