  This work provides a comprehensive scaling law based performance analysis for
multi-cell multi-user massive multiple-input-multiple-output (MIMO) downlink
systems. Imperfect channel state information (CSI), pilot contamination, and
channel spatial correlation are all considered. First, a sum- rate lower bound
is derived by exploiting the asymptotically deterministic property of the
received signal power, while keeping the random nature of other components in
the signal-to-interference-plus-noise-ratio (SINR) intact. Via a general
scaling model on important network parameters, including the number of users,
the channel training energy and the data transmission power, with respect to
the number of base station antennas, the asymptotic scaling law of the
effective SINR is obtained, which reveals quantitatively the tradeoff of the
network parameters. More importantly, pilot contamination and pilot
contamination elimination (PCE) are considered in the analytical framework. In
addition, the applicability of the derived asymptotic scaling law in practical
systems with large but finite antenna numbers are discussed. Finally,
sufficient conditions on the parameter scalings for the SINR to be
asymptotically deterministic in the sense of mean square convergence are
provided, which covers existing results on such analysis as special cases and
shows the effect of PCE explicitly.
