  In this paper, we analyze the performance of the uplink communication of
massive multi-cell multiple-input multiple-output (MIMO) systems under the
effects of pilot contamination and delayed channels because of terminal
mobility. The base stations (BSs) estimate the channels through the uplink
training, and then use zero-forcing processing to decode the transmit signals
from the users. The probability density function (PDF) of the
signal-to-interference-plus-noise ratio is derived for any finite number of
antennas. From this PDF, we derive an achievable ergodic rate with a finite
number of BS antennas in closed form. Insights of the impact of the Doppler
shift (due to terminal mobility) at the low signal-to-noise ratio regimes are
exposed. In addition, the effects on the outage probability are investigated.
Furthermore, the power scaling law and the asymptotic performance result by
infinitely increasing the numbers of antennas and terminals (while their ratio
is fixed) are provided. The numerical results demonstrate the performance loss
for various Doppler shifts. Among the interesting observations revealed is that
massive MIMO is favorable even in channel aging conditions.
