  Massive multiple-input multiple-output (MIMO) is recognized as a promising
technology for the next generation of wireless networks because of its
potential to increase the spectral efficiency. In initial studies of massive
MIMO, the system has been considered to be perfectly synchronized throughout
the entire cells. However, perfect synchronization may be hard to attain in
practice. Therefore, we study a massive MIMO system whose cells are not
synchronous to each other, while transmissions in a cell are still synchronous.
We analyze an asynchronous downlink massive MIMO system in terms of the
coverage probability and the ergodic rate by means of the stochastic geometry
tool. For comparison, we also obtain the results for the synchronous systems.
In addition, we investigate the effect of the uplink power control and the
number of pilot symbols on the downlink ergodic rate, and we observe that there
is an optimal value for the number of pilot symbols maximizing the downlink
ergodic rate of a cell. Our results also indicate that, compared to the cases
with synchronous transmission, the downlink ergodic rate is more sensitive to
the uplink power control in the asynchronous mode.
