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Massive multiple-input multiple-output (M-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 M-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 M-MIMO system whose cells are not synchronous to each other, while transmissions in a cell are still synchronous. We analyze an asynchronous downlink M-MIMO system in terms of the coverage probability and the ergodic rate by means of the stochastic geometry tool. For comparison, we also obtain results for the corresponding synchronous system. 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 …