We consider the uplink of a multicell multiuser single-input multiple-output system where the channel experiences both small and large-scale fading. The data detection is done by using the linear zero-forcing technique, assuming the base station (BS) has perfect channel state information of all users in its cell. We derive  new, exact analytical expressions for the uplink rate, symbol error rate, and outage probability per user, as well as alower bound on the achievable rate. This bound is very tight and becomes exact in the large-number-of-antennas limit. We further study the asymptotic system performance in the regimes of high signal-to-noise ratio (SNR), large number of antennas, and large number of users per cell. We show that at high SNRs, the system is interference-limited and hence, we cannot improve the system performance by increasing the transmit power of each user. Instead, by increasing the number of BS antennas, the effects of interference and noise can be reduced, thereby improving the system performance. We demonstrate that, with very large antenna arrays at the BS, the transmit power of each user can be made inversely proportional to the number of BS antennas while maintaining a desired quality-of-service. Numerical results are presented to verify our analysis.