  We consider the uplink of massive multipleinput multiple-output systems in a
multicell environment. Since the base station (BS) estimates the channel state
information (CSI) using the pilot signals transmitted from the users, each BS
will have imperfect CSI in practice. Assuming zero-forcing method to eliminate
the multi-user interference, we derive the exact analytical expressions for the
probability density function (PDF) of the signal-to-interference-plus-noise
ratio (SINR), the corresponding achievable rate, the outage probability, and
the symbol error rate (SER) when the BS has imperfect CSI. An upper bound of
the SER is also derived for an arbitrary number of antennas at the BS.
Moreover, we derive the upper bound of the achievable rate for the case where
the number of antennas at the BS goes to infinity, and the analysis is verified
by presenting numerical results.
