  Base stations with a large number of transmit antennas have the potential to
serve a large number of users simultaneously at higher rates. They also promise
a lower power consumption due to coherent combining at the receiver. However,
the receiver processing in the uplink relies on the channel estimates which are
known to suffer from pilot interference. In this work, we perform an uplink
large system analysis of multi-cell multi-antenna system when the receiver
employs a matched filtering with a pilot contaminated estimate. We find the
asymptotic Signal to Interference plus Noise Ratio (SINR) as the number of
antennas and number of users per base station grow large while maintaining a
fixed ratio. To do this, we make use of the similarity of the uplink received
signal in a multi-antenna system to the representation of the received signal
in CDMA systems. The asymptotic SINR expression explicitly captures the effect
of pilot contamination and that of interference averaging. This also explains
the SINR performance of receiver processing schemes at different regimes such
as instances when the number of antennas are comparable to number of users as
well as when antennas exceed greatly the number of users. Finally, we also
propose that the adaptive MMSE symbol detection scheme, which does not require
the explicit channel knowledge, can be employed for cellular systems with large
number of antennas.
