  A massive MIMO system entails a large number (tens or hundreds) of base
station antennas serving a much smaller number of terminals. These systems
demonstrate large gains in spectral and energy efficiency compared with
conventional MIMO technology. As the number of antennas grows, the performance
of a massive MIMO system gets limited by the interference caused by pilot
contamination. Earlier A. Ashikhmin and T. Marzetta proposed (under the name of
Pilot Contamination Precoding) Large Scale Fading Precoding (LSFP) and Decoding
(LSFD) based on limited cooperation between base stations. They showed that
Zero-Forcing LSFP and LSFD eliminate pilot contamination entirely and lead to
an infinite throughput as the number of antennas grows.
  In this paper, we focus on the uplink and show that even in the case of a
finite number of base station antennas, LSFD yields a very large performance
gain. In particular, one of our algorithms gives a more than 140 fold increase
in the 5% outage data transmission rate! We show that the performance can be
improved further by optimizing the transmission powers of the users. Finally,
we present decentralized LSFD that requires limited cooperation only between
neighboring cells.
