  A wireless massive MIMO system entails a large number (tens or hundreds) of
base station antennas serving a much smaller number of users, with large gains
in spectral-efficiency and energy-efficiency compared with conventional MIMO
technology. Until recently it was believed that in multi-cellular massive MIMO
system, even in the asymptotic regime, as the number of service antennas tends
to infinity, the performance is limited by directed inter-cellular
interference. This interference results from unavoidable re-use of reverse-link
training sequences (pilot contamination) by users in different cells.
  We devise a new concept that leads to the effective elimination of inter-cell
interference in massive MIMO systems. This is achieved by outer multi-cellular
precoding, which we call Large-Scale Fading Precoding (LSFP). The main idea of
LSFP is that each base station linearly combines messages aimed to users from
different cells that re-use the same training sequence. Crucially, the
combining coefficients depend only on the slow-fading coefficients between the
users and the base stations. Each base station independently transmits its
LSFP-combined symbols using conventional linear precoding that is based on
estimated fast-fading coefficients. Further, we derive estimates for downlink
and uplink SINRs and capacity lower bounds for the case of massive MIMO systems
with LSFP and a finite number of base station antennas.
