  In this paper, a new state-of-the-art multi-cell MMSE scheme is proposed for
massive MIMO networks, which includes an uplink MMSE detector and a downlink
MMSE precoder. The main novelty is that it exploits all available pilots for
interference suppression. Specifically, let $K$ and $B$ denote the number of
users per cell and the number of orthogonal pilot sequences in the network,
respectively, where $\beta = B/K$ is the pilot reuse factor. Then our
multi-cell MMSE scheme utilizes all $B$ channel directions, that can be
estimated locally at each base station, to actively suppress both intra-cell
and inter-cell interference. The proposed scheme is particularly practical and
general, since power control for the pilot and payload, imperfect channel
estimation and arbitrary pilot allocation are all accounted for. Simulations
show that significant spectral efficiency (SE) gains are obtained over the
single-cell MMSE scheme and the multi-cell ZF, particularly for large $\beta$
and/or $K$. Furthermore, large-scale approximations of the uplink and downlink
SINRs are derived, which are asymptotically tight in the large-system limit.
The approximations are easy to compute and very accurate even for small system
dimensions. Using these SINR approximations, a low-complexity power control
algorithm is also proposed to maximize the sum SE.
