  In this paper, a new multi-cell MMSE precoder is proposed for massive MIMO
systems. We consider a multi-cell network where each cell has $K$ users and $B$
orthogonal pilot sequences are available, with $B = \beta K$ and $\beta \ge 1$
being the pilot reuse factor over the network. In comparison with conventional
single-cell precoding which only uses the $K$ intra-cell channel estimates, the
proposed multi-cell MMSE precoder utilizes all $B$ channel directions that can
be estimated locally at a base station, so that the transmission is designed
spatially to suppress both parts of the inter-cell and intra-cell interference.
To evaluate the performance, a large-scale approximation of the downlink SINR
for the proposed multi-cell MMSE precoder is derived and the approximation is
tight in the large-system limit. Power control for the pilot and payload,
imperfect channel estimation and arbitrary pilot allocation are accounted for
in our precoder. Numerical results show that the proposed multi-cell MMSE
precoder achieves a significant sum spectral efficiency gain over the classical
single-cell MMSE precoder and the gain increases as $K$ or $\beta$ grows.
Compared with the recent M-ZF precoder, whose performance degrades drastically
for a large $K$, our M-MMSE can always guarantee a high and stable performance.
Moreover, the large-scale approximation is easy to compute and shown to be
accurate even for small system dimensions.
