  In this paper, a new multi-cell MMSE detector is proposed for massive MIMO
systems. Let $K$ and $B$ denote the number of users in each cell and the number
of available pilot sequences in the network, respectively, with $B = \beta K$,
where $\beta \ge 1 $ is called the pilot reuse factor. The novelty of the
multi-cell MMSE detector is that it utilizes all $B$ channel directions that
can be estimated locally at a base station, so that intra-cell interference,
parts of the inter-cell interference and the noise can all be actively
suppressed, while conventional detectors only use the $K$ intra-cell channels.
Furthermore, in the large-system limit, a deterministic equivalent expression
of the uplink SINR for the proposed multi-cell MMSE is derived. The expression
is easy to compute and accounts for power control for the pilot and payload,
imperfect channel estimation and arbitrary pilot allocation. Numerical results
show that significant sum spectral efficiency gains can be obtained by the
multi-cell MMSE over the conventional single-cell MMSE and the recent
multi-cell ZF, and the gains become more significant as $\beta$ and/or $K$
increases. Furthermore, the deterministic equivalent is shown to be very
accurate even for relatively small system dimensions.
