  In this paper, the downlink of a multi-cell massive MIMO system is considered
where the channel state information (CSI) is estimated via pilot symbols that
are orthogonal in a cell but re-used in other cells. Re-using the pilots,
however, contaminates the CSI estimate at each base station (BS) by the channel
of the users sharing the same pilot in other cells. The resulting inter-cell
interference does not vanish even when the number of BS antennas $M$ is large,
i.e., $M\rightarrow\infty$, and thus the rates achieved by treating
interference as noise (TIN) saturate even if $M\rightarrow\infty$. In this
paper, interference aware decoding schemes based on simultaneous unique
decoding (SD) and simultaneous non-unique decoding (SND) of the full
interference or a part of the interference (PD) are studied with two different
linear precoding techniques: maximum ratio transmission (MRT) and zero forcing
(ZF). The resulting rates are shown to grow unbounded as $M\rightarrow\infty$.
In addition, the rates achievable via SD/SND/PD for finite $M$ are derived
using a worst-case uncorrelated noise technique, which are shown to scale as
$\mathcal{O}(\log M)$. To compare the performance of different schemes, the
maximum symmetric rate problem is studied, where it is confirmed that with
large, yet practical, values of $M$, SND strictly outperforms TIN, and also
that PD strictly outperforms SND.
