  We present the analysis of a single-carrier massive MIMO system for the
frequency selective Gaussian multi-user channel, in both uplink and downlink
directions. We develop expressions for the achievable sum rate when there is
spatial correlation among antennas at the base station. It is known that the
channel matched filter precoder (CMFP) performs the best in a spatially
uncorrelated downlink channel. However, we show that, in a spatially correlated
downlink channel with two different correlation patterns and at high long-term
average power, two other precoders have better performance. For the uplink
channel, part of the equivalent noise in the channel goes away, and
implementing two conventional equalizers leads to a better performance compared
to the channel matched filter equalizer (CMFE). These results are verified for
uniform linear and uniform planar arrays. In the latter, due to more
correlation, the performance drop with a spatially correlated channel is
larger, but the performance gain against channel matched filter precoder or
equalizer is also bigger. In highly correlated cases, the performance can be a
significant multiple of that of the channel matched filter precoder or
equalizers.}
