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We present the analysis of a single-carrier massive MIMO system for thefrequency selective Gaussian multi-user channel, in both uplink and downlinkdirections. We develop expressions for the achievable sum rate when there isspatial correlation among antennas at the base station. It is known that thechannel matched filter precoder (CMFP) performs the best in a spatiallyuncorrelated downlink channel. However, we show that, in a spatially correlateddownlink channel with two different correlation patterns and at high long-termaverage power, two other precoders have better performance. For the uplinkchannel, part of the equivalent noise in the channel goes away, andimplementing two conventional equalizers leads to a better performance comparedto the channel matched filter equalizer (CMFE). These results are verified foruniform linear and uniform planar arrays. In the latter, due to morecorrelation, the performance drop with a spatially correlated channel islarger, but the performance gain against channel matched filter precoder orequalizer is also bigger. In highly correlated cases, the performance can be asignificant multiple of that of the channel matched filter precoder orequalizers.}

The Effect of Spatial Correlation on the Performance of Uplink and Downlink Single-Carrier Massive MIMO Systems