Spatial Correlation in Single-Carrier Massive MIMO Systems

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.