Uplink Performance of RIS-aided Cell-Free Massive MIMO System Over Spatially Correlated Channels

We consider a practical spatially correlated reconfigurable intelligent surface (RIS)-aided cell-free (CF) massive multiple-input-multiple-output (mMIMO) system with multi-antenna access points (APs) over spatially correlated Rician fading channels. The minimum mean square error (MMSE) channel estimator is adopted to estimate the aggregated RIS channels. Then, we investigate the uplink spectral efficiency (SE) with the maximum ratio (MR) and the local minimum mean squared error (L-MMSE) combining at the APs and obtain the closed-form expression for characterizing the performance of the former. The accuracy of our derived analytical results has been verified by extensive Monte-Carlo simulations. Our results show that increasing the number of RIS elements is always beneficial, but with diminishing returns when the number of RIS elements is sufficiently large. Furthermore, the effect of the number of AP antennas on system performance is more pronounced under a small number of RIS elements, while the spatial correlation of RIS elements imposes a more severe negative impact on the system performance than that of the AP antennas.