Reconfigurable intelligent surfaces (RISs) have been proposed as a promising technology for future wireless communication systems to achieve both high spectral and energy efficiency. In this paper, we investigate a RIS-assisted downlink multi-cell communication system, where the RIS is deployed at the cell edges to serve the users in blind spots, with only statistical channel state information (CSI) being available. Under these assumptions, we investigate the optimization of beamforming at the BSs and phase shift at the RIS to maximize the approximated ergodic weighted sum spectral efficiency (WSSE). The complex circle manifold based algorithm is proposed to obtain the sub-optimal phase shift matrix while the statistical maximum ratio transmission (MRT) is applied to design the sub-optimal beamforming vectors. Our simulation results show that the approximate ergodic spectral efficiency expression is very close to the exact Monte-Carlo simulation, whilst the robustness of the ergodic WSSE is verified.

multi-cell; statistical CSI; weighted sum spectral efficiency maximization; RIS