Two-Timescale Transmission Design for RIS-Aided Cell-Free Massive MIMO Systems

This paper investigates the performance of two-timescale transmission design for uplink reconfigurable intelligent surface (RIS)-aided cell-free massive multiple-input multiple-output (CF-mMIMO) systems. We consider the Rician channel model and design the passive beamforming of RISs based on the long-time statistical channel state information (CSI), while the maximum ratio combining (MRC) technique is utilized to design the active beamforming of base stations (BSs) based on the instantaneous overall channels, which are the superposition of the direct and RIS-reflected channels. Firstly, we derive the closed-form expressions of uplink achievable rate for arbitrary numbers of BS antennas and RIS reflecting elements. Relying on the derived expressions, we theoretically analyze the benefits of RIS-aided cell-free mMIMO systems and draw explicit insights. Then, based on closed-form expressions under statistical CSI, we maximize the sum user rate and the minimum user rate by optimizing the phase shifts of the RISs based on the genetic algorithm (GA). Finally, the numerical results demonstrate the feasibility and the benefits of deploying large-size RISs into conventional cell-free mMIMO systems. Besides, our results validate the effectiveness of the proposed two-timescale scheme in the RIS-aided cell-free mMIMO systems.