Performance of Multi-RIS-aided Cell-Free Massive MIMO: Do More RISs Always Help?

Cell free (CF) massive multiple-input multiple-output (mMIMO) is a promising technology in realizing beyond fifth generation (B5G) networks. Massive deployment of access points (APs) in a CF-mMIMO system increases the spectral efficiency, however it also increases the energy consumption and fronthaul requirements. Since recently reconfigurable intelligent surface (RIS) is shown to be a cost-effective solution to improve performance of wireless networks, RIS can be a promising technology to enhance the performance of CF-mMIMO systems. In this work, we study the downlink (DL) performance of CF-mMIMO system aided by multiple RISs, while considering correlated Rician fading channels, discrete RIS phase-shifts and low-complexity channel estimation (CE) protocol. Given the obtained imperfect channel state information (CSI), we derive lower bounds on the rates achieved using conjugate beamforming (CB) and zero-forcing (ZF) precoders. The obtained bounds depend on channel statistics, RIS phase-shifts and number of RIS elements. To optimize the performance with respect to RIS phase-shifts, we formulate a maximization problem and propose a sub-optimal genetic algorithm (GA)-based solution. Through simulations, we demonstrate that distributed RIS deployment outperforms centralized RIS deployment in terms of DL throughput. Interestingly, we demonstrate that the DL throughput improves as number of RISs increases until an optimal number of distributed RISs over which the DL performance of the system starts to drop. We discuss this effect under varying the number of APs and RISs. We extend the analysis by considering different precoders, CE and RIS optimization schemes, and verify the accuracy of our derived analytical results by Monte-Carlo simulations.