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.

This work makes the preliminary contribution of studying the asymptotic performance of a multi-user intelligent reflecting surface (IRS) assisted-multiple-input single-output (MISO) downlink system under imperfect CSI. We first extend the existing least squares (LS) ON/OFF channel estimation protocol to a multi-user system, where we derive minimum mean squared error (MMSE) estimates of all IRS-assisted channels over multiple sub-phases. We also consider a low-complexity direct estimation (DE) scheme, where the BS obtains the MMSE estimate of the overall channel in a single sub-phase. Under both protocols, the BS implements maximum ratio transmission (MRT) precoding while the IRS design is studied in the large system limit, where we derive deterministic equivalents of the signal-to-interference-plus-noise ratio (SINR) and the sum-rate. The derived asymptotic expressions, which depend only on channel statistics, reveal that under Rayleigh fading IRS-to-users channels, the IRS phase-shift values do not play a significant role in improving the sum-rate but the IRS still provides an array gain. Simulation results confirm the accuracy of the derived deterministic equivalents and show that under Rayleigh fading, the IRS gains are more significant in noise-limited scenarios. We also conclude that the DE of the overall channel yields better performance when considering large systems.