Performance analysis of RIS-Aided CF-mMIMO systems with variant conjugate beamforming under correlated Rician fading channels

In this paper, we investigate a downlink (DL) cell-free massive multiple-input multiple-output (CF-mMIMO) system equipped with reconfigurable intelligent surfaces (RISs) and explore how RISs affect the DL rate under spatially correlated Rician fading channels and variant conjugate beamforming (CB) schemes. Relying on the imperfect channel state information, tight closed-form achievable rate expressions under the enhanced CB (ECB) and normalized CB (NCB) schemes are derived, which facilitates the comprehensive analysis with respect to important system parameters, such as the numbers of RISs, access points (APs), elements per RIS, antennas per AP, user equipment, and antenna correlation. Apart from this, we formulate the design of RIS phase shifts and AP power allocation factors as an optimization problem aimed at maximizing the DL weighted sum rate (WSR). To tackle its difficulties, we decouple the original problem into two sub-problems and propose a particle swarm optimization-based phase shift optimization algorithm together with a geometric programming-based power allocation algorithm to determine numerical solutions. Simulation results indicate that ECB achieves a better DL rate than both NCB and conventional CB can achieve under various scenarios. Additionally, optimizing the RIS phase shifts is necessary and it results in a superior rate gain compared to the benchmark unoptimized scheme. Furthermore, the proposed power allocation algorithm has a fast convergence rate and can significantly improve the DL sum rates compared to the benchmark power allocation strategy.