Enhancing Spectral Efficiency: The Impact of RIS Elements Association on Multi-User Cell-Free Wireless Networks

This paper proposes a hybrid mathematical method to optimize the association of reconfigurable intelligent surface (RIS) elements in cell-free wireless communication networks (CFWCN) assisted by multiple RISs, achieving maximum sum spectral efficiency (SSE). In the proposed approach the RIS elements are associated jointly with both access points (APs) and users equipment (UEs), addressing a previously unexplored aspect of RIS integration. Our proposed method incorporates the joint optimization of digital beamforming at the AP, analog beamforming at the RIS, association of RIS elements to UEs, and association of RIS elements to APs. It addresses the challenge of a mixed-integer non-convex problem through a combination of fractional programming (FP) and simulated annealing (SA) techniques. In this work, we also compare, for the first time, the performance of three elements association modes: association only with APs, association only with UEs, and joint association with both APs and UEs. Additionally, we investigate the impact of non-selective elements interference (NSEI) on RIS elements associations with both APs and UEs. We then expand our model to a more realistic one, incorporating spatial correlations both between AP antennas and among RIS elements. Simulation results show that our hybrid association approach outperforms the conventional methods for different channel models. Key findings include a 42% improvement in SSE when UEs are close to RISs. This enhancement is due to narrower beamformings achieved through optimized element categorization. The analysis reveals that optimal RIS element association with distant entities (APs or UEs) yields near-optimal performance.