Max-Min Fairness Power Allocation in Uplink RIS-Aided Cell-Free Massive MIMO

This paper evaluates the uplink spectral efficiency (SE) achieved by a reconfigurable intelligent surface (RIS)-aided cell-free massive MIMO system with max-min fairness (MMF) power allocation. We provide an exact closed-form expression for an achievable SE expression which assumes maximum ratio receive combining at the access points (APs) and centralized large-scale fading decoding at the central processing unit. The derived SE expression also accounts for imperfect channel estimation and spatially correlated Ricean fading channels for both direct (APs-users) and cascaded (APs-RISs-users) links. Alongside this, we provide a generalized SE expression and evaluate the performance achieved by local partial minimum mean-squared error combining. Finally, we optimally solve the RIS phase-shift selection problem in order to maximize the aggregate channel gains, and derive a closed-form solution to the MMF power allocation problem. Simulation results validate the effectiveness of the proposed framework in enhancing the unlink SE with resnect to various benchmarks.