Statistical CSI-based Optimization for Uplink RIS-Aided Cell-Free Massive MIMO Systems

We address comprehensive optimization of uplink spectral efficiency (SE) and resource allocation in multiple reconfigurable intelligent surfaces (RIS)-aided cell-free massive MIMO (CF-mMIMO) systems. While integrating CF-mMIMO with RISs enhances SE, existing solutions assume ideal conditions or separately optimize access point (AP) clustering, large-scale fading decoding (LSFD), RIS phase-shifts, and power allocation. To bridge these gaps, we propose a unified statistical channel state information (CSI)-based optimization (SCOP) framework that jointly optimizes AP clustering, LSFD, RIS phase-shift control, and uplink power allocation to maximize the minimum uplink SE. A closed-form SE expression is derived for maximum ratio (MR) combining, accounting for both direct and cascaded channels with spatially correlated Ricean fading. Leveraging statistical CSI significantly reduces real-time acquisition overhead while enabling robust and efficient uplink transmission design. SCOP is solved via a multi-step strategy: (i) for fixed power, an iterative algorithm computes joint optimization parameters (JOP) vector representing a combination of AP clustering, LSFD, and RIS phase-shift parameters; (ii) a closed-form solution updates power allocation; and (iii) an alternating optimization jointly refines both. We also introduce a novel method to extract the optimal system parameters from the JOP. Simulation results show that, in a representative 60 APs, 30 users, and 4 RISs scenario, the proposed SCOP framework lifts the median uplink SE from 2.4 bit/s/Hz to 3.9 bit/s/Hz (+65%) and more than doubles the bottom 5% rate, with similar 60-120% gains in other setups.