A Novel SROCR-Based Passive Beamforming for STAR-RIS-Aided Cell-Free Massive MIMO Systems

In this study, we consider a more general scenario involving multiple simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) in cell-free massive multiple-input multiple-output (CF-mMIMO) systems. Our objective is to maximize the weighted sum rate for users by decoupling the original problem into two components: the active beamforming design at the access points (APs) and the passive beamforming design at the STAR-RIS. We employ fractional programming to optimize these components alternately. The rank-one constraint in the passive beamforming design, which is proven to be an NP-hard problem, represents the primary challenge. To address this issue, we introduce a novel low-complexity algorithm based on sequential rank-one constraint relaxation (SROCR). Instead of entirely eliminating the rank-one constraint, our SROCR algorithm utilizes a progressive relaxation approach to gradually ease the constraint and identify a generic rank-one suboptimal feasible solution, ultimately converging to a solution that satisfies the rank-one condition. Numerical results demonstrate that our algorithm achieves comparable performance to existing algorithms while significantly reducing complexity, thus outperforming other baseline algorithms.