Weighted Sum-Rate Maximization for Multi-STAR-RIS-Assisted mmWave Cell-Free Networks

The cell-free network is regarded as an enabling technology for alleviating inter-cell interference due to its user-centric network paradigm. Reconfigurable intelligent surfaces (RISs) are used to assist cell-free networks in improving network capacity at a low cost. However, only half-space coverage can be achieved by RISs. With the unique capability of extending half-space coverage to full-space coverage, simultaneously transmitting and reflecting RIS (STAR-RIS) is emerged as an attractive technology. Motivated by this distinctive characteristic, multiple STAR-RISs deployed in millimeter wave (mmWave) cell-free systems to assist users in downlink transmission are investigated in this paper. Our objective is to maximize the weighted sum-rate (WSR) via joint optimization of association indicators, active beamforming vectors at mmWave base stations (MBSs) as well as transmission and reflection beamforming vectors of STAR-RISs, while the limits of STAR-RIS-user association, each MBS maximum transmit power as well as passive coefficients of STAR-RISs ought to be satisfied. To handle the non-convex problem, we develop the Lagrangian dual transform (LDT)-quadratic transform (QT)-based algorithm. To be specific, the LDT and QT are utilized for reformulating the non-convex problem as a more solvable equivalent one, afterwards, the transformed problem is decomposed into five subproblems via the alternating optimization (AO) method. Particularly, the solutions of association indicators, active beamforming vectors, and passive beamforming vectors are obtained through the linear conic relaxation (LCR)-based association scheme, the rank-one relaxation approach as well as the penalty-based norm approximation algorithm, respectively. Simulation results indicate that the proposed method can obtain better WSR performance over benchmarks. Some useful guidances are also provided for mmWave cell-free systems.