Design of dynamic active-passive beamforming for reconfigurable intelligent surfaces assisted hybrid VLC/RF communications

The hybrid visible light communication (VLC)/radio frequency (RF) communications are investigated with the aid of reconfigurable intelligent surfaces (RISs) in dynamic wireless networks, where the RIS access selection processes of VLC/RF users are updated depending on the channel quality dynamically. Specifically, a dynamic optimization problem due to the mobility of users and time-varying selection strategy is formulated. Under the constraints of the average minimum rate for VLC/RF users and the maximum transmit power constraints for VLC/RF access points (APs), the target is to minimize the average long-term power consumption, by jointly considering the active beamforming at APs and the passive beamforming at RISs. Based on the Lyapunov optimization framework and the drift-plus-penalty (DPP) algorithm, the original optimization problem is transformed into corresponding short-term problems at each frame. Furthermore, the closed form solutions with active-passive beamforming are derived using the fractional programming method based on the Lagrangian dual theory. Finally, numerical results demonstrate the convergence and effectiveness of the proposed optimization algorithm.