###### Abstract  
As an emerging technology, reconfigurable intelligent surface (RIS) has attracted increasing attention due to the ability to configure the wireless propagation environment. Parallel multiple-input multiple-output (MIMO) visible light communication (VLC) is suitable for some scenarios, e.g., multi-user time-division multiple access for indoor VLCs. The application of RIS in VLC is a promising trend in the future, and this paper investigates the employment of RIS in a parallel MIMO VLC system with asymptotic capacity maximization. To this end, the RIS-aided parallel MIMO VLC channel model is derived in this paper under the point source assumption, and then, as for the non-convex optimization problem, instead of searching exhaustively for the optimal solution, we propose a low-complexity near-optimal relaxing particle swarm optimization (RPSO) algorithm to optimize the RIS parameters. Meanwhile, we discover that the convex relaxation is an effective method for the optimization problems. Finally, numerical results indicate the effectiveness of the proposed design of RIS, and meanwhile, the asymptotic capacity can be improved to a great degree by adopting RIS in the parallel MIMO VLC system. visible light communication (VLC); reconfigurable intelligent surface (RIS); multiple-input multiple-output (MIMO); asymptotic capacity; optimization algorithm +
Footnote †: journal: Applied Sciences  
the fact that the modulation mode adopted in VLC popularly is intensity-modulation and direct-detection (IM/DD). The reconfigurable intelligent surface (RIS) can be considered as an efficient method to help VLC overcome the shortcoming. As an emerging technology, RIS can change the wireless propagation environment by modifying the parameters of a surface composed of synthetic meta-atoms. This promising technology has been used in RF communication to enhance the performance in recent years [9; 10; 11; 12]. Based on the character changing wireless propagation environment adaptively, combined with the shortcomings of VLC, a lot of study has been carried out on RIS in VLC to improve the communication performance of VLC systems [13; 14; 15; 16; 17; 18; 19; 20; 21]. As of writing, there is very little research on RIS-aided MIMO-VLC systems, and the work in this area with high relevance can be found in [20]. The aim of paper [20] is to minimize the mean square error (MSE) of demodulated signals at the receiver. In addition, the model in this paper is focused on the general MIMO VLC systems. In consideration of the advantages of RIS and the challenge faced by MIMO technology, combined with the research value of parallel MIMO VLC channel, this paper investigates the application of RIS in parallel MIMO VLC channel and formulate an optimization problem with asymptotic capacity maximization to configure the RIS parameters. Commonly, the parameters of RIS in RF communications refer to phase and amplitude coefficients. However, owing to the difference between RF communications and VLC, the main parameters of RIS in VLC usually are the orientation angles of mirrors in mirror array-based VLC RIS and phase information in meta surface-based VLC RIS. Furthermore, based on the work in [22], a mirror array-based VLC RIS is superior to a meta surface-based VLC RIS, and consequently, VLC RIS based on a mirror array is adopted in the remainder of the paper. The current research on VLC RIS is related to optimizing the orientations of mirrors to achieve the goal of communication performance enhancement. Motivated by the content as mentioned above, we consider the application of RIS in parallel MIMO VLC channel and propose an effective design to configure RIS. As of writing, there is no literature on the asymptotic capacity of RIS-aided parallel MIMO VLC systems. We make the first attempt and obtain a proper design of RIS in this scenario (parallel MIMO VLC). We organize the remainder of this paper in the following order: Section 2 provides the RIS-aided parallel MIMO VLC system model.