Multi-hop Multi-RIS Wireless Communication Systems: Multi-reflection Path Scheduling and Beamforming

Reconfigurable intelligent surface (RIS) provides a promising way to proactively augment propagation environments for better transmission performance in wireless communications. Existing multi-RIS works mainly focus on link-level optimization with predetermined transmission paths, which cannot be directly extended to system-level management, since they neither consider the interference caused by undesired scattering of RISs, nor the performance balancing between different transmission paths. To address this, we study an innovative multi-hop multi-RIS communication system, where a base station (BS) transmits information to a set of distributed users over multi-RIS configuration space in a multi-hop manner. The signals for each user are subsequently reflected by the selected RISs via multi-reflection line-of-sight (LoS) links. To ensure that all users have fair access to the system to avoid excessive number of RISs serving one user, we aim to find the optimal beam reflecting path for each user, while judiciously determining the path scheduling strategies with the corresponding beamforming design to ensure the fairness. Due to the presence of interference caused by undesired scattering of RISs, it is highly challenging to solve the formulated multi-RIS multi-path beamforming optimization problem. To solve it, we first derive the optimal RISs' phase shifts and the corresponding reflecting path selection for each user based on its practical deployment location. With the optimized multi-reflection paths, we obtain a feasible user grouping pattern for effective interference mitigation by constructing the maximum independent sets (MISs). Finally, we propose a joint heuristic algorithm to iteratively update the beamforming vectors and the group scheduling policies to maximize the minimum equivalent data rate of all users.