Optimal Configuration of Reconfigurable Intelligent Surfaces Under Non-Uniform Phase Quantization

Existing research on reconfigurable intelligent surface (RIS) beamforming in wireless communications predominantly assumes uniform phase quantization across reflecting units. However, in practical applications, engineering challenges and design requirements often lead to non-uniform phase and bit resolution of RIS units, which significantly limits the performance potential of conventional approaches. Current optimization frameworks struggle to effectively handle this non-uniform phase discretization due to the inherent non-convexity and high-dimensional nature of the resultant beamforming problem. To address this issue, this paper pioneers the study of discrete non-uniform phase configuration in RIS-assisted multi-user communication and formulates an optimization model to rigorously define the problem. For single-user scenarios, the paper proposes a partition-and-traversal (PAT) algorithm that efficiently achieves the global optimal solution through systematic search and traversal. For larger-scale multi-user scenarios, to further balance performance and computational complexity, a parameter tuning mechanism is introduced into the PAT algorithm, enhancing its flexibility and scalability. This mechanism optimizes the search strategy, significantly reduces computational overhead, and achieves linear complexity. Numerical simulations confirm the effectiveness and superiority of the proposed PAT algorithm. Additionally, we provide a detailed analysis of the impact of non-uniform phase quantization on the system performance.