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.

The reconfigurable intelligent surface (RIS) has garnered considerable attention due to its substantial potential in reconfiguring the electromagnetic environment. In RIS-aided communications, constrained ℓ2-norm maximization problems frequently arise due to the phase configuration requirements. This paper investigates a general discrete ℓp-norm maximization problem, with power aggregation through RIS as a specific example. We propose a mathematically concise iterative framework composed of alternating inner product maximizations, which is well-suited for addressing both ℓ1- and ℓ2-norm maximizations under either discrete or continuous uni-modular variable constraints. The iteration process is proven to be monotonically non-decreasing. Additionally, this framework exhibits a distinctive capability to mitigate performance degradation caused by discrete quantization in practical systems, which is applicable to any algorithm intended for the continuous solution. Furthermore, as an integral component of the alternating iterations framework, we present a divide-and-sort (DaS) method to tackle the discrete inner product maximization problem. In the realm of ℓ∞-norm maximization, the DaS method ensures the identification of the global optimum with polynomial search complexity. We validate the proposed methods’ effectiveness and superiority through numerical and prototype experiments. Finally, we demonstrate that the proposed framework can be extended and applied to a wide range of other engineering problems.

The existing methods for Reconfigurable Intelligent Surface (RIS) beamforming in wireless communication are typically limited to uniform phase quantization. However, in real world applications, the phase and bit resolution of RIS units are often non-uniform due to practical requirements and engineering challenges. To fill this research gap, we formulate an optimization problem for discrete non-uniform phase configuration in RIS assisted multiple-input single-output (MISO) communications. Subsequently, a partition-and-traversal (PAT) algorithm is proposed to solve that, achieving the global optimal solution. The efficacy and superiority of the PAT algorithm are validated through numerical simulations, and the impact of non-uniform phase quantization on system performance is analyzed.

A fair beam allocation framework through reconfigurable intelligent surfaces (RISs) is proposed, incorporating the Max-min criterion. This framework focuses on explicit RIS beamforming functionalities through optimization. Firstly, realistic models, grounded in geometrical optics, are introduced to characterize the input/output behaviors of RISs. Then, a highly efficient algorithm is developed for Max-min optimizations involving quadratic forms. Leveraging the Moreau-Yosida approximation, we successfully reformulate the original problem and propose an iterative algorithm to obtain the optimal solution. The proposed approach exhibits excellent extensibility, making it readily applicable to address a broader class of Max-min optimization problems. Finally, numerical and prototype experiments are conducted to validate the effectiveness of the framework. With the proposed beam allocation framework and algorithm, we clarify that several crucial redistribution functionalities of RISs, such as explicit beam-splitting, fair beam allocation, and wide-beam generation, can be effectively implemented.

A fair beam allocation framework through reconfigurable intelligent surfaces (RISs) is proposed, incorporating the Max-min criterion. This framework focuses on designing explicit beamforming functionalities through optimization. Firstly, realistic models, grounded in geometrical optics, are introduced to characterize the input/output behaviors of RISs, effectively bridging the gap between the requirements on explicit beamforming operations and their practical implementations. Then, a highly efficient algorithm is developed for Max-min optimizations involving quadratic forms. Leveraging the Moreau-Yosida approximation, we successfully reformulate the original problem and propose an iterative algorithm to obtain the optimal solution. A comprehensive analysis of the algorithm’s convergence is provided. Importantly, this approach exhibits excellent extensibility, making it readily applicable to address a broader class of Max-min optimization problems. Finally, numerical and prototype experiments are conducted to validate the effectiveness of the framework. With the proposed beam allocation framework and algorithm, we clarify that several crucial redistribution functionalities of RISs, such as explicit beam-splitting, fair beam allocation, and wide-beam generation, can be effectively implemented. These explicit beamforming functionalities have not been thoroughly examined previously.