Transmissive RIS-Based Fair Beam Synthesis and Directional Suppression

Existing research on reconfigurable intelligent surfaces (RISs) faces significant challenges in achieving flexible and accurate beam synthesis, which is an essential capability for enhancing physical layer security in wireless communications. This paper proposes a Max-min optimization framework with nonlinear constraints, leveraging phase optimization techniques to enable simultaneous multi-beam synthesis and directional suppression using transmissive RIS. A realistic model grounded in geometrical optics is first established to characterize the input/output behavior of RIS. Subsequently, a highly efficient bisection-based algorithm (BIS) for constrained Max-min optimization is developed, utilizing an auxiliary variable and Moreau envelope to iteratively reach the optimal solution. The proposed algorithm is applicable to a wide range of constrained Maxmin problems and demonstrates superior performance over existing methods in terms of beam accuracy, robustness, and received power performance. This framework enables effective beam enhancement or selective suppression at specified spatial directions, making it well-suited for applications such as multiuser communication, physical layer security, and interference mitigation. Numerical results validate the effectiveness and advantages of the proposed method.