Flexible Multi-Beam Synthesis and Directional Suppression Through Transmissive RIS

Despite extensive research on reconfigurable intelligent surfaces (RISs) in recent years, existing beamforming methods still face significant challenges in achieving flexible and robust beam synthesis, which is an essential capability for a wide range of communication scenarios. This paper introduces a Max-min criterion with nonlinear constraints, leveraging optimization techniques to simultaneously enable flexible multi-beam synthesis and directional suppression using transmissive RIS. Firstly, a realistic model grounded in geometrical optics is introduced to characterize the input/output behaviors of transmissive RISs, effectively bridging the gap between explicit beamforming requirements and practical implementations. Subsequently, a highly efficient algorithm for constrained Max-min optimizations involving quadratic forms is developed. By introducing an auxiliary variable and applying the compensated convexity transform, we successfully reformulate the original non-convex problem and obtain the optimal solution iteratively. This approach is readily applicable to a wide range of constrained Max-min optimization problems. Finally, numerical simulations and prototype experiments are conducted to validate the effectiveness of the proposed framework. The results demonstrate that the proposed algorithm can effectively enhance or selectively suppress signal beams in designated spatial directions, outperforming existing methods in terms of beam control accuracy and robustness. This framework provides valuable insights and references for practical communications applications such as physical layer security and interference mitigation.