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Flexible Multi-Beam Synthesis and Directional Suppression Through Transmissive RIS

Rujing Xiong, Ke Yin, Jialong Lu, Kai Wan, Tiebin Mi, Robert Caiming Qiu

TL;DR

This work tackles flexible multi-beam synthesis and directional suppression in transmissive RIS by formulating a constrained Max-min problem that maximizes the minimum received power for served UEs while limiting power toward unauthorized directions. It combines a geometrical optics–based physical model with a novel auxiliary-variable and compensated convexity transform to produce a smooth surrogate, solved efficiently via a bisection-based algorithm whose inner problems use accelerated gradient methods. The approach enables beam splitting, aggregation, and targeted sidelobe suppression, and is validated through extensive simulations and a 16×16 1-bit RIS prototype, showing superior beam-control accuracy and robustness compared with baseline methods. The framework holds promise for practical applications in multi-user communications, interference mitigation, and physical-layer security with scalable computational properties and broad applicability to RIS architectures.

Abstract

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.

Flexible Multi-Beam Synthesis and Directional Suppression Through Transmissive RIS

TL;DR

This work tackles flexible multi-beam synthesis and directional suppression in transmissive RIS by formulating a constrained Max-min problem that maximizes the minimum received power for served UEs while limiting power toward unauthorized directions. It combines a geometrical optics–based physical model with a novel auxiliary-variable and compensated convexity transform to produce a smooth surrogate, solved efficiently via a bisection-based algorithm whose inner problems use accelerated gradient methods. The approach enables beam splitting, aggregation, and targeted sidelobe suppression, and is validated through extensive simulations and a 16×16 1-bit RIS prototype, showing superior beam-control accuracy and robustness compared with baseline methods. The framework holds promise for practical applications in multi-user communications, interference mitigation, and physical-layer security with scalable computational properties and broad applicability to RIS architectures.

Abstract

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.

Paper Structure

This paper contains 23 sections, 4 theorems, 29 equations, 15 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. Outline
  4. Reproducible Research
  5. Notations
  6. System Model and problem formulation
  7. System Model
  8. Optimization Formulation
  9. Optimization Method for the Constrained max-min problem.
  10. Problem Reformulation and Method for Optimal Solution.
  11. Convergence Analysis and Computational Complexity
  12. Numerical Simulation Evaluations
  13. Directional Suppression
  14. Flexible Beam Synthesis
  15. Beam-spliting and beam-aggregation
  16. ...and 8 more sections

Key Result

Theorem 1

The function $F(t)$ is monotonically decreasing in $t$.

Figures (15)

  • Figure 1: The communication system involving a transmitter architecture using transmissive RIS
  • Figure 2: System model of transmissive RIS-assisted communications.
  • Figure 3: Beam synthesis through Transmissive RIS. The undesired direction may correspond to unauthorized users or users from neighboring cells.
  • Figure 4: The radiation pattern for beam synthesis illustration. A single signal source (Tx1) is employed; the observation UE angle is set to be $-20^{\circ}$ and $30^{\circ}$. The suppression interval is $[-10^{\circ},0^{\circ}]$, bounded by two red dashed lines. (a) The power plot. (b) The normalized polar power plot.
  • Figure 5: The normalized 3-dimensional (3D) beam radiation pattern. (a) The unconstraint radiation pattern generated by the MA algorithm xiong2024fair. (b) The sidelobe beams are suppressed within the elevation angle range of $[0^{\circ}, 20^{\circ}]$ and the azimuth angle range of $[179^{\circ}, 181^{\circ}]$ through the proposed method.
  • ...and 10 more figures

Theorems & Definitions (10)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Remark 1
  • Theorem 4
  • proof
  • Remark 2