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.

中文翻译：

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通过可重构的智能表面实现公平的光束分配


该文提出了一种通过可重构智能表面 （RIS） 的公平光束分配框架，并结合了 Max-min 准则。该框架侧重于通过优化来设计显式波束成形功能。首先，引入基于几何光学的真实模型来表征 RIS 的输入/输出行为，有效地弥合了显式波束成形操作的要求与其实际实施之间的差距。然后，开发了一种高效的算法，用于涉及二次形式的 Max-min 优化。利用 Moreau-Yosida 近似，我们成功地重新表述了原始问题，并提出了一种迭代算法来获得最优解。提供了对算法收敛性的全面分析。重要的是，这种方法具有出色的可扩展性，使其易于适用于解决更广泛的 Max-min 优化问题。最后，进行数值和原型实验以验证框架的有效性。通过提出的光束分配框架和算法，我们阐明了 RIS 的几个关键重分配功能，例如显式分束、公平光束分配和宽光束生成，可以有效实现。这些显式波束成形功能以前没有经过彻底研究。