In reconfigurable intelligent surfaces (RISs) aided communications, the existing passive beamforming (PB) design involves polynomial complexity in the number of reflecting elements, and thus is difficult to implement due to a massive number of reflecting elements. To overcome this difficulty, we propose a reflection-angle-based cascaded channel model by adopting the generalized Snell's law, in which the dimension of the variable space involved in optimization is significantly reduced, resulting in a simplified hierarchical passive beamforming (HPB) design. We develop an efficient two-stage HPB algorithm, which exploits the angular domain property of the channel, to maximize the achievable rate of the target user. Simulation results demonstrate the appealing performance and low complexity of the proposed HPB design.

翻译：在可重新配置的智能表面辅助通信中,现有的被动波束成型设计涉及反射元素数目的多元复杂性,因此难以执行,因为反射元素数量众多。为克服这一困难,我们建议采用普遍Snell法,采用反射角级联频道模式,在这种模式中,优化所涉及的可变空间范围大大减少,从而导致简化了上层被动波束成型设计。我们开发了高效的两阶段HPB算法,利用该频道的角域属性,以最大限度地提高目标用户的可实现率。模拟结果显示了拟议HPB设计具有吸引力和低复杂性。