We address the reflection optimization problem for a reconfigurable intelligent surface (RIS), where the RIS elements feature a set of non-uniformly spaced discrete phase shifts. This is motivated by the actual behavior of practical RIS elements, where it is shown that a uniform phase shift assumption is not realistic. A problem is formulated to find the optimal refection amplitudes and reflection phase shifts of the RIS elements such that the channel capacity of the target user is maximized. We first prove that in the optimal configuration, each RIS element is either turned off or operates at maximum amplitude. We then develop a method that finds the optimal reflection amplitudes and phases with complexity linear in the number of RIS elements. Some new and interesting insight into the reflection optimization problem is also provided.

翻译：针对可重构智能表面（RIS）的反射优化问题，提出一种考虑非均匀离散相位配置的求解方法。实际RIS元件的物理特性表明，均匀相位假设与真实场景存在偏差，为此构建以目标用户信道容量最大化为目标的反射幅度与相位联合优化模型。首先证明最优配置下每个RIS元件要么关闭要么以最大幅度工作，继而提出一种复杂度与RIS元件数量呈线性关系的反射幅度与相位求解方法。该研究还揭示了反射优化问题中的若干新颖见解。