In this paper, we consider a reconfigurable intelligent surface (RIS) and model it by using multiport network theory. We first compare the representation of RIS by using $Z$-parameters and $S$-parameters, by proving their equivalence and discussing their distinct features. Then, we develop an algorithm for optimizing the RIS configuration in the presence of electromagnetic mutual coupling. We show that the proposed algorithm based on optimizing the $S$-parameters results in better performance than existing algorithms based on optimizing the $Z$-parameters. This is attributed to the fact that small perturbations of the step size of the proposed algorithm result in larger variations of the $S$-parameters, hence increasing the convergence speed of the algorithm.

翻译：本文考虑可重构智能表面（RIS），并采用多端口网络理论对其进行建模。我们首先通过证明$Z$参数与$S$参数表示的等价性并讨论其各自特点，对这两种RIS表示方法进行比较。随后，我们提出一种在电磁互耦存在条件下优化RIS配置的算法。研究表明，基于$S$参数优化的算法相比现有基于$Z$参数优化的算法能够获得更优性能。该优势源于所提算法步长的微小扰动会引发$S$参数的更大变化，从而提升算法收敛速度。