Multiport network theory has been proved to be a suitable abstraction model for analyzing and optimizing reconfigurable intelligent surfaces (RISs), especially for studying the impact of the electromagnetic mutual coupling among radiating elements that are spaced less than half of the wavelength. Both representations in terms of $Z$-parameter (impedance) and $S$-parameter (scattering) matrices are widely utilized. In this paper, we embrace multiport network theory for analyzing and optimizing the reradiation properties of RIS-aided channels, and provide four new contributions. (i) First, we offer a thorough comparison between the $Z$-parameter and $S$-parameter representations. This comparison allows us to unveil that the typical scattering models utilized for RIS-aided channels ignore the structural scattering from the RIS, which results in an unwanted specular reflection. (ii) Then, we develop an iterative algorithm for optimizing, in the presence of electromagnetic mutual coupling, the tunable loads of the RIS based on the $S$-parameters representation. We prove that small perturbations of the step size of the algorithm result in larger variations of the $S$-parameter matrix compared with the $Z$-parameter matrix, resulting in a faster convergence rate. (iii) Subsequently, we generalize the proposed algorithm to suppress the specular reflection due to the structural scattering, while maximizing the received power towards the direction of interest, and analyze the effectiveness and tradeoffs of the proposed approach. (iv) Finally, we validate the theoretical findings and algorithms with numerical simulations and a commercial full-wave electromagnetic simulator based on the method of moments.

翻译：多端口网络理论已被证明是分析和优化可重构智能表面(RIS)的合适抽象模型，尤其适用于研究间距小于半波长的辐射单元间电磁互耦效应的影响。基于Z参数（阻抗）矩阵和S参数（散射）矩阵的两种表示方法均被广泛采用。本文采用多端口网络理论分析和优化RIS辅助信道的再辐射特性，并提出四项新贡献：(i) 首先，我们对Z参数与S参数表示方法进行了全面比较。通过比较揭示，现有RIS辅助信道的典型散射模型忽略了RIS的结构散射，导致产生非期望的镜面反射。(ii) 其次，基于S参数表示方法，我们开发了一种迭代算法，用于在存在电磁互耦的情况下优化RIS的可调负载。我们证明，相较于Z参数矩阵，算法步长的微小扰动会引起S参数矩阵更大的变化，从而获得更快的收敛速度。(iii) 随后，我们将所提算法推广至抑制因结构散射产生的镜面反射，同时最大化目标方向的接收功率，并分析了该方法的有效性与权衡关系。(iv) 最后，我们通过数值仿真及基于矩量法的商用全波电磁仿真器验证了理论结果与算法。