Reconfigurable intelligent surface (RIS) enables the control of wireless channels to improve coverage. To further extend coverage, multi-RIS aided systems have been explored, where multiple RISs steer the signal via a multi-hop path. However, deriving a physics-compliant channel model for multi-RIS aided systems is still an open problem. In this study, we fill this gap by modeling multi-RIS aided systems through multiport network theory, and deriving a channel model accounting for impedance mismatch, mutual coupling, and structural scattering. The derived physics-compliant model differs from the model widely used in literature, which omits the RIS structural scattering. To quantify this difference, we derive the channel gain scaling laws of the two models under line-of-sight (LoS) and multipath channels. Theoretical insights, validated by numerical results, show an important discrepancy between the physics-compliant and the widely used models, increasing with the number of RISs and multipath richness. In a multi-hop system aided by four 128-element RISs with multipath channels, optimizing the RISs using the widely used model and applying their solutions to the physics-compliant model achieves only 7% of the maximum channel gain. This highlights how severely mismatched channel models can be, calling for more accurate models in communication theory.

翻译：可重构智能表面（RIS）能够调控无线信道以改善覆盖。为进一步扩展覆盖范围，多RIS辅助系统已被探索，其中多个RIS通过多跳路径引导信号。然而，为多RIS辅助系统推导符合物理约束的信道模型仍是一个开放性问题。本研究通过多端口网络理论对多RIS辅助系统进行建模，并推导出考虑阻抗失配、互耦效应与结构散射的信道模型，填补了这一空白。所推导的符合物理约束的模型与文献中广泛使用的、忽略RIS结构散射的模型存在差异。为量化这一差异，我们推导了两种模型在视距（LoS）信道与多径信道下的信道增益缩放定律。理论分析与数值验证表明，符合物理约束的模型与广泛使用的模型之间存在显著差异，且该差异随RIS数量与多径丰富度的增加而增大。在一个由四个128单元RIS辅助、存在多径信道的多跳系统中，使用广泛采用的模型优化RIS配置并将其解应用于符合物理约束的模型时，仅能实现最大信道增益的7%。这凸显了信道模型可能存在严重失配，表明通信理论需要更精确的建模方法。