We analytically derive from first physical principles the functional dependence of wireless channels on the RIS configuration for generic (i.e., potentially complex-scattering) RIS-parametrized radio environments. The wireless channel is a linear input-output relation that depends non-linearly on the RIS configuration because of two independent mechanisms: i) proximity-induced mutual coupling between close-by RIS elements; ii) reverberation-induced long-range coupling between all RIS elements. Mathematically, this "structural" non-linearity originates from the inversion of an "interaction" matrix that can be cast as the sum of an infinite Born series [for i)] or Born-like series [for ii)] whose $K$th term physically represents paths involving $K$ bounces between the RIS elements [for i)] or wireless entities [for ii)]. We identify the key physical parameters that determine whether these series can be truncated after the first and second term, respectively, as tacitly done in common cascaded models of RIS-parametrized wireless channels. Numerical results obtained with the physics-compliant PhysFad model and experimental results obtained with a RIS prototype in an anechoic (echo-free) chamber and rich-scattering reverberation chambers corroborate our analysis. Our findings raise doubts about the reliability of existing performance analysis and channel-estimation protocols for cases in which cascaded models poorly describe the physical reality.

翻译：我们从第一性原理出发，解析推导了在一般（即可能复杂散射）RIS参数化无线电环境中，无线信道对RIS配置的函数依赖关系。无线信道是一种线性输入-输出关系，但由于两种独立机制，它非线性地依赖于RIS配置：i) 相邻RIS单元间由近场引起的互耦；ii) 所有RIS单元间由混响引起的长程耦合。数学上，这种“结构性”非线性源于对“相互作用”矩阵的求逆，该矩阵可表示为无穷Born级数[对于i)]或Born类级数[对于ii)]的和，其第K项物理上代表涉及RIS单元间K次弹跳[对于i)]或无线实体间K次弹跳[对于ii)]的路径。我们识别了决定这些级数能否分别在第一项和第二项后截断的关键物理参数，而这正是常见RIS参数化无线信道级联模型中隐性采用的假设。使用符合物理原理的PhysFad模型获得的数值结果，以及在无回声（无回声）室和丰富散射混响室中使用RIS原型获得的实验结果，佐证了我们的分析。我们的发现对于级联模型未能良好描述物理现实的情况，对现有性能分析和信道估计协议的可靠性提出了质疑。