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:我们从初步物理原则中分析出,无线频道对TRIS配置的功能依赖性取决于通用(即,潜在复杂隔热)IRIS平衡的无线电环境。无线频道是一种线性输入-输出关系,非线性输入-输出关系,因为有两个独立机制:一) 近距离引起的由RIIS元素密切连接的相互联动;二) 反动引起的所有RIS元素之间长期联动。从数学角度讲,这种“结构”非线性来自“互动”矩阵的反演,这种“互动”矩阵可以被描绘成无穷无尽的Born系列[用于i]或类似系列[用于ii)]的总和。无线频道的直线输入-输出是一个线性投入-输出关系,它实际上代表RIS元素[i]或无线实体[用于i]之间反弹跳动的路径;二) 我们确定关键物理参数,以确定这些序列是否能够在第一和第二期之后被曲解,分别来自一个共同的RIS-平衡矩阵矩阵矩阵矩阵矩阵矩阵矩阵,可以被描绘成一个无限的物理和类似序列序列序列,而我们从一个不甚可靠的轨道上得到的精确分析结果,并用一个不甚精确的磁分析。