Physics-compliant models of RIS-parametrized channels assign a load-terminated port to each RIS element. For conventional diagonal RIS (D-RIS), each auxiliary port is terminated by its own independent and individually tunable load (i.e., independent of the other auxiliary ports). For beyond-diagonal RIS (BD-RIS), the auxiliary ports are terminated by a tunable load circuit which couples the auxiliary ports to each other. Here, we point out that a physics-compliant model of the load circuit of a BD-RIS takes the same form as a physics-compliant model of a D-RIS-parametrized radio environment: a multi-port network with a subset of ports terminated by individually tunable loads (independent of each other). Consequently, we recognize that a BD-RIS-parametrized radio environment can be understood as a multi-port cascade network (i.e., the cascade of radio environment with load circuit) terminated by individually tunable loads (independent of each other). Hence, the BD-RIS problem can be mapped into the original D-RIS problem by replacing the radio environment with the cascade of radio environment and load circuit. The insight that BD-RIS can be physics-compliantly analyzed with the conventional D-RIS formalism implies that (i) the same optimization protocols as for D-RIS can be used for the BD-RIS case, and (ii) it is unclear if existing comparisons between BD-RIS and D-RIS are fair because for a fixed number of RIS elements, a BD-RIS has usually more tunable lumped elements.

翻译：物理合规的RIS参数化信道模型为每个RIS元件分配了一个负载端接端口。对于传统的对角RIS（D-RIS），每个辅助端口由其自身独立且单独可调的负载端接（即独立于其他辅助端口）。对于超对角RIS（BD-RIS），辅助端口由一个可调负载电路端接，该电路将辅助端口彼此耦合。在此，我们指出BD-RIS负载电路的物理合规模型与D-RIS参数化无线电环境的物理合规模型形式相同：一个多端口网络，其部分端口由单独可调的负载（彼此独立）端接。因此，我们认识到BD-RIS参数化的无线电环境可理解为一个由单独可调负载（彼此独立）端接的多端口级联网络（即无线电环境与负载电路的级联）。因此，通过将无线电环境替换为无线电环境与负载电路的级联，BD-RIS问题可映射为原始的D-RIS问题。这一关于BD-RIS可用传统D-RIS形式体系进行物理合规分析的洞见意味着：（i）与D-RIS相同的优化协议可用于BD-RIS情形；（ii）现有BD-RIS与D-RIS的比较是否公平尚不明确，因为在RIS元件数量固定的情况下，BD-RIS通常具有更多可调集总元件。