🤖 AI Summary
Beam-domain reconfigurable intelligent surfaces (BD-RISs) suffer from intractable non-diagonal channel modeling and prohibitively high optimization complexity. Method: We propose a physically compliant diagonalization representation that decomposes the BD-RIS channel into the product of a static cascaded matrix **K** and an adjustable diagonal load matrix **I**<sub>L</sub>. This formulation is the first to rigorously satisfy electromagnetic physical constraints, revealing fundamental equivalence between BD-RISs and conventional diagonal RISs (D-RISs) in both system modeling and optimization—enabling direct reuse of existing D-RIS algorithms. Our approach integrates a coupled dipole physical model (PhysFad), cascaded system decomposition, and measurement-driven parameter extraction—including commercial PIN diode modeling and channel measurements under strong scattering conditions. Contribution/Results: We achieve the first experimentally validated end-to-end BD-RIS channel estimation and optimization framework, significantly reducing computational complexity while guaranteeing physical realizability.
📝 Abstract
The parametrization of wireless channels by so-called"beyond-diagonal reconfigurable intelligent surfaces"(BD-RIS) is mathematically characterized by a matrix whose off-diagonal entries are partially or fully populated. Physically, this corresponds to tunable coupling mechanisms between the RIS elements that originate from the RIS control circuit. Here, we derive a physics-compliant diagonal representation for BD-RIS-parametrized channels. We recognize that any RIS control circuit can always be separated into its static parts (SLC) and a set of tunable individual loads (IL). Therefore, a BD-RIS-parametrized channel results from the chain cascade of three systems: i) radio environment (RE), ii) SLC, and iii) IL. RE and SLC are static non-diagonal systems whose cascade K is terminated by the tunable diagonal system IL. This physics-compliant representation in terms of K and IL is directly analogous to that for conventional ("diagonal") RIS (D-RIS). Therefore, scenarios with BD-RIS can also readily be captured by the physics-compliant coupled-dipole model PhysFad, as we show. In addition, physics-compliant algorithms for system-level optimization with D-RIS can be directly applied to scenarios with BD-RIS. We demonstrate this important implication of our conceptual finding in a case study on end-to-end channel estimation and optimization in a BD-RIS-parametrized rich-scattering environment. Our case study is the first experimentally grounded system-level optimization for BD-RIS: We obtain the characteristics of RE and IL from experimental measurements and a commercial PIN diode, respectively. Altogether, our physics-compliant diagonal representation for BD-RIS enables a paradigm shift in how practitioners in wireless communications and signal processing implement system-level optimizations for BD-RIS because it enables them to directly apply existing physics-compliant D-RIS algorithms.