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Physics-compliant diagonal representation of beyond-diagonal RIS

Philipp del Hougne

TL;DR

This paper reframes beyond-diagonal RIS (BD-RIS) within a physics-compliant multi-port network framework. It shows that the BD-RIS load circuit is itself a multi-port network and that the BD-RIS end-to-end channel is the cascade of the radio environment and this load circuit. By mapping the BD-RIS problem to the conventional D-RIS framework using Zcasc for the cascade impedance and Psi for the diagonal load, existing D-RIS optimization methods can be applied, and hardware complexity considerations can be properly accounted for. The work thus treats BD-RIS as a physics-consistent extension that does not require new optimization algorithms and invites fair hardware-based comparisons.

Abstract

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.

Physics-compliant diagonal representation of beyond-diagonal RIS

TL;DR

This paper reframes beyond-diagonal RIS (BD-RIS) within a physics-compliant multi-port network framework. It shows that the BD-RIS load circuit is itself a multi-port network and that the BD-RIS end-to-end channel is the cascade of the radio environment and this load circuit. By mapping the BD-RIS problem to the conventional D-RIS framework using Zcasc for the cascade impedance and Psi for the diagonal load, existing D-RIS optimization methods can be applied, and hardware complexity considerations can be properly accounted for. The work thus treats BD-RIS as a physics-consistent extension that does not require new optimization algorithms and invites fair hardware-based comparisons.

Abstract

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.
Paper Structure (7 sections, 11 equations, 2 figures)

This paper contains 7 sections, 11 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Background on conventional D-RIS
  3. The concept of BD-RIS
  4. Contributions
  5. The multi-port network cascade underlying the BD-RIS concept
  6. Implications
  7. Conclusion

Figures (2)

  • Figure 1: Clarification of the notion of a port being a "two-terminal pair" for a simple 2-port $\pi$-network. (a) Schematic circuit topology. (b) Detailed circuit topology clearly showing both conductors and both terminals for each port. (c) Replacement of the three impedances in (b) with three auxiliary ports that are to be terminated by individual independent load impedances. The two terminals of each port and of each auxiliary port are clearly shown. The $\pi$-network involves one series and two parallel impedances (or auxiliary load-terminated ports).
  • Figure 2: This figure summarizes the key insight of the present paper.