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Performance Analysis of Systems with Coupled and Decoupled RISs

Dominik Semmler, Josef A. Nossek, Michael Joham, Wolfgang Utschick

TL;DR

This work tackles mutual coupling in RIS-aided systems by contrasting a low-complexity element-wise algorithm with decoupling networks. It develops a unit-modulus phase formulation that enables rank-one updates and closed-form SISO gains, while showing how decoupling networks can restore an uncoupled-like channel, yielding analytic array-gain results including a potential $N^4$ scaling in end-fire in lossless settings. The paper demonstrates that decoupled RIS attain superior performance and lower per-iteration complexity than coupling-aware methods, though hardware costs scale quadratically with $N$; this motivates exploring partially connected networks. Overall, the study provides both a practical, computationally efficient algorithm and a physically grounded decoupling approach that enables tractable, closed-form performance analysis for RIS with mutual coupling.

Abstract

We analyze and compare different methods for handling the mutual coupling in RIS-aided communication systems. A new mutual coupling aware algorithm is derived where the reactance of each element is updated successively with a closed-form solution. In comparison to existing element-wise methods, this approach leads to a considerably reduced computational complexity. Furthermore, we introduce decoupling networks for the RIS array as a potential solution for handling mutual coupling. With these networks, the system model reduces to the same structure as when no mutual coupling were present. Including decoupling networks, we can optimize the channel gain of a RIS-aided SISO system in closed-form which allows to analyze the scenario under mutual coupling analytically and to draw connections to the conventional transmit array gain. In particular, a super-quadratic channel gain can be achieved which scales as N^4 where N is the number of RIS elements.

Performance Analysis of Systems with Coupled and Decoupled RISs

TL;DR

This work tackles mutual coupling in RIS-aided systems by contrasting a low-complexity element-wise algorithm with decoupling networks. It develops a unit-modulus phase formulation that enables rank-one updates and closed-form SISO gains, while showing how decoupling networks can restore an uncoupled-like channel, yielding analytic array-gain results including a potential scaling in end-fire in lossless settings. The paper demonstrates that decoupled RIS attain superior performance and lower per-iteration complexity than coupling-aware methods, though hardware costs scale quadratically with ; this motivates exploring partially connected networks. Overall, the study provides both a practical, computationally efficient algorithm and a physically grounded decoupling approach that enables tractable, closed-form performance analysis for RIS with mutual coupling.

Abstract

We analyze and compare different methods for handling the mutual coupling in RIS-aided communication systems. A new mutual coupling aware algorithm is derived where the reactance of each element is updated successively with a closed-form solution. In comparison to existing element-wise methods, this approach leads to a considerably reduced computational complexity. Furthermore, we introduce decoupling networks for the RIS array as a potential solution for handling mutual coupling. With these networks, the system model reduces to the same structure as when no mutual coupling were present. Including decoupling networks, we can optimize the channel gain of a RIS-aided SISO system in closed-form which allows to analyze the scenario under mutual coupling analytically and to draw connections to the conventional transmit array gain. In particular, a super-quadratic channel gain can be achieved which scales as N^4 where N is the number of RIS elements.
Paper Structure (16 sections, 41 equations, 9 figures)

This paper contains 16 sections, 41 equations, 9 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Element-Wise Algorithm
  4. Change of Optimization Parameters
  5. SISO Channel Gain
  6. Complexity
  7. Extensions
  8. Decoupling Networks
  9. New Cannnel Model
  10. Optimization
  11. Array Gain Analysis
  12. No Coupling
  13. Numerical Results
  14. Algorithm Comparison
  15. Analysis of the Decoupling Network
  16. ...and 1 more sections

Figures (9)

  • Figure 1: Multiport Model of NewChannelModel with an additional decoupling network $\bm{Z}_{\text{DeN}}$
  • Figure 2: SISO Link with $N$ Elements at the RIS
  • Figure 3: Method Comparison for $N = 4$ and end-fire direction
  • Figure 4: Method Comparison for $N = 4$ and end-fire direction with $d= \frac{\lambda}{4}$
  • Figure 5: Array Gain for the front-fire direction of the array
  • ...and 4 more figures