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Optimization of RIS-aided SISO Systems Based on a Mutually Coupled Loaded Wire Dipole Model

Nemanja Stefan Perović, Le-Nam Tran, Marco Di Renzo, Mark F. Flanagan

TL;DR

This work develops a circuit-based, mutually coupled loaded wire dipole model for RIS-aided SISO communications and proposes a gradient-based algorithm to optimize RIS impedances with a fixed real part and bounded imaginary parts. The optimization uses the exact end-to-end transfer function $h_{\mathrm{E2E}}$ and a line-search with gradient $\nabla_{\mathbf{z}_{\mathrm{RIS},\mathrm{Im}}} f$, guaranteeing monotone improvement and convergence to a stationary point. Complexity is analyzed, showing a dominant $\mathcal{O}(N_{\mathrm{RIS}}^{3})$ term from matrix inversions, with per-iteration cost scaling accordingly. Numerical results demonstrate faster convergence and comparable or better performance than a benchmark that uses an approximate transfer function, and they reveal that reducing inter-element spacing enhances performance when mutual coupling is included in the design.

Abstract

The electromagnetic (EM) features of reconfigurable intelligent surfaces (RISs) fundamentally determine their operating principles and performance. Motivated by these considerations, we study a single-input single-output (SISO) system in the presence of an RIS, which is characterized by a circuit-based EM-consistent model. Specifically, we model the RIS as a collection of thin wire dipoles controlled by tunable load impedances, and we propose a gradient-based algorithm for calculating the optimal impedances of the scattering elements of the RIS in the presence of mutual coupling. Furthermore, we prove the convergence of the proposed algorithm and derive its computational complexity in terms of number of complex multiplications. Numerical results show that the proposed algorithm provides better performance and converges faster than a benchmark algorithm.

Optimization of RIS-aided SISO Systems Based on a Mutually Coupled Loaded Wire Dipole Model

TL;DR

This work develops a circuit-based, mutually coupled loaded wire dipole model for RIS-aided SISO communications and proposes a gradient-based algorithm to optimize RIS impedances with a fixed real part and bounded imaginary parts. The optimization uses the exact end-to-end transfer function and a line-search with gradient , guaranteeing monotone improvement and convergence to a stationary point. Complexity is analyzed, showing a dominant term from matrix inversions, with per-iteration cost scaling accordingly. Numerical results demonstrate faster convergence and comparable or better performance than a benchmark that uses an approximate transfer function, and they reveal that reducing inter-element spacing enhances performance when mutual coupling is included in the design.

Abstract

The electromagnetic (EM) features of reconfigurable intelligent surfaces (RISs) fundamentally determine their operating principles and performance. Motivated by these considerations, we study a single-input single-output (SISO) system in the presence of an RIS, which is characterized by a circuit-based EM-consistent model. Specifically, we model the RIS as a collection of thin wire dipoles controlled by tunable load impedances, and we propose a gradient-based algorithm for calculating the optimal impedances of the scattering elements of the RIS in the presence of mutual coupling. Furthermore, we prove the convergence of the proposed algorithm and derive its computational complexity in terms of number of complex multiplications. Numerical results show that the proposed algorithm provides better performance and converges faster than a benchmark algorithm.
Paper Structure (11 sections, 1 theorem, 19 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 11 sections, 1 theorem, 19 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Problem Formulation
  5. Proposed Optimization Algorithm
  6. Convergence and Complexity Analysis
  7. Convergence Analysis
  8. Complexity Analysis
  9. Simulation Results
  10. Conclusion
  11. Proof of Lemma \ref{['lem:Gradient_Zris']}

Key Result

Lemma 1

The gradient of $f(\mathbf{z}_{\mathrm{RIS}})$ with respect to $\mathbf{z}_{\mathrm{RIS,Im}}$is where and $a=\bigl(\tilde{\mathrm{z}}_{\mathrm{T}}\tilde{\mathrm{z}}_{\mathrm{R}}-\phi_{\mathrm{TR}}^{2}\bigr)^{-1}$.

Figures (4)

  • Figure 1: Objective functions of the proposed and benchmark algorithms versus the number of iterations.
  • Figure 2: Objective functions of the proposed and benchmark algorithms versus the execution time.
  • Figure 3: Objective function of the proposed algorithm versus the inter-distance between adjacent RIS elements for an RIS of fixed size ($R_{0}=10^{-3}$ Ohm).
  • Figure 4: Objective function of the proposed algorithm versus the inter-distance between adjacent RIS elements for an RIS of fixed size and for a variable length of the RIS elements ($R_{0}=10^{-3}$ Ohm).

Theorems & Definitions (1)

  • Lemma 1