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A Novel Q-stem Connected Architecture for Beyond-Diagonal Reconfigurable Intelligent Surfaces

Xiaohua Zhou, Tianyu Fang, Yijie Mao

TL;DR

Simulations show that the proposed BD-RIS architecture is capable of attaining the sum channel gain achieved by fully connected RIS while reducing the circuit complexity, and the proposed LS-based quasi-Newton algorithm significantly outperforms the baselines while the LS algorithm provides comparable performance with a substantial reduction in computational complexity.

Abstract

Beyond-diagonal reconfigurable intelligent surface (BD-RIS) has garnered significant research interest recently due to its ability to generalize existing reconfigurable intelligent surface (RIS) architectures and provide enhanced performance through flexible inter-connection among RIS elements. However, current BD-RIS designs often face challenges related to high circuit complexity and computational complexity, and there is limited study on the trade-off between system performance and circuit complexity. To address these issues, in this work, we propose a novel BD-RIS architecture named Q-stem connected RIS that integrates the characteristics of existing single connected, tree connected, and fully connected BD-RIS, facilitating an effective trade-off between system performance and circuit complexity. Additionally, we propose two algorithms to design the RIS scattering matrix for a Q-stem connected RIS aided multi-user broadcast channels, namely, a low-complexity least squares (LS) algorithm and a suboptimal LS-based quasi-Newton algorithm. Simulations show that the proposed architecture is capable of attaining the sum channel gain achieved by fully connected RIS while reducing the circuit complexity. Moreover, the proposed LS-based quasi-Newton algorithm significantly outperforms the baselines, while the LS algorithm provides comparable performance with a substantial reduction in computational complexity.

A Novel Q-stem Connected Architecture for Beyond-Diagonal Reconfigurable Intelligent Surfaces

TL;DR

Simulations show that the proposed BD-RIS architecture is capable of attaining the sum channel gain achieved by fully connected RIS while reducing the circuit complexity, and the proposed LS-based quasi-Newton algorithm significantly outperforms the baselines while the LS algorithm provides comparable performance with a substantial reduction in computational complexity.

Abstract

Beyond-diagonal reconfigurable intelligent surface (BD-RIS) has garnered significant research interest recently due to its ability to generalize existing reconfigurable intelligent surface (RIS) architectures and provide enhanced performance through flexible inter-connection among RIS elements. However, current BD-RIS designs often face challenges related to high circuit complexity and computational complexity, and there is limited study on the trade-off between system performance and circuit complexity. To address these issues, in this work, we propose a novel BD-RIS architecture named Q-stem connected RIS that integrates the characteristics of existing single connected, tree connected, and fully connected BD-RIS, facilitating an effective trade-off between system performance and circuit complexity. Additionally, we propose two algorithms to design the RIS scattering matrix for a Q-stem connected RIS aided multi-user broadcast channels, namely, a low-complexity least squares (LS) algorithm and a suboptimal LS-based quasi-Newton algorithm. Simulations show that the proposed architecture is capable of attaining the sum channel gain achieved by fully connected RIS while reducing the circuit complexity. Moreover, the proposed LS-based quasi-Newton algorithm significantly outperforms the baselines, while the LS algorithm provides comparable performance with a substantial reduction in computational complexity.

Paper Structure

This paper contains 12 sections, 1 theorem, 26 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Proposed Q-Stem Connected RIS
  5. Connection Between Q-stem Connected RIS and Other RIS Architectures
  6. Circuit Complexity of Q-Stem Connected RIS
  7. Problem Formulation
  8. Proposed Efficient Algorithm
  9. Theoretical Upper Bound Analysis for Problem \ref{['eq:pro-formula']}
  10. Proposed Least Square-based Algorithms for Problem \ref{['eq:pro-formula']}
  11. Simulation Results
  12. Conclusion

Key Result

Proposition 1

Fully connected RIS can not achieve the performance upper bound in eq:upper-bound when the DoF for the compact effective channels $\mathbf F$ is larger than 1, i.e., $M>1$. It only achieves the performance upper bound when $M=1$.

Figures (5)

  • Figure 1: The circuit architecture of Q-stem connected RIS and its graph representation.
  • Figure 2: The shape of a feasible susceptance matrix $\mathbf{B}$ for Q-stem connected RIS. The non-zero elements in $\mathbf{B}$ are represented in orange.
  • Figure 3: Channel gain versus the value of $Q$ in $\mathbf{B}$ when $L=K=4$ and $N=64$.
  • Figure 4: Channel gain versus the number of BD-RIS elements when $L=K=4$.
  • Figure 5: Channel gain versus the number of streams when $L=5$ and $N=64$.

Theorems & Definitions (4)

  • Definition 1
  • Definition 2
  • Proposition 1
  • Definition 3