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Phase Selection and Analysis for Multi-frequency Multi-user RIS Systems Employing Subsurfaces in Correlated Ricean and Rayleigh Environments

Amy S. Inwood, Peter J. Smith, Philippa A. Martin, Graeme K. Woodward

Abstract

Phase selection design for reconfigurable intelligent surfaces (RISs) is a significant research challenge, as a closed-form optimal solution for a multi-user (MU) system is believed to be intractable. While existing methods achieve strong near-optimal performance, they typically entail high computational complexity. In this work, we take a different approach and propose a practical method that achieves competitive performance while substantially reducing computational complexity. To do so, we consider a RIS divided into subsurfaces. Each subsurface is designed specifically for one user, who is served on their own frequency band. The other subsurfaces (those not designed for this user) provide additional uncontrolled scattering. We derive the exact closed-form expression for the mean signal-to-noise ratio (SNR) for the proposed subsurface design (SD) when all channels experience correlated Ricean fading. We simplify this to find the mean SNR for line-of-sight (LoS) channels and channels experiencing correlated Rayleigh fading. An iterative SD (ISD) process is proposed, where subsurfaces are designed sequentially, and the phases that are already set are used to enhance the design of the remaining subsurfaces. This is extended to a converged ISD (CISD), where the ISD process is repeated multiple times until the SNR increases by less than a specified tolerance. The ISD and CISD both provide a performance improvement over SD, which increases as the number of RIS elements increases. The SD is significantly simpler than the lowest complexity MU method we know of, and despite each user having less bandwidth, the SD outperforms the existing method in some key scenarios. The SD is more robust to strongly LoS channels and clustered users, as it does not rely on spatial multiplexing like other MU methods. Combined with the complexity reduction, this makes the SD an attractive phase selection method.

Phase Selection and Analysis for Multi-frequency Multi-user RIS Systems Employing Subsurfaces in Correlated Ricean and Rayleigh Environments

Abstract

Phase selection design for reconfigurable intelligent surfaces (RISs) is a significant research challenge, as a closed-form optimal solution for a multi-user (MU) system is believed to be intractable. While existing methods achieve strong near-optimal performance, they typically entail high computational complexity. In this work, we take a different approach and propose a practical method that achieves competitive performance while substantially reducing computational complexity. To do so, we consider a RIS divided into subsurfaces. Each subsurface is designed specifically for one user, who is served on their own frequency band. The other subsurfaces (those not designed for this user) provide additional uncontrolled scattering. We derive the exact closed-form expression for the mean signal-to-noise ratio (SNR) for the proposed subsurface design (SD) when all channels experience correlated Ricean fading. We simplify this to find the mean SNR for line-of-sight (LoS) channels and channels experiencing correlated Rayleigh fading. An iterative SD (ISD) process is proposed, where subsurfaces are designed sequentially, and the phases that are already set are used to enhance the design of the remaining subsurfaces. This is extended to a converged ISD (CISD), where the ISD process is repeated multiple times until the SNR increases by less than a specified tolerance. The ISD and CISD both provide a performance improvement over SD, which increases as the number of RIS elements increases. The SD is significantly simpler than the lowest complexity MU method we know of, and despite each user having less bandwidth, the SD outperforms the existing method in some key scenarios. The SD is more robust to strongly LoS channels and clustered users, as it does not rely on spatial multiplexing like other MU methods. Combined with the complexity reduction, this makes the SD an attractive phase selection method.

Paper Structure

This paper contains 22 sections, 64 equations, 9 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Review of Related Literature
  3. Contributions
  4. System Model
  5. Channel Model
  6. Phase Selection Methods
  7. LoS Phase Selection Method
  8. Extended Subsurface Design for NLoS Systems
  9. Iterative Phase Alignment
  10. Analysis
  11. Mean SNR for Correlated Ricean Systems
  12. Special Case 1: Mean SNR for Correlated Ricean $\mathbf{H}_\mathrm{rb}$ with Correlated Rayleigh UE Channels
  13. Special Case 2: Mean SNR for LoS $\mathbf{H}_\mathrm{rb}$ with Correlated Rayleigh UE Channels
  14. Numerical Results
  15. Mean SNR Comparison of Subsurface Methods in Sec. \ref{['sec:phase_selection_methods']}
  16. ...and 7 more sections

Figures (9)

  • Figure 1: System model showing channels for 1 in band 1.
  • Figure 2: User drop configurations for one cluster (a), two clusters (b) and random (c).
  • Figure 3: Comparison of mean for a randomly selected for different subsurface phase selection methods while varying the number of elements.
  • Figure 4: Mean number of iterations of the required for convergence.
  • Figure 5: Comparison of mean sum rate for different phase selection methods while varying the - channel K-factor, and hence $\eta_\mathrm{d}$.
  • ...and 4 more figures

Theorems & Definitions (8)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Remark 8