Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Wideband Channel Capacity Maximization With Beyond Diagonal RIS Reflection Matrices

Özlem Tuğfe Demir, Emil Björnson

TL;DR

This work addresses maximizing wideband capacity using Beyond Diagonal RIS (BD-RIS) by deriving a principled SISO-OFDM model for a fully-connected BD-RIS and formulating a capacity expression that depends on the BD-RIS reflection matrix $\mathbf{\Psi}$. A two-stage, divide-and-conquer optimization is proposed: first maximize the total channel gain across subcarriers by solving a quadratic form in $\boldsymbol{\psi}=\mathrm{vec}(\mathbf{\Psi})$ via eigen-decomposition of $\mathbf{A}$ and projection to BD-RIS constraints, followed by a projection to the nearest symmetric-unitary solution $\mathbf{\Psi}=\mathbf{S}\mathbf{S}^{\mathrm{T}}$ and a final diagonal-phase refinement. The results show that BD-RIS substantially improves wideband capacity in NLOS conditions, with gains up to roughly $\approx 50\%$, while gains shrink in the presence of strong LOS paths or static channels; the algorithm remains computationally efficient for practical RIS sizes. These findings support BD-RIS as a viable approach for enhancing wideband communications, particularly when multipath richness and absence of static paths prevail.

Abstract

Following the promising beamforming gains offered by reconfigurable intelligent surfaces (RISs), a new hardware architecture, known as \emph{beyond diagonal RIS (BD-RIS)}, has recently been proposed. This architecture enables controllable signal flows between the RIS elements, thereby providing greater design flexibility. However, the physics-imposed symmetry and orthogonality conditions on the non-diagonal reflection matrix make the design challenging. In this letter, we analyze how a BD-RIS can improve a wideband channel, starting from fundamental principles and deriving the capacity. Our analysis considers the effects of various channel taps and their frequency-domain characteristics. We introduce a new algorithm designed to optimize the configuration of the BD-RIS to maximize wideband capacity. The proposed algorithm has better performance than the benchmarks. A BD-RIS is beneficial compared to a conventional RIS in the absence of static path or when the Rician $κ$-factor is smaller than $10$.

Wideband Channel Capacity Maximization With Beyond Diagonal RIS Reflection Matrices

TL;DR

This work addresses maximizing wideband capacity using Beyond Diagonal RIS (BD-RIS) by deriving a principled SISO-OFDM model for a fully-connected BD-RIS and formulating a capacity expression that depends on the BD-RIS reflection matrix . A two-stage, divide-and-conquer optimization is proposed: first maximize the total channel gain across subcarriers by solving a quadratic form in via eigen-decomposition of and projection to BD-RIS constraints, followed by a projection to the nearest symmetric-unitary solution and a final diagonal-phase refinement. The results show that BD-RIS substantially improves wideband capacity in NLOS conditions, with gains up to roughly , while gains shrink in the presence of strong LOS paths or static channels; the algorithm remains computationally efficient for practical RIS sizes. These findings support BD-RIS as a viable approach for enhancing wideband communications, particularly when multipath richness and absence of static paths prevail.

Abstract

Following the promising beamforming gains offered by reconfigurable intelligent surfaces (RISs), a new hardware architecture, known as \emph{beyond diagonal RIS (BD-RIS)}, has recently been proposed. This architecture enables controllable signal flows between the RIS elements, thereby providing greater design flexibility. However, the physics-imposed symmetry and orthogonality conditions on the non-diagonal reflection matrix make the design challenging. In this letter, we analyze how a BD-RIS can improve a wideband channel, starting from fundamental principles and deriving the capacity. Our analysis considers the effects of various channel taps and their frequency-domain characteristics. We introduce a new algorithm designed to optimize the configuration of the BD-RIS to maximize wideband capacity. The proposed algorithm has better performance than the benchmarks. A BD-RIS is beneficial compared to a conventional RIS in the absence of static path or when the Rician -factor is smaller than .
Paper Structure (5 sections, 1 theorem, 30 equations, 3 figures, 1 algorithm)

This paper contains 5 sections, 1 theorem, 30 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Derivation of the Wideband System Model
  3. Wideband Capacity Maximization
  4. Numerical Results
  5. Conclusions

Key Result

Theorem 1

Let $\mathbf{S}\mathbf{\Sigma}\mathbf{S}^{\hbox{\tiny $\mathrm{T}$}}$ denote the singular value decomposition of $\frac{\overline{\mathbf{\Psi}}+\overline{\mathbf{\Psi}}^{\hbox{\tiny $\mathrm{T}$}}}{2}$. The optimal solution to eq:optimization4 is

Figures (3)

  • Figure 1: The capacity achieved for differently configured surfaces without a static path and with NLOS channels between the transmitter/receiver and RIS.
  • Figure 2: The capacity achieved for differently configured surfaces when the static channel is zero and the bandwidth is $B=30$ MHz.
  • Figure 3: The capacity achieved for differently configured surfaces when the static channel is non-zero and the $\kappa$-factor of the channels is zero.

Theorems & Definitions (2)

  • Theorem 1
  • proof