Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Rate Analysis and Optimization of LoS Beyond Diagonal RIS-assisted MIMO Systems

Ignacio Santamaria, Jesus Gutierrez, Mohammad Soleymani, Eduard Jorswieck

TL;DR

This work tackles rate maximization in a BD-RIS-assisted MIMO link where the forward and backward RIS channels are LoS while the direct Tx-Rx link is NLoS. It develops a closed-form expression for the achievable rate under a rank-1 BD-RIS perturbation and derives the optimal BD-RIS configuration via Takagi/SVD-based factorization, complemented by an alternating optimization over the Tx covariance ${\bf R}_{xx}$. The key contribution is a provably optimal BD-RIS design with a closed-form phase and amplitude characterization, yielding a rate gain $\log(1 + \Delta)$ and reduced computational complexity compared to iterative BD-RIS schemes. The results show that the LoS BD-RIS design can outperform diagonal RIS and remain competitive under Ricean fading, offering practical benefits in energy efficiency and directional control for BD-RIS-assisted MIMO systems.

Abstract

In this letter, we derive an expression for the achievable rate in a multiple-input multiple-output (MIMO) system assisted by a beyond-diagonal reconfigurable intelligent surface (BD-RIS) when the channels to and from the BD-RIS are line-of-sight (LoS) while the direct link is non-line-of-sight (NLoS). The rate expression allows to derive the optimal unitary and symmetric scattering BD-RIS matrix in closed form. Our simulation results show that the proposed solution is competitive even under the more usual Ricean channel fading model when the direct link is weak.

Rate Analysis and Optimization of LoS Beyond Diagonal RIS-assisted MIMO Systems

TL;DR

This work tackles rate maximization in a BD-RIS-assisted MIMO link where the forward and backward RIS channels are LoS while the direct Tx-Rx link is NLoS. It develops a closed-form expression for the achievable rate under a rank-1 BD-RIS perturbation and derives the optimal BD-RIS configuration via Takagi/SVD-based factorization, complemented by an alternating optimization over the Tx covariance . The key contribution is a provably optimal BD-RIS design with a closed-form phase and amplitude characterization, yielding a rate gain and reduced computational complexity compared to iterative BD-RIS schemes. The results show that the LoS BD-RIS design can outperform diagonal RIS and remain competitive under Ricean fading, offering practical benefits in energy efficiency and directional control for BD-RIS-assisted MIMO systems.

Abstract

In this letter, we derive an expression for the achievable rate in a multiple-input multiple-output (MIMO) system assisted by a beyond-diagonal reconfigurable intelligent surface (BD-RIS) when the channels to and from the BD-RIS are line-of-sight (LoS) while the direct link is non-line-of-sight (NLoS). The rate expression allows to derive the optimal unitary and symmetric scattering BD-RIS matrix in closed form. Our simulation results show that the proposed solution is competitive even under the more usual Ricean channel fading model when the direct link is weak.

Paper Structure

This paper contains 5 sections, 2 theorems, 24 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System model
  3. Optimal BD-RIS and achievable rate
  4. Simulation Results
  5. Conclusion

Key Result

Proposition 1

Let ${\bf B} = {\bf A} + \alpha e^{j \theta} {\bf f} {\bf g}^H$ be a rank-1 perturbation of the $n \times m$ complex matrix ${\bf A}$. Then, where $\Delta = Z \alpha^2 + 2\alpha \operatorname{Re} \left ( e^{j \theta} \gamma_3 \right)$, $Z = |\gamma_3|^2 + \gamma_1 (\|{\bf g}\|^2 - \gamma_2)$, and Note that $\gamma_1 \geq 0$ and $\gamma_2 \geq 0$ are real values, whereas $\gamma_3$ is a complex

Figures (3)

  • Figure 1: BD-RIS-aided MIMO communication system. The BD-RIS is strategically deployed to have a direct LoS path to the transmitter (${\bf G}$) and receiver (${\bf F}$). The signal from the Tx arrives at the Rx by several NLoS paths shown in dashed line.
  • Figure 2: Achievable rate in a $4 \times 4$ MIMO system with pure LoS forward and backward channels for i) the proposed BD-RIS with optimal ${\bf R}_{xx}$ (Alg. 1); ii) the proposed BD-RIS with isotropic ${\bf R}_{xx}$; iii) the single-stream iterative method in NeriniTWC2023; and iv) a random BD-RIS with isotropic ${\bf R}_{xx}$.
  • Figure 3: Achievable rate vs $K$ (Ricean factor for the BD-RIS channels) for several competing schemes.

Theorems & Definitions (6)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Remark 1: Diagonal RIS
  • Remark 2: Group-connected BD-RIS