Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Beyond Diagonal RIS Design for Parameter Estimation With and Without Eavesdropping

Özlem Tuğfe Demir, Sinan Gezici

TL;DR

This work addresses secure parameter estimation in wireless systems by leveraging beyond-diagonal RIS (BD-RIS) to maximize information at the legitimate receiver while curbing eavesdropping. It develops BD-RIS optimization for both non-reciprocal and reciprocal configurations, using unitary BD-RIS matrices and Fisher information as the key metric, with a penalty dual decomposition framework to enforce secrecy constraints. The core contribution includes a closed-form optimal solution for the non-reciprocal case, a manifold-optimization approach for reciprocal BD-RIS, and a detailed inner/outer iteration scheme (4.1–4.3) to handle the secure design problem under Eve’s information leakage bound $\epsilon$. Numerical results show BD-RIS markedly improves estimation (lower CRB/MSE) at Bob compared to diagonal RIS, while effectively limiting Eve’s information, highlighting BD-RIS as a practical and powerful tool for secure parameter estimation in next-generation wireless networks.

Abstract

In this letter, we investigate the transmission of a complex-valued parameter vector from a transmitter to an intended receiver, considering both the presence and absence of an eavesdropper. The direct links from the transmitter to both the intended receiver and the eavesdropper are assumed to be blocked, and communications occur solely through cascaded channels facilitated by a beyond-diagonal reconfigurable intelligent surface (BD-RIS). While previous research has considered this system under conventional (diagonal) RIS assistance, we extend the setup to incorporate BD-RIS and quantify the resulting improvement in estimation performance at the intended receiver. This performance is measured by the trace of the Fisher information matrix (FIM), or equivalently, the average Fisher information, while simultaneously limiting the estimation capability of the eavesdropper. We propose solutions and algorithms for optimizing the BD-RIS response matrix and demonstrate their effectiveness. Numerical results reveal that the BD-RIS provides a significant enhancement in estimation quality compared to conventional diagonal RIS architectures.

Beyond Diagonal RIS Design for Parameter Estimation With and Without Eavesdropping

TL;DR

This work addresses secure parameter estimation in wireless systems by leveraging beyond-diagonal RIS (BD-RIS) to maximize information at the legitimate receiver while curbing eavesdropping. It develops BD-RIS optimization for both non-reciprocal and reciprocal configurations, using unitary BD-RIS matrices and Fisher information as the key metric, with a penalty dual decomposition framework to enforce secrecy constraints. The core contribution includes a closed-form optimal solution for the non-reciprocal case, a manifold-optimization approach for reciprocal BD-RIS, and a detailed inner/outer iteration scheme (4.1–4.3) to handle the secure design problem under Eve’s information leakage bound . Numerical results show BD-RIS markedly improves estimation (lower CRB/MSE) at Bob compared to diagonal RIS, while effectively limiting Eve’s information, highlighting BD-RIS as a practical and powerful tool for secure parameter estimation in next-generation wireless networks.

Abstract

In this letter, we investigate the transmission of a complex-valued parameter vector from a transmitter to an intended receiver, considering both the presence and absence of an eavesdropper. The direct links from the transmitter to both the intended receiver and the eavesdropper are assumed to be blocked, and communications occur solely through cascaded channels facilitated by a beyond-diagonal reconfigurable intelligent surface (BD-RIS). While previous research has considered this system under conventional (diagonal) RIS assistance, we extend the setup to incorporate BD-RIS and quantify the resulting improvement in estimation performance at the intended receiver. This performance is measured by the trace of the Fisher information matrix (FIM), or equivalently, the average Fisher information, while simultaneously limiting the estimation capability of the eavesdropper. We propose solutions and algorithms for optimizing the BD-RIS response matrix and demonstrate their effectiveness. Numerical results reveal that the BD-RIS provides a significant enhancement in estimation quality compared to conventional diagonal RIS architectures.
Paper Structure (9 sections, 1 theorem, 28 equations, 4 figures, 1 algorithm)

This paper contains 9 sections, 1 theorem, 28 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. BD-RIS Design without Eavesdropping
  4. Secure BD-RIS Design in the Presence of Eavesdropping
  5. Update ${\bf \Omega}$ of PDD Inner Layer Iteration
  6. Update ${\bf \Psi}$ of PDD Inner Layer Iteration
  7. Update of PDD Outer Layer Iteration
  8. Numerical Results
  9. Conclusion

Key Result

Lemma 1

The optimal BD-RIS response matrix for the problem eq:optimization1 is given as where $\boldsymbol{V}_E$ and $\boldsymbol{V}_M$ are the unitary matrices with the columns as the eigenvectors of $\boldsymbol{E}_b$ and $\boldsymbol{M}$, respectively. The eigenvectors are arranged to correspond to the eigenvalues, which are sorted in descending order.

Figures (4)

  • Figure 1: Trace of FIM at Bob achieved by non-reciprocal BD-RIS, reciprocal BD-RIS, and conventional RIS in both the presence and absence of eavesdropping for $r=36$ and $k=10$.
  • Figure 2: CRB (equivalently, MSE of the MLE) at Bob achieved by non-reciprocal BD-RIS, reciprocal BD-RIS, and conventional RIS in both the presence and absence of eavesdropping for $r=36$ and $k=10$.
  • Figure 3: Trace of FIM at Bob achieved by non-reciprocal BD-RIS, reciprocal BD-RIS, and conventional RIS in both the presence and absence of eavesdropping for $r=64$ and $k=15$.
  • Figure 4: CRB (equivalently, MSE of the MLE) at Bob achieved by non-reciprocal BD-RIS, reciprocal BD-RIS, and conventional RIS in both the presence and absence of eavesdropping for $r=64$ and $k=15$.

Theorems & Definitions (2)

  • Lemma 1
  • proof