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Beyond-Diagonal RIS For Enhanced Secrecy and Sensing Gains in Secure ISAC Networks: An Optimization Framework

This paper proposes an optimization framework for a secure Beyond-Diagonal RIS (BD-RIS) aided Integrated Sensing and Communication (ISAC) network that maximizes target sensing performance while ensuring secrecy against eavesdropping targets, demonstrating superior gains over traditional diagonal RIS designs through an alternating optimization approach.

Original authors: Elmehdi Illi, Marwa Qaraqe

Published 2026-04-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Elmehdi Illi, Marwa Qaraqe

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to have a secret conversation with a friend in a crowded, noisy room (the wireless network). At the same time, you need to shout out loud to a specific spot in the room to check if a hidden object is there (sensing). The problem? There are spies (malicious targets) trying to listen in on your conversation, and there are walls blocking your direct line of sight.

This paper introduces a high-tech solution to this problem using a new kind of "smart mirror" called a Beyond-Diagonal Reconfigurable Intelligent Surface (BD-RIS).

Here is the breakdown of the paper using simple analogies:

1. The Problem: The "Noisy Room" and the "Spy"

ISAC (Integrated Sensing and Communication): Usually, we use one signal to talk to our phones and a different signal to detect cars or planes. This paper suggests using the same signal for both. It's like using a single flashlight to both read a book and scan the room for intruders.
The Challenge:
- No Line of Sight: If there are walls, the signal can't reach the user or the target.
- The Spy: The "targets" we are trying to sense are actually eavesdroppers. They want to steal the secret message while we are trying to detect them.
- The Trade-off: Usually, if you shout louder to be heard (better sensing), the spy hears you better too (worse security). If you whisper to hide from the spy, you might not be able to sense the target.

2. The Old Solution: The "Standard Smart Mirror" (D-RIS)

Think of a standard Reconfigurable Intelligent Surface (RIS) as a wall covered in thousands of tiny, independent mirrors.

How it works: Each tiny mirror can tilt slightly to reflect light (the signal) in a specific direction.
The Limitation: In the old design, every mirror acts alone. It's like a choir where every singer can only change their own volume, but they can't talk to each other to harmonize. This limits how well they can focus the beam or hide the signal from the spy.

3. The New Solution: The "Super-Connected Mirror" (BD-RIS)

The paper proposes a BD-RIS. Imagine that same wall of mirrors, but now, every single mirror is connected to every other mirror by tiny, invisible wires.

The Magic: When a signal hits Mirror A, it doesn't just bounce off; it can "talk" to Mirror B, which passes some energy to Mirror C, and so on. They work together as a single, coordinated team.
The Benefit: This gives the system "superpowers." It can shape the signal beam much more precisely. It can focus a tight beam on the target (for sensing) while simultaneously creating a "noise bubble" around the spy to confuse them, all without wasting energy.

4. The Strategy: The "Tightrope Walk" (Optimization)

The authors had to solve a very difficult math puzzle: How do we adjust the mirrors, the transmitter, and the "noise" to get the best result?

The Goal: Maximize the "echo" from the targets (so we can see them clearly) while ensuring the spies hear nothing but static.
The Method (Alternating Optimization):
- Imagine you are tuning a complex radio. You can't adjust the frequency, the volume, and the antenna direction all at once perfectly.
- So, the authors' algorithm does it step-by-step:
  1. Step A: Keep the transmitter fixed, and adjust the "Super Mirror" to get the best reflection.
  2. Step B: Keep the mirror fixed, and adjust the transmitter's beam and the "noise" to confuse the spy.
  3. Step C: Repeat.
- They use a special mathematical tool (Riemannian Conjugate Gradient) to navigate this "hilly" landscape of possibilities to find the highest peak (the best solution) without getting stuck in a small valley.

5. The Results: Why It Matters

The simulations showed that this new "Super Mirror" is a game-changer:

Better Vision: It can sense targets much more clearly than the old mirrors, even when the spies are trying to jam the signal.
No Compromise: In the old system, if you wanted more security, you had to sacrifice sensing ability. With the BD-RIS, you can get more security AND better sensing at the same time. It breaks the usual trade-off.
Efficiency: It does this without needing more power or bigger antennas; it just uses the "smart" connections between the mirror elements more effectively.

Summary Analogy

Think of the old system as a group of people trying to throw a ball to a friend while a thief tries to catch it. They can only throw the ball in one direction. If they throw it hard (sensing), the thief catches it. If they throw it softly (security), the friend doesn't get it.

The new BD-RIS system is like having a team of people with a giant, flexible trampoline. They can bounce the ball off the trampoline in a way that:

The ball hits the friend perfectly.
The ball bounces around the thief, confusing them.
The ball hits a hidden sensor on the wall to confirm the thief's location.

The paper proves that this "smart trampoline" (BD-RIS) is the future of secure, dual-purpose wireless networks.

1. Problem Statement

The paper addresses the challenges in Integrated Sensing and Communication (ISAC) networks, specifically in environments where Line-of-Sight (LoS) links are obstructed and where sensed targets act as malicious eavesdroppers.

Context: A Dual-Functional Radar-Communication (DFRC) Base Station (BS) serves multiple downlink users while simultaneously sensing $L$ targets.
Threat Model: The targets are assumed to be malicious entities attempting to eavesdrop on the legitimate communication signals.
Limitations of Traditional RIS: Conventional Reconfigurable Intelligent Surfaces (RIS) use a Diagonal RIS (D-RIS), where the reflection matrix is diagonal (only phase shifts per element, no coupling between elements). This limits the degrees of freedom (DoF) for beamforming and creates a trade-off between secrecy and sensing performance.
Objective: To design a secure ISAC scheme using a Beyond-Diagonal RIS (BD-RIS) that maximizes sensing performance (reflected power to targets) while strictly maintaining information-theoretic secrecy (preventing targets from decoding user data) and adhering to power constraints.

2. System Model

Network Architecture: A DFRC BS with $J_T$ transmit and $J_R$ receive antennas serves $K$ users and senses $L$ targets. An $M$ -element BD-RIS assists propagation by creating virtual LoS links.
BD-RIS Characteristics: Unlike D-RIS, the BD-RIS reflection matrix $\Psi$ is unitary and non-diagonal. It allows interconnections between elements, enabling signal coupling and more flexible beam steering. The paper assumes a fully-connected, asymmetric BD-RIS architecture.
Signal Model: The BS transmits a superposition of information signals (beamformed via matrix $Q$ ) and Artificial Noise (AN) (covariance $R_z$ ). The AN is designed to degrade the eavesdroppers' Signal-to-Interference-plus-Noise Ratio (SINR) while enhancing sensing illumination.
Performance Metrics:
- Secrecy: Measured by Secrecy Capacity (SC), defined as the difference between the legitimate channel capacity and the eavesdropper's capacity.
- Sensing: Measured by the per-target reflected power ( $V_s^{(l)}$ ), which correlates with target detection probability.

3. Methodology and Optimization Framework

The authors formulate a non-convex optimization problem to maximize the weighted sum of reflected powers subject to secrecy, power, and unitary constraints.

Optimization Problem ( $P_1$ ):

Objective: Maximize $\sum \alpha_l V_s^{(l)}$ .
Constraints:
- Minimum Secrecy Capacity ( $C_S \geq C_{th}$ ).
- Total transmit power limit.
- Rank-one constraints on beamforming matrices.
- Unitary constraint on the BD-RIS matrix ( $\Psi^H\Psi = I$ ).

Solution Approach: Alternating Optimization (AO)
The problem is decomposed into two sub-problems solved iteratively:

BD-RIS Scattering Matrix Optimization ( $\Psi$ ):
- Challenge: The problem is non-convex due to the quartic dependence on $\Psi$ and the unitary constraint.
- Method: Riemannian Conjugate Gradient (RCG) optimization on the Stiefel Manifold.
- Technique: The unitary matrix $\Psi$ is decomposed into an initial guess $\Psi_0$ and a unitary rotation matrix $X$ ( $\Psi = \Psi_0 X$ ). The algorithm optimizes $X$ using gradient descent rules adapted for the manifold, utilizing a Lagrangian formulation to handle secrecy constraints.
Beamforming and AN Covariance Optimization ( $Q, R_z$ ):
- Challenge: Non-convex rank-one constraints.
- Method: Semidefinite Relaxation (SDR).
- Technique: The rank-one constraint is relaxed to allow the problem to be solved as a convex Semidefinite Program (SDP). After solving, a rank-one solution is recovered using Eigenvalue Decomposition (EVD), selecting the principal eigenvector.
Lagrangian Multiplier Update: Multipliers associated with the secrecy constraints are updated iteratively to ensure constraint satisfaction.

4. Key Contributions

Novel Scheme: Proposes the first secure ISAC framework utilizing BD-RIS where targets act as eavesdroppers.
Optimization Framework: Develops a hybrid AO-RCG-SDR algorithm to jointly optimize the BD-RIS scattering matrix, transmit beamforming, and artificial noise covariance.
Manifold Optimization: Introduces a Riemannian conjugate gradient approach to handle the non-convex unitary constraint of the BD-RIS efficiently.
Trade-off Analysis: Demonstrates that BD-RIS can break the traditional secrecy-sensing trade-off found in D-RIS systems.

5. Numerical Results

The paper validates the proposed scheme through simulations with the following key findings:

Convergence: The proposed AO algorithm converges rapidly (within 25–30 iterations, often fewer for lower secrecy requirements).
Sensing Gain: BD-RIS significantly outperforms D-RIS. With $M=64$ elements, BD-RIS achieves a beampattern gain of at least 3 dB compared to D-RIS.
Secrecy-Sensing Trade-off:
- D-RIS: Increasing secrecy requirements (stricter SINR constraints for users) forces a reduction in Artificial Noise power directed at targets, severely degrading sensing performance.
- BD-RIS: Can maintain or even increase sensing performance (reflected power) while improving secrecy. The extra degrees of freedom allow the system to steer the signal effectively without sacrificing sensing illumination.
Parameter Sensitivity:
- Increasing the number of transmit antennas ( $J_T$ ) and BD-RIS elements ( $M$ ) improves sensing power.
- The system is robust to the spatial offset between users and targets; larger BD-RIS sizes better preserve sensing power even when targets are close to legitimate users.

6. Significance

This work is significant because it bridges the gap between physical-layer security and radar sensing in next-generation 6G networks. By leveraging Beyond-Diagonal RIS, the authors demonstrate that it is possible to overcome the limitations of traditional RIS architectures. The proposed framework proves that advanced RIS topologies can simultaneously enhance target detection capabilities and secure communications against eavesdropping, offering a viable solution for secure ISAC deployments in non-LoS environments.