⚡ electrical engineering

Secure RSMA-based Visible Light Networks under Spatial Correlation

This paper investigates the secrecy sum rate of RSMA-based visible light communication systems under spatial correlation, proposing a channel similarity reduction clustering strategy and two optimization algorithms (CCCP and SDR) to effectively mitigate performance degradation caused by high spatial correlation and internal eavesdropping.

Original authors: Hung K. Hoang, Chuyen T. Nguyen, Thang K. Nguyen, Thanh V. Pham, Anh T. Pham

Published 2026-06-02

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CC BY 4.0

Original authors: Hung K. Hoang, Chuyen T. Nguyen, Thang K. Nguyen, Thanh V. Pham, Anh T. Pham

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 a room filled with smart light bulbs (LEDs) that do double duty: they light up the room and also beam secret messages to your phone or tablet. This technology is called Visible Light Communication (VLC).

The paper you provided tackles a tricky problem: How do we keep these secret messages safe when the "listeners" (the users) are sitting right next to each other?

Here is a breakdown of the paper's ideas using simple analogies:

1. The Problem: The "Crowded Room" Effect

In a perfect world, every light bulb sends a message to just one person, and no one else can hear it. But in reality, light spreads out. If two people are sitting close together, the light beams hitting them look almost identical.

The Analogy: Imagine a teacher trying to whisper a secret to two students sitting side-by-side. Because they are so close, the sound waves hit both of them almost exactly the same way. It becomes very hard for the teacher to whisper to Student A without Student A accidentally hearing what was meant for Student B.
The Paper's Term: This is called Spatial Correlation (or "Channel Similarity"). When users are too close, their "channel" (the path the light takes) becomes too similar, making it impossible to separate the messages securely.

2. The Solution Part 1: The "Split-Message" Strategy (RSMA)

To handle interference, the researchers use a technique called Rate-Splitting Multiple Access (RSMA).

The Analogy: Instead of trying to whisper a single secret to one person, the teacher splits the message into two parts:
1. The "Common" Part: A general announcement that everyone in the room is allowed to hear (like "Class is starting").
2. The "Private" Part: A specific secret meant only for one student.
How it works: Everyone listens to the common part first and ignores it. Once they "cancel out" the common noise, they try to decode their own private secret. This is like peeling an onion; you remove the outer layer (common data) to get to the core (private data).

3. The Problem with the Strategy: The "Ceiling"

The researchers found that even with this clever splitting strategy, there is a limit. If the students are too close together (high spatial correlation), the light beams are so mixed up that the "private" part of the message leaks out, no matter how much power the light bulb uses.

The Analogy: It's like trying to whisper a secret in a room where the walls are made of mirrors. No matter how quietly you speak, the sound bounces around so much that everyone hears everything. The researchers call this a "Secrecy Performance Ceiling." You can turn up the volume (power), but it just makes the noise louder, not the secret clearer.

4. The Solution Part 2: The "Smart Seating Chart" (CSR Clustering)

To break this ceiling, the paper proposes a new way to organize the room before sending any messages. They call this Channel Similarity Reduction (CSR) Clustering.

The Analogy: Instead of letting students sit wherever they want, the teacher (the system) actively rearranges the seating chart.
- The Goal: Group students who are far apart from each other into "teams" (cells) and assign specific light bulbs to each team.
- The Trick: The system uses a smart algorithm (called NSGA-II, which acts like a super-organized game of musical chairs) to find the perfect arrangement. It tries to balance two things:
  1. Make sure everyone gets a strong signal (bright light).
  2. Make sure the people in the same group are far enough apart that their light beams don't mix up.
The Result: By reshaping the "seating chart," the system creates clear, separate paths for the light. This restores the ability to whisper secrets securely, even in a crowded room.

5. The Math Behind the Magic

The paper also details two different mathematical "tools" (algorithms) to figure out exactly how to aim the light beams once the seating is arranged:

Tool A (CCCP): A step-by-step method that tweaks the angles until it finds a good solution.
Tool B (CCCP-SDR): A more robust method that uses a different mathematical shortcut to handle complex situations, especially when there are many lights and many users.

The Bottom Line

The paper proves that in a world of light-based internet:

Proximity is the enemy: If users are too close, security breaks down.
Power isn't the answer: Turning up the brightness doesn't fix the security leak caused by crowding.
Organization is key: The best solution is to proactively group users and lights in a way that keeps them "spatially distinct."

By using this "Smart Seating Chart" strategy, the system can significantly outperform older methods, keeping secrets safe even when the room is packed tight.

Technical Summary: Secure RSMA-based Visible Light Networks under Spatial Correlation

Problem Statement
This paper investigates the secrecy sum rate (SSR) of Rate-Splitting Multiple Access (RSMA)-based Visible Light Communication (VLC) systems operating in indoor environments. The study focuses on a worst-case security model where legitimate users act as potential internal eavesdroppers, capable of intercepting private data streams intended for other users. A critical challenge identified is spatial correlation, quantified by Channel Similarity (CS). In dense VLC deployments, users located in close proximity or symmetric positions exhibit highly correlated channel vectors. This correlation reduces the effective rank of the channel matrix, thereby collapsing the spatial Degrees of Freedom (DoF) required for secure precoding. The authors argue that under high CS conditions, conventional beamforming and power allocation strategies fail to suppress information leakage, leading to a "secrecy-performance ceiling" regardless of transmit power increases.

Methodology
The paper proposes a two-pronged approach to address the non-convex optimization problem of maximizing SSR under amplitude and power constraints:

Precoding Optimization:
The authors formulate an SSR maximization problem that is inherently non-convex due to coupled secrecy rate expressions and RSMA power allocation constraints. To solve this, two suboptimal algorithms are developed:
- CCCP Approach: Utilizes the Convex-Concave Procedure (CCCP) with first-order Taylor approximations to iteratively solve a locally convex surrogate of the problem.
- CCCP-SDR Approach: Combines CCCP with Semidefinite Relaxation (SDR). This method reformulates the problem using matrix variables ( $Q_k = w_k w_k^T$ ) to handle rank-one constraints, subsequently projecting the solution back to a rank-one space.
- Initialization: A Zero-Forcing (ZF) for private streams and Maximum Ratio Transmission (MRT) for common messages initialization strategy is introduced to accelerate convergence and reduce computational overhead.
Channel Similarity Reduction (CSR) Clustering:
To proactively mitigate the geometric limitations imposed by high CS, the paper proposes a CSR clustering framework. This strategy reconfigures the user-to-LED association topology before precoding.
- Formulation: The problem is modeled as a Constrained Multi-Objective Combinatorial Optimization (CMOCO) task. The objectives are to maximize aggregate channel gain (promoting signal strength) and minimize intra-cell channel similarity (preserving spatial DoF).
- Algorithm: A modified Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to find the Pareto-optimal set of user-LED partitions. The framework incorporates integer-based encoding, a Constrained-Domination Principle (CDP) for feasibility, and custom genetic operators (crossover with repair) to handle structural constraints (e.g., minimum users per cell, LED-to-user ratios).
- Selection: A specific operating point is selected from the Pareto front by normalizing objectives and maximizing a joint quality score that balances channel gain and low correlation.

Key Contributions

Problem Formulation: The authors formulate the SSR maximization for multi-user MISO VLC systems under an internal eavesdropping model, explicitly accounting for RSMA power allocation and VLC amplitude constraints.
Algorithmic Solutions: Two efficient precoding schemes (CCCP and CCCP-SDR) are developed to handle the non-convexity of the SSR maximization problem, with the SDR-based approach shown to be more robust for large-scale systems.
Insight on Spatial Correlation: The work demonstrates that high CS fundamentally reduces the effective rank of the channel matrix, creating a secrecy performance ceiling that cannot be overcome by power allocation alone.
CSR Clustering Framework: A novel clustering strategy is proposed that jointly partitions users and LEDs to minimize intra-cell correlation while maximizing channel gain. This is the first work to explicitly investigate secrecy-aware clustering in RSMA-based VLC systems.
Performance Validation: Extensive simulations validate that the CSR framework significantly outperforms conventional user-centric clustering and non-clustering baselines, particularly in dense networks with strong spatial correlation.

Results
Numerical results indicate that:

Convergence: The CCCP-SDR approach converges faster than the standard CCCP method in large-scale systems (e.g., $N_T=16$ LEDs) and maintains lower execution times.
Impact of CS: As CS increases from 0.2 to 0.9, the maximum SSR drops significantly (from ~13.4 to ~8.7 bps/Hz), confirming the detrimental effect of spatial correlation.
RSMA Adaptability: RSMA partially alleviates DoF deficiency by adaptively shifting power to the common stream when spatial DoF is constrained, though this has limits.
Clustering Efficacy: The proposed CSR-clustering strategy achieves a secrecy sum rate gain of approximately 2 bps/Hz compared to conventional distance-based clustering (C-UCC) and significantly outperforms non-clustering schemes. It effectively restores spatial separability, allowing the system to bypass the secrecy saturation caused by geometry-induced correlation.
FOV Impact: A wider Field of View (FOV) increases channel similarity and degrades SSR, with a notable decoupling effect observed where SSR continues to decline even after CS saturation.

Significance
The paper claims that its primary significance lies in addressing the fundamental geometric limitations of VLC systems that are often overlooked in favor of external reconfiguration (e.g., RIS). By demonstrating that high spatial correlation fundamentally limits the transmitter's ability to suppress interference, the authors argue for proactive system architecture reconfiguration. The proposed CSR framework provides a mechanism to reshape the effective channel geometry, thereby restoring the spatial DoF necessary for robust secure transmission. This approach is presented as essential for enabling reliable and secure RSMA-based VLC in future dense 6G indoor networks where user proximity and channel correlation are inevitable.