Secrecy Sum Rate Maximization for OIRS-Aided Visible Light Communications with Confidential Messages

Technical Summary: Secrecy Sum Rate Maximization for OIRS-Aided Visible Light Communications with Confidential Messages

Problem Statement
This paper addresses the challenge of securing multi-user visible light communication (VLC) systems operating under physical line-of-sight (LoS) blockages and internal eavesdropping threats. While optical intelligent reflecting surfaces (OIRS) offer a solution to bypass physical obstructions by establishing controllable non-LoS (NLoS) links, their deployment introduces new security complexities. Specifically, the additional reflection paths created by OIRS can inadvertently strengthen wiretap channels among legitimate users (internal eavesdropping), thereby increasing the risk of information leakage. Existing literature often focuses on improving sum rate or spectral efficiency, or addresses physical layer security (PLS) only against external eavesdroppers while neglecting LoS blockages. This work formulates a joint optimization problem to maximize the Secrecy Sum Rate (SSR) by simultaneously designing the transmission precoder and the assignment of OIRS units, accounting for both physical blockages and confidential message transmission among users.

Methodology
The core of the proposed approach is a joint optimization framework that co-designs the transmission precoding matrix ($W$) and the OIRS assignment tensor ($F$). The problem is initially formulated as a Mixed-Integer Non-Linear Program (MINLP), which is highly non-convex due to:

1. Binary Constraints: The OIRS assignment variables are binary (indicating whether a specific unit reflects a signal from a specific LED to a specific user).
2. Coupled Variables: The secrecy rate expressions involve non-linear interactions between the continuous precoding vectors and the discrete assignment variables.
3. Non-Concave Objective: The secrecy rate function itself is non-concave.

To render the problem tractable, the authors employ an Alternating Optimization (AO) framework combined with the Concave-Convex Procedure (CCCP) and first-order Taylor approximations. The methodology proceeds as follows:

• Problem Reformulation: The original problem is transformed by introducing slack variables to decouple the objective function and constraints, creating a new formulation ($P1$).
• Relaxation and Penalty: The binary constraints on the OIRS assignment are relaxed to continuous bounds $[0, 1]$, and a penalty term is added to the objective function to encourage convergence toward binary solutions.
• Iterative Solving:
  • OIRS Assignment Subproblem: With a fixed precoder, the assignment problem is solved iteratively. Non-convex constraints and the penalty term are linearized using first-order Taylor approximations at each iteration, converting the subproblem into a convex form solvable by standard tools (e.g., CVX).
  • Precoder Subproblem: With a fixed OIRS assignment, the precoding matrix is updated similarly using CCCP and Taylor approximations to handle non-convex constraints.
• Convergence: The two subproblems are solved alternately until the overall objective function converges.

Key Contributions

• Joint Optimization Framework: The paper proposes a novel joint optimization scheme for OIRS-aided VLC that simultaneously handles LoS blockages and internal eavesdropping, a scenario not fully addressed in prior works.
• Algorithmic Development: An efficient AO-based algorithm is developed to solve the resulting intractable MINLP. The integration of CCCP and first-order Taylor approximations allows for the handling of coupled binary and continuous variables.
• System Modeling: The study incorporates a realistic system model where OIRS units serve only one user at a time due to the law of specular reflection, and explicitly models the impact of physical obstacles on channel availability.

Simulation Results
Numerical simulations were conducted in a 5m $\times$ 5m $\times$ 3m indoor environment with four LEDs and multiple users, including scenarios with one and two blocked users.

• Convergence: The proposed AO-based scheme demonstrates reliable convergence. The relative error of the objective value decreases monotonically, reaching the convergence threshold ($10^{-4}$) within a few iterations (3 to 8 iterations depending on the number of OIRS units).
• SSR Gains: Increasing the number of OIRS reflecting units yields significant SSR improvements. For instance, increasing units from 18 to 160 raised the SSR from approximately 1 to 3.6 bps/Hz in the one-blocked-user scenario, and from 1.5 to 4.7 bps/Hz in the two-blocked-user scenario.
• Blockage Mitigation: The results confirm that the proposed scheme effectively maintains high secrecy performance even under severe physical blockages by leveraging OIRS to establish alternative NLoS links.
• Internal Eavesdropping Observation: Interestingly, the simulations showed that scenarios with more blocked users (relying more heavily on OIRS) achieved higher SSR than those with fewer blocked users. The authors attribute this to the simplified reflection model where OIRS forms highly directional specular beams, reducing inter-user leakage compared to wide-coverage LoS links, though they note that actual optical propagation is more complex.

Significance and Claims
The paper claims that the proposed scheme provides a robust solution for enhancing physical layer security in indoor wireless networks where VLC is susceptible to physical obstructions. By demonstrating that increasing the number of OIRS units provides substantial SSR gains, the work highlights the potential of OIRS-assisted VLC for secure multi-user communications. The authors position their work as a necessary step beyond existing studies that either ignore blockages or fail to address internal eavesdropping in the context of OIRS-assisted systems. They conclude that their approach successfully balances the trade-off between connectivity restoration (via OIRS) and security enhancement (via joint precoding and assignment optimization).