Visible Light Indoor Positioning with a Single LED and Distributed Single-Element OIRS: An Iterative Approach with Adaptive Beam Steering

TL;DR

The paper tackles indoor localization in visible light using a single LED anchor and distributed single-element OIRSs. It introduces an indirect two-step framework with closed-form ML estimators for LoS and NLoS distances, plus a relaxed ML variant, and an iterative localization algorithm that uses adaptive beam steering to reorient OIRSs toward the PD without prior position knowledge. The key contributions are CRLB derivations for distance and position, a low-complexity IWLS-based position estimator with path-dependent weighting, and extensive simulations showing mm-level accuracy and near-PEB performance with significantly reduced computational cost compared to direct ML methods. The results demonstrate robust localization under OIRS misalignment and provide practical guidance for deploying OIRS-assisted VLC systems in indoor environments.

Abstract

The integration of Optical Intelligent Reflective Surfaces (OIRSs) into Visible Light Communication (VLC) systems is gaining momentum as a valid alternative to RF technologies, harnessing the existing lighting infrastructures and the vast unlicensed optical spectrum to enable higher spectral efficiency, improved resilience to Line-of-Sight (LoS) blockages, and enhanced positioning capabilities. This paper investigates the problem of localizing a low-cost Photo Detector (PD) in a VLC-based indoor environment consisting of only a single Light Emitting Diode (LED) as an active anchor, and multiple spatially distributed single-element OIRSs. We formulate the problem within an indirect, computationally efficient localization framework: first, the optimal Maximum Likelihood (ML) estimators of the LoS and Non-Line-of-Sight (NLoS) distances are derived, using a suitable OIRS activation strategy to prevent interferences. To overcome the grid-based optimization required by the ML NLoS estimator, we devise a novel algorithm based on an unstructured noise variance transformation, which admits a closed-form solution. The set of estimated LoS/NLoS distances are then used within a low-complexity localization algorithm combining an Iterative Weighted Least Squares (IWLS) procedure, whose weights are set according to the inverse of the Cramér-Rao Lower Bound (CRLB), with an adaptive beam steering strategy that allows the OIRSs network to dynamically align with the PD, without any prior knowledge of its position. Accordingly, we derive the CRLB for both LoS/NLoS distance estimation and PD position estimation. Simulation results demonstrate the effectiveness of our approach in terms of localization accuracy, robustness against OIRSs misalignment conditions, and low number of iterations required to attain the theoretical bounds.

Figures (11)

• Figure 1: (a) Representative scenario of -based indoor positioning supported by a single and a network of $N$ distributed ; (b) Orientation control of the $n$-th via its vertical tilt angle $\beta_n$ and horizontal tilt angle $\alpha_n$ (the green dotted contour indicates the initial orientation of the ).
• Figure 2: RMSE of the ML and RML distance estimators, along with the corresponding DEB, as a function of the SNR, for different values of $K$.
• Figure 3: RMSE of the ML and RML NLoS distance estimators, along with the corresponding DEB, for different values of $K_1$, as a function of the azimuthal angle representing the change in the position along a circular arc.
• Figure 4: RMSE of the ML and RML NLoS distance estimators, along with the corresponding DEB, for different values of $K_1$, as a function of the horizontal distance between the and the .
• Figure 5: RMSE of ML and RML NLoS distance estimators, compared against the DEB, for different values of $K_1$, as a function of the SNR with (a) initial orientation of and (b) perfectly steered toward the .