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Visible Light Positioning with Intelligent Reflecting Surfaces under Mismatched Orientations

Issifu Iddrisu, Sinan Gezici

TL;DR

This paper addresses the localization accuracy of visible-light positioning with IRSs when IRS element orientations are imperfectly known. It introduces a misspecified CRLB (MCRB) framework and a mismatched ML (MML) estimator to quantify and characterize performance loss due to orientation mismatches, and it compares these with the conventional ML/CRB under perfect orientation. The main findings show that orientation mismatches can cause substantial degradation at high SNR, emphasizing the need to model and mitigate misalignment in IRS-VLP systems. The work provides analytical bounds and an estimators’ framework that can guide robust system design and IRS configuration in indoor VLC environments.

Abstract

Accurate localization can be performed in visible light systems in non-line-of-sight (NLOS) scenarios by utilizing intelligent reflecting surfaces (IRSs), which are commonly in the form of mirror arrays with adjustable orientations. When signals transmitted from light emitting diodes (LEDs) are reflected from IRSs and collected by a receiver, the position of the receiver can be estimated based on power measurements by utilizing the known parameters of the LEDs and IRSs. Since the orientation vectors of IRS elements (mirrors) cannot be adjusted perfectly in practice, it is important to evaluate the effects of mismatches between desired and true orientations of IRS elements. In this study, we derive the misspecified Cramer-Rao lower bound (MCRB) and the mismatched maximum likelihood (MML) estimator for specifying the estimation performance and the lower bound in the presence of mismatches in IRS orientations. We also provide comparisons with the conventional maximum likelihood (ML) estimator and the CRB in absence of orientation mismatches for quantifying the effects of mismatches. It is shown that orientation mismatches can result in significant degradation in localization accuracy at high signal-to-noise ratios.

Visible Light Positioning with Intelligent Reflecting Surfaces under Mismatched Orientations

TL;DR

This paper addresses the localization accuracy of visible-light positioning with IRSs when IRS element orientations are imperfectly known. It introduces a misspecified CRLB (MCRB) framework and a mismatched ML (MML) estimator to quantify and characterize performance loss due to orientation mismatches, and it compares these with the conventional ML/CRB under perfect orientation. The main findings show that orientation mismatches can cause substantial degradation at high SNR, emphasizing the need to model and mitigate misalignment in IRS-VLP systems. The work provides analytical bounds and an estimators’ framework that can guide robust system design and IRS configuration in indoor VLC environments.

Abstract

Accurate localization can be performed in visible light systems in non-line-of-sight (NLOS) scenarios by utilizing intelligent reflecting surfaces (IRSs), which are commonly in the form of mirror arrays with adjustable orientations. When signals transmitted from light emitting diodes (LEDs) are reflected from IRSs and collected by a receiver, the position of the receiver can be estimated based on power measurements by utilizing the known parameters of the LEDs and IRSs. Since the orientation vectors of IRS elements (mirrors) cannot be adjusted perfectly in practice, it is important to evaluate the effects of mismatches between desired and true orientations of IRS elements. In this study, we derive the misspecified Cramer-Rao lower bound (MCRB) and the mismatched maximum likelihood (MML) estimator for specifying the estimation performance and the lower bound in the presence of mismatches in IRS orientations. We also provide comparisons with the conventional maximum likelihood (ML) estimator and the CRB in absence of orientation mismatches for quantifying the effects of mismatches. It is shown that orientation mismatches can result in significant degradation in localization accuracy at high signal-to-noise ratios.
Paper Structure (11 sections, 51 equations, 4 figures)

This paper contains 11 sections, 51 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Estimation under Mismatched Orientations: MML and MCRB
  4. MML Estimator
  5. MCRB
  6. Derivation of the Pseudo-True Parameter
  7. MCRB Derivation
  8. Numerical Results
  9. Concluding Remarks
  10. Appendices
  11. First and Second Derivatives of Channel Coefficient

Figures (4)

  • Figure 1: A depiction of the IRS elements on the walls of the room.
  • Figure 2: Performance of the MML estimator versus k for $\sigma^2 \in \{10^{-15},10^{-16} ,10^{-17}\}$ in NLOS scenario when the VLC receiver is positioned at (0.5, 0.5, 0.85) meters.
  • Figure 3: RMSE performance of the MML estimator and the theoretical limits versus $10\log_{10}(1/\sigma^2)$ for $\rm{k} \in \{0.5, 1\}$ in NLOS scenario when the VLC receiver is positioned at (0.5, 0.5, 0.85) meters.
  • Figure 4: RMSE performance of the MML estimator and the theoretical limits versus $10\log_{10}(1/\sigma^2)$ for $\rm{k} \in \{0.25, 1\}$ in NLOS scenario and the VLC receiver is positioned at (0.5, 0.5, 0.85) meters.