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arxiv: 2606.08774 · v1 · pith:BDHBZNLWnew · submitted 2026-06-07 · 💻 cs.IT · math.IT

Non-Uniform Codebook Design for Optical IRS-Assisted VLC Systems

Rashid Iqbal , Dimitrios Bozanis , Dimitrios Tyrovolas , Christos K. Liaskos , Muhammad Ali Imran , George K. Karagiannidis , Hanaa Abumarshoud This is my paper

Pith reviewed 2026-06-27 17:38 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords optical IRSvisible light communicationcodebook designnon-uniform codebookgeometric opticsbeam steeringVLC coverage
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The pith

Non-uniform codebooks per IRS element achieve uniform user-plane coverage with fewer codewords than uniform angular designs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Uniform codebooks with fixed angular steps fail to deliver uniform coverage on the user plane in optical IRS-assisted VLC systems because the mapping from steering angles to reflection locations is nonlinear. The paper proposes a geometric-optics method that builds a separate codebook for each IRS element based on its position, spacing the reflected beams more evenly across the plane. This yields better spatial uniformity and requires fewer total codewords. Simulations further show that sweep-angle resolution influences accuracy more than tilt-angle resolution.

Core claim

The proposed geometric-optics-based non-uniform codebook design constructs an individual codebook for each IRS element according to its geometric position, so that the reflected beams are distributed more uniformly over the user plane. The codebook accuracy is evaluated using the Frobenius norm of the channel error matrix.

What carries the argument

Per-element geometric-optics non-uniform codebook that compensates the nonlinear angle-to-position mapping

If this is right

  • The design provides more uniform spatial mapping with fewer codewords than the uniform codebook.
  • Sweep-angle resolution has a stronger effect on the codebook accuracy than the tilt-angle resolution.
  • Finite offline codebooks become practical, avoiding repeated real-time optimisation of mirror orientations.
  • Coverage of indoor VLC systems improves through more even beam distribution on the user plane.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The per-element approach could lower the computational cost of deploying OIRS in real VLC environments by enabling fully offline codebooks.
  • Similar geometric compensation might apply to other nonlinear beam-steering tasks in optical wireless links.
  • Field tests would need to check whether non-ideal mirror properties or multipath effects erode the simulated uniformity gains.

Load-bearing premise

The nonlinear mapping from steering angles to reflection locations on the user plane can be compensated by constructing individual codebooks per IRS element based on geometric position using geometric optics.

What would settle it

A simulation or measurement in which the Frobenius norm of the channel error matrix is not smaller and spatial uniformity is not improved under the proposed per-element non-uniform codebooks relative to a uniform angular codebook.

Figures

Figures reproduced from arXiv: 2606.08774 by Christos K. Liaskos, Dimitrios Bozanis, Dimitrios Tyrovolas, George K. Karagiannidis, Hanaa Abumarshoud, Muhammad Ali Imran, Rashid Iqbal.

Figure 1
Figure 1. Figure 1: Optical IRS System Model with Codebook Design [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Frobenius norm ∥∆H∥F versus ∆φ [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Frobenius norm ∥∆H∥F versus ∆ϑ. stronger impact on performance because it determines how closely the codewords are spaced along each ring. A larger ∆φ results in fewer points along the arc, which leads to a higher mismatch between the desired and actual reflection directions. Therefore, the results indicate that improving the angular resolution along the rings is more important for reducing the error, whil… view at source ↗
Figure 4
Figure 4. Figure 4: illustrates the element-dependent spatial mapping of the proposed non-uniform codebook for a 3 × 3 OIRS. Since each reflecting element occupies a different position on the OIRS plane, the incident direction, reference sweep angle, and generated steering codewords are computed separately for each element. Consequently, the reflected beam-hit points on the user plane are shifted differently for different ele… view at source ↗
Figure 5
Figure 5. Figure 5: Uniform versus non-uniform codebook. represents how many times a location on the user plane is reached by the reflected beams from different codewords and different IRS elements. It can be observed that the hit density is distributed over the entire area without large empty regions, which indicates that the proposed non-uniform codebook provides good spatial coverage when all elements operate together. In … view at source ↗
Figure 6
Figure 6. Figure 6: Aggregated Hit Density at z = 1.0 m. V. CONCLUSION This paper proposes a geometric-optics based non-uniform codebook design for OIRS-assisted VLC systems. Unlike a uniform codebook, the proposed design accounts for the nonlinear mapping between steering angles and beam reflec￾tion points on the user plane, which leads to more balanced spatial coverage. The method has been further extended to a multi-elemen… view at source ↗
read the original abstract

Optical intelligent reflecting surfaces (OIRS) can improve the coverage of indoor visible light communication (VLC) systems, however, practical deployment requires a finite offline codebook to avoid repeated real-time optimisation of mirror orientations. A uniform codebook with fixed angular steps does not provide uniform coverage on the user plane, because the mapping from steering angles to reflection locations on the user plane is nonlinear. To address this problem, this paper proposes a geometric-optics-based non-uniform codebook design for OIRS-assisted VLC systems. The proposed method constructs an individual codebook for each IRS element according to its geometric position, so that the reflected beams are distributed more uniformly over the user plane. The codebook accuracy is evaluated using the Frobenius norm of the channel error matrix. Simulation results show that the proposed design provides more uniform spatial mapping with fewer codewords than the uniform codebook, and that the sweep-angle resolution has a stronger effect on the codebook accuracy than the tilt-angle resolution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a geometric-optics-based non-uniform codebook design for optical intelligent reflecting surfaces (OIRS) in visible light communication (VLC) systems. Individual codebooks are constructed per IRS element according to its geometric position to compensate for the nonlinear mapping from steering angles to reflection locations on the user plane. Codebook accuracy is quantified by the Frobenius norm of the channel error matrix. Simulations are reported to demonstrate that the non-uniform design achieves more uniform spatial mapping with fewer codewords than a uniform angular grid and that sweep-angle resolution affects accuracy more than tilt-angle resolution.

Significance. If the reported gains prove robust, the work supplies a concrete, offline method for practical OIRS codebook design that directly targets the nonuniform coverage problem in indoor VLC. The per-element geometric construction and the explicit comparison of angular resolutions constitute targeted engineering contributions that could reduce reliance on real-time mirror optimization.

major comments (1)
  1. [Simulation Results] Simulation section: both the non-uniform codebook construction and the Monte-Carlo evaluation of the Frobenius-norm channel error employ the identical geometric-optics ray model. Consequently the reported uniformity advantage is shown only under the forward model used to derive the codebook; no cross-check against wave-optics effects (diffraction, finite-aperture scattering) is described. This is load-bearing for the central claim that the design yields practically superior coverage.
minor comments (2)
  1. [Abstract] The abstract and introduction would benefit from explicit statement of the number of IRS elements, room dimensions, and LED/receiver parameters used in the simulations.
  2. [Proposed Design] Notation for the per-element codebook construction (e.g., how the nonlinear angle-to-position inversion is discretized) should be introduced with a short equation or pseudocode block for reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment. We provide a point-by-point response below.

read point-by-point responses

  1. Referee: Simulation section: both the non-uniform codebook construction and the Monte-Carlo evaluation of the Frobenius-norm channel error employ the identical geometric-optics ray model. Consequently the reported uniformity advantage is shown only under the forward model used to derive the codebook; no cross-check against wave-optics effects (diffraction, finite-aperture scattering) is described. This is load-bearing for the central claim that the design yields practically superior coverage.

    Authors: We acknowledge the observation. The codebook construction and error evaluation are both performed under the geometric-optics ray model because the non-uniform angular steps are derived directly from the closed-form geometric mapping between steering angles and reflection points on the user plane. This model is standard in VLC and OIRS literature when mirror apertures are large relative to the optical wavelength. We agree that the absence of a wave-optics cross-check (e.g., diffraction or finite-aperture scattering) limits the strength of the practical-superiority claim. In the revision we will add an explicit paragraph in Section IV (or a new subsection) stating the geometric-optics assumptions, their validity regime, and the fact that wave-optics verification remains future work. This revision clarifies scope without changing the reported numerical results. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes a geometric-optics-based non-uniform codebook constructed per IRS element to invert the known nonlinear angle-to-location mapping, then evaluates accuracy via the independent Frobenius norm of the channel error matrix and compares against a uniform angular grid. No equations, self-citations, or fitted parameters are shown to reduce the reported uniformity gain or resolution effects to the inputs by construction. The design method and Monte-Carlo validation remain self-contained against external benchmarks such as wave-optics models or measurements, which are outside the paper's scope but do not create internal circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no specific free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.1-grok · 5729 in / 1053 out tokens · 25132 ms · 2026-06-27T17:38:44.154542+00:00 · methodology

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Reference graph

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