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arxiv: 2605.03976 · v1 · submitted 2026-05-05 · 📡 eess.SP

Modeling and Modulation Optimization for OWC Limited by Electronic and Photonic Bandwidth

Xiaochen Liu , Jean-Paul M. G. Linnartz , Thiago E. B. Cunha This is my paper

Pith reviewed 2026-05-07 13:49 UTC · model grok-4.3

classification 📡 eess.SP
keywords optical wireless communicationDCO-OFDMbandwidth limitationgain-to-noise ratiopole-zero transfer functionLagrangian optimizationmodulation optimization
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The pith

In optical wireless links limited by component bandwidths, a multi-stage pole-zero model of the gain-to-noise ratio allows optimized DCO-OFDM spectra to deliver higher throughput at frequencies above the 3 dB point.

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

The authors model the frequency-dependent limitations from electronic and photonic components in optical wireless communication as a low-pass M-zero N-pole transfer function for the gain-to-noise ratio. They then use Lagrangian optimization to shape the power spectral density of DCO-OFDM signals, enabling effective modulation beyond the conventional 3 dB bandwidth cutoff. Numerical comparisons show that incorporating multiple stages in the model improves the resulting throughput when applied to real measured and simulated responses. This matters for OWC because hardware components, not spectrum rules, set the practical speed limits, so better modeling can extract more capacity without new hardware.

Core claim

The paper establishes that expressing the end-to-end GNR of an OWC link as an M-zero N-pole low-pass function permits a Lagrangian-based optimization of the DCO-OFDM signal PSD that maximizes throughput for a given maximum modulation frequency, and that a multi-stage version of this model, which accounts for successive component limitations, yields superior performance compared to simpler models when optimizing over theoretical, measured, and simulated GNR profiles.

What carries the argument

The M-zero N-pole low-pass transfer function model of the gain-to-noise ratio, which represents the cumulative effect of bandwidth-limited components and supports derivation of the optimal signal power allocation.

Load-bearing premise

The combined frequency response from all components in the OWC link can be sufficiently well approximated by one rational low-pass transfer function with M zeros and N poles.

What would settle it

A hardware experiment that measures the actual bit-error rate or throughput achieved with the Lagrangian-optimized PSD on a real OWC link and compares it to the rate predicted by the model; if the measured gain over baseline allocations is much smaller than expected, the modeling assumption would be falsified.

Figures

Figures reproduced from arXiv: 2605.03976 by Jean-Paul M. G. Linnartz, Thiago E. B. Cunha, Xiaochen Liu.

Figure 1
Figure 1. Figure 1: OWC system components and their corresponding frequency characteristics (Response (in blue) and GNR (in red) as a function of view at source ↗
Figure 2
Figure 2. Figure 2: Beam Squint for OPA or RIS. Inset: frequency response for view at source ↗
Figure 3
Figure 3. Figure 3: Block diagram of a DCO-OFDM OWC system. diagram of the system is shown in view at source ↗
Figure 4
Figure 4. Figure 4: (a) An example of a non-monotonically low-pass view at source ↗
Figure 5
Figure 5. Figure 5: Two bit-loading scenarios and their corresponding lookup view at source ↗
Figure 6
Figure 6. Figure 6: Characteristics of signal response, noise PSD, and GNR: A comparison of the fitted pole-zero functions (red curves) against the view at source ↗
Figure 8
Figure 8. Figure 8: (a) Result of optimized signal PSD optimized by NT and view at source ↗
read the original abstract

In contrast to radio frequency (RF), where the modulation bandwidth is restricted by regulations to avoid interference, the available bandwidth in optical wireless communication (OWC) is primarily constrained by system components. To investigate their frequency characteristics, we review the bandwidth limitations of components in the PHY layer of OWC links. Such limitations typically contribute to a decay in the frequency profile of the gain-to-noise ratio (GNR), which can be modeled by a pole-zero transfer function that is generally low-pass. To boost performance, we optimize the signal power spectral density (PSD) of DC-biased optical orthogonal frequency-division multiplexing (DCO-OFDM) which allows for modulation beyond the 3-dB end-to-end bandwidth. We express the Lagrangian-optimized throughput versus the maximum modulation frequency, for an M-zero N-pole low-pass GNR optical link. For optimization implementation, we compare a novel Newton-based algorithm with a newly accelerated version of the Hughes-Hartogs (HH) algorithm, to find the (near-) optimal signal spectrum for theoretical, measured and simulated GNR responses. As demonstrated numerically, employing the proposed multi-stage response model for optimization improves performance in dealing with the successive bandwidth limitations.

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

2 major / 2 minor

Summary. The paper claims that successive electronic and photonic bandwidth limits in OWC produce a composite GNR decay that can be represented by a single M-zero N-pole low-pass rational transfer function. Using this model, the authors derive a Lagrangian optimization of the DCO-OFDM PSD that maximizes throughput beyond the 3 dB bandwidth and implement it via a Newton-based solver and an accelerated Hughes-Hartogs algorithm. Numerical experiments on theoretical, measured, and simulated GNR profiles are said to demonstrate performance gains from the proposed modeling and optimization approach.

Significance. If the M-zero N-pole approximation remains sufficiently accurate for real composite responses, the framework offers a systematic way to allocate power across subcarriers in bandwidth-limited OWC links without requiring new hardware. The explicit comparison of two optimization algorithms and the use of measured responses are positive features. The work sits at the intersection of device modeling and information-theoretic resource allocation, which is relevant to eess.SP.

major comments (2)
  1. [numerical results / optimization formulation] The central claim that the optimized PSD remains near-optimal rests on the fidelity of the single M-zero N-pole GNR model to the true end-to-end response. The manuscript does not report quantitative fitting residuals, maximum deviation, or sensitivity of the resulting throughput to model mismatch (e.g., unmodeled resonances or non-minimum-phase zeros) in the numerical-results section. Without these metrics it is impossible to judge whether the reported gains survive when the model is replaced by the actual measured or simulated GNR.
  2. [Lagrangian optimization section] The Lagrangian derivation of throughput versus maximum modulation frequency assumes the GNR is exactly the rational low-pass function; any systematic deviation therefore propagates directly into the power allocation. The paper should supply an explicit error-propagation or robustness analysis (perhaps via Monte-Carlo perturbation of pole/zero locations) to bound the sub-optimality gap.
minor comments (2)
  1. [modeling section] Notation for the GNR transfer function (H(f) or GNR(f)) and the number of zeros/poles (M, N) should be introduced once and used consistently; occasional switches between “multi-stage response” and “M-zero N-pole model” are distracting.
  2. [algorithm comparison] The description of the accelerated Hughes-Hartogs algorithm would benefit from a short pseudocode block or explicit step-by-step comparison with the standard HH procedure so that readers can reproduce the acceleration.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which highlight important aspects of model validation and robustness. We address each major comment below and will incorporate the suggested analyses in the revised manuscript to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [numerical results / optimization formulation] The central claim that the optimized PSD remains near-optimal rests on the fidelity of the single M-zero N-pole GNR model to the true end-to-end response. The manuscript does not report quantitative fitting residuals, maximum deviation, or sensitivity of the resulting throughput to model mismatch (e.g., unmodeled resonances or non-minimum-phase zeros) in the numerical-results section. Without these metrics it is impossible to judge whether the reported gains survive when the model is replaced by the actual measured or simulated GNR.

    Authors: We agree that quantitative fitting metrics and sensitivity analysis are necessary to fully substantiate the near-optimality claim. In the revised manuscript we will add, in the numerical-results section, explicit fitting residuals (RMSE and maximum absolute deviation) between the fitted M-zero N-pole model and the measured/simulated GNR profiles. We will also include a sensitivity study that perturbs pole/zero locations within the observed fitting uncertainty and recomputes the optimized throughput, thereby quantifying the impact of model mismatch on the reported performance gains. revision: yes

  2. Referee: [Lagrangian optimization section] The Lagrangian derivation of throughput versus maximum modulation frequency assumes the GNR is exactly the rational low-pass function; any systematic deviation therefore propagates directly into the power allocation. The paper should supply an explicit error-propagation or robustness analysis (perhaps via Monte-Carlo perturbation of pole/zero locations) to bound the sub-optimality gap.

    Authors: We concur that an explicit robustness analysis is warranted. The revised manuscript will contain a Monte-Carlo perturbation experiment in which the pole and zero locations of the M-zero N-pole model are randomly varied according to the fitting residuals obtained from the measured and simulated channels. The resulting distribution of optimized throughputs will be used to bound the sub-optimality gap relative to the ideal rational-model case, confirming that the performance improvements remain significant under realistic model deviations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from assumed GNR model

full rationale

The paper reviews component bandwidth limits, posits an M-zero N-pole low-pass GNR transfer function as the end-to-end model, and derives the Lagrangian-optimized DCO-OFDM PSD allocation directly from that model to maximize throughput. Numerical comparisons of Newton and accelerated Hughes-Hartogs algorithms are performed on theoretical, measured, and simulated GNR responses using the same assumed functional form. No claimed result reduces by construction to a fitted parameter from the evaluation data, no self-citation supplies a load-bearing uniqueness theorem or ansatz, and the performance gain is shown under the explicit model assumptions rather than being forced by re-use of the same inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that component bandwidth limits combine into a low-pass pole-zero GNR model; no free parameters are explicitly named in the abstract but M and N are chosen per link.

free parameters (1)
  • M and N (number of zeros and poles)
    Determined from component characterization or fitting; directly sets the shape of the GNR used in the Lagrangian.
axioms (1)
  • domain assumption The frequency profile of the gain-to-noise ratio can be modeled by a pole-zero transfer function that is generally low-pass.
    Invoked to justify the multi-stage response model and the optimization beyond the 3 dB point.

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