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arxiv: 2606.20222 · v1 · pith:D6GVJL5Dnew · submitted 2026-06-18 · 📡 eess.SP

Reliable ORIS-assisted FSO Communications via HARQ

Georgios D. Chondrogiannis , Athanasios P. Chrysologou , Vasilis K. Papanikolaou , Alexandros-Apostolos A. Boulogeorgos , Nestor D. Chatzidiamantis , Robert Schober This is my paper

Pith reviewed 2026-06-26 15:45 UTC · model grok-4.3

classification 📡 eess.SP
keywords outage probabilityHARQORISFSOpointing errorsatmospheric turbulenceretransmissiondiversity order
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The pith

A tractable reflected-channel model yields closed-form outage expressions for HARQ in ORIS-assisted FSO links.

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

The paper constructs a statistical description of the end-to-end reflected path that folds atmospheric turbulence, surface-induced pointing errors, and geometric loss into a single tractable distribution. Using this description it derives exact outage-probability formulas for Chase-combining HARQ and tight upper bounds for incremental-redundancy HARQ that hold for any finite number of retransmission rounds. High-SNR asymptotics then supply the diversity order of each scheme, while separate expressions track the average number of transmission attempts and the conditional delay given success. These results let link designers quantify reliability gains from retransmission without repeated Monte-Carlo runs for every turbulence or jitter setting.

Core claim

The joint statistical model of the Tx-ORIS-Rx reflected channel permits closed-form outage probability expressions for HARQ with Chase combining and analytical upper bounds for HARQ with incremental redundancy that remain valid for an arbitrary maximum number of transmission rounds; the same model supplies the diversity order at high SNR and the mean number of rounds needed for successful decoding.

What carries the argument

The tractable statistical model for the Tx-ORIS-Rx reflected channel that jointly accounts for atmospheric turbulence, ORIS-induced pointing errors, and geometric attenuation.

If this is right

  • HARQ with Chase combining admits exact closed-form outage probability for any finite number of rounds.
  • HARQ with incremental redundancy admits analytical outage upper bounds valid for arbitrary round limits.
  • Both protocols exhibit explicit diversity orders obtained from the high-SNR expansion of the outage expressions.
  • The mean number of transmission rounds and the conditional mean given success fully characterize the delay of the truncated HARQ process.
  • Incremental-redundancy HARQ yields lower outage and lower average delay than Chase-combining HARQ even with few retransmissions.

Where Pith is reading between the lines

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

  • The same channel model could be reused to obtain outage expressions for other combining or coding schemes without re-deriving the underlying distribution.
  • Designers could choose the number of allowed retransmissions by balancing the closed-form outage target against the derived mean-round expressions.
  • The framework supplies a benchmark against which measured outage data from real ORIS deployments could be compared.
  • Similar statistical reductions might be attempted for visible-light or infrared surface-assisted links that share the same impairment types.

Load-bearing premise

The reflected channel admits a single tractable distribution that still incorporates turbulence, pointing errors, and loss in a form allowing closed-form outage derivations.

What would settle it

Monte Carlo simulations of the same channel parameters that produce outage curves visibly different from the derived closed-form expressions or upper bounds.

Figures

Figures reproduced from arXiv: 2606.20222 by Alexandros-Apostolos A. Boulogeorgos, Athanasios P. Chrysologou, Georgios D. Chondrogiannis, Nestor D. Chatzidiamantis, Robert Schober, Vasilis K. Papanikolaou.

Figure 1
Figure 1. Figure 1: Illustration of ORIS-assisted FSO system with HARQ. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: PDF of the ORIS-enabled e2e channel. by (9) and (10). For simulation, we plot the histogram of the channel coefficient h for 108 samples and 100 bins given by (2). More specifically, [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: OP of HARQ-CC and HARQ-IR versus transmit SNR, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: OP of HARQ-CC and HARQ-IR versus common sway level for the Tx, Rx, and ORIS. Different numbers of maximum transmissions are plotted under fog conditions with transmit SNR, γ¯ = 60 dB. a smaller retransmission budget can even outperform HARQ￾CC with a larger one. For example, HARQ-IR with M = 3 can achieve a lower OP than HARQ-CC with M = 4. This illustrates that the coding-gain advantage of HARQ-IR can par… view at source ↗
Figure 7
Figure 7. Figure 7: Mean number of HARQ rounds versus transmit SNR [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Unconditional and conditional mean HARQ delay [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
read the original abstract

This paper studies a free-space optical (FSO) link assisted by an optical reconfigurable intelligent surface (ORIS) and enhanced by a hybrid automatic repeat request (HARQ) scheme. The ORIS creates a virtual line-of-sight path around obstacles, while HARQ recovers frames corrupted by turbulence, pointing jitter, and geometric loss through retransmission and combining. We first derive a tractable statistical model for the end-to-end transmitter-ORIS-receiver (Tx-ORIS-Rx) reflected channel by jointly accounting for atmospheric turbulence, ORIS-induced pointing errors, and geometric attenuation. Building on these results, we obtain closed-form outage probability (OP) expressions for HARQ with Chase combining (HARQ-CC) and analytical outage upper bounds for HARQ with incremental redundancy (HARQ-IR), valid for an arbitrary maximum number of transmission rounds. We further conduct a high signal-to-noise ratio (SNR) analysis that provides a thorough characterization of the outage behavior and reveals the diversity order of both schemes. In addition, we characterize the delay behavior of the truncated HARQ process through the mean number of transmission rounds and the conditional mean number of rounds given successful decoding. Finally, numerical and Monte Carlo results validate the proposed analysis and show that HARQ substantially improves ORIS-assisted FSO reliability, with HARQ-IR achieving lower outage and delay than HARQ-CC, even for a small number of retransmission rounds.

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 develops a tractable statistical model for the end-to-end Tx-ORIS-Rx channel in an FSO system that jointly incorporates atmospheric turbulence, ORIS-induced pointing errors, and geometric attenuation. Building on this model, it derives closed-form outage probability expressions for HARQ with Chase combining (HARQ-CC) and analytical upper bounds for HARQ with incremental redundancy (HARQ-IR) that hold for an arbitrary number of transmission rounds, performs high-SNR diversity-order analysis, characterizes delay via mean transmission rounds, and validates the results through numerical evaluation and Monte Carlo simulations demonstrating substantial reliability gains from HARQ.

Significance. If the claimed closed-form expressions and diversity orders are rigorously obtained without unstated approximations, the work would supply useful analytical tools for evaluating and optimizing reliability in ORIS-assisted FSO links under realistic impairments, potentially informing the design of retransmission protocols for high-reliability optical wireless systems.

major comments (2)
  1. [HARQ-CC outage probability derivation] The central claim of closed-form OP expressions for HARQ-CC (abstract and the HARQ-CC analysis section) rests on obtaining the CDF of the sum of per-round SNRs under the joint turbulence+pointing+geometric model. While a single-link gain may admit a Meijer-G or Fox-H representation, the distribution of the sum across an arbitrary number of rounds generally does not; the manuscript must explicitly show in the relevant derivation how the sum remains in closed form (or state any moment-matching/bounding step used) rather than implicitly assuming tractability.
  2. [High-SNR analysis] The high-SNR diversity-order results (high-SNR analysis section) are load-bearing for the reliability claims. The diversity order for HARQ-CC should be derived directly from the asymptotic behavior of the sum CDF; any mismatch between the stated diversity order and the actual asymptotic slope of the derived OP expression would undermine the comparison between HARQ-CC and HARQ-IR.
minor comments (2)
  1. [Channel model section] Notation for the joint channel PDF/CDF should be introduced with explicit dependence on the turbulence, pointing, and geometric parameters to improve readability when the expressions are later summed over rounds.
  2. [Numerical results] Figure captions for the Monte Carlo validation plots should state the number of realizations used and the exact parameter values (e.g., turbulence strength, pointing jitter variance) rather than referring only to 'typical' values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the manuscript's contributions. We address each major comment below with point-by-point responses and indicate planned revisions for clarity.

read point-by-point responses

  1. Referee: [HARQ-CC outage probability derivation] The central claim of closed-form OP expressions for HARQ-CC (abstract and the HARQ-CC analysis section) rests on obtaining the CDF of the sum of per-round SNRs under the joint turbulence+pointing+geometric model. While a single-link gain may admit a Meijer-G or Fox-H representation, the distribution of the sum across an arbitrary number of rounds generally does not; the manuscript must explicitly show in the relevant derivation how the sum remains in closed form (or state any moment-matching/bounding step used) rather than implicitly assuming tractability.

    Authors: We thank the referee for highlighting the need for explicit steps. The end-to-end Tx-ORIS-Rx channel is modeled as a product of Gamma-Gamma turbulence, pointing errors, and geometric loss, yielding a Meijer-G PDF/CDF for each round's SNR. For HARQ-CC with i.i.d. rounds, the CDF of the summed SNR is derived via successive convolution; the Meijer-G class is closed under this operation for the specific parameters arising from the joint impairment model, resulting in a single Meijer-G expression for the combined CDF (and thus the OP). No moment-matching or bounding is employed. We will insert the full intermediate convolution steps and the resulting expression in the revised HARQ-CC section to remove any implicit assumptions. revision: partial

  2. Referee: [High-SNR analysis] The high-SNR diversity-order results (high-SNR analysis section) are load-bearing for the reliability claims. The diversity order for HARQ-CC should be derived directly from the asymptotic behavior of the sum CDF; any mismatch between the stated diversity order and the actual asymptotic slope of the derived OP expression would undermine the comparison between HARQ-CC and HARQ-IR.

    Authors: We agree that the diversity order must follow directly from the asymptotic expansion of the sum CDF. In the high-SNR section we start from the small-argument expansion of the single-link Meijer-G CDF (which behaves as γ^δ where δ is the diversity order of the joint channel) and then apply the property that the CDF of the sum of L i.i.d. positive random variables scales as the L-fold product of the individual small-argument terms, yielding diversity order Lδ for HARQ-CC. This is consistent with the closed-form OP expression's high-SNR slope. We will expand the derivation with the explicit asymptotic steps and confirm numerical agreement with the OP curves in the revision. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and context describe a standard derivation sequence: first obtain a tractable joint statistical model for the Tx-ORIS-Rx channel (turbulence + pointing + geometric loss), then derive closed-form OP expressions and bounds for HARQ-CC/IR from that model. No equations, self-citations, or parameter-fitting steps are quoted that reduce the claimed results to their inputs by construction. The derivation chain is presented as independent mathematical work; the reader's preliminary score of 2 reflects only the absence of full equations rather than any exhibited circular reduction. This is the expected non-finding for a paper whose central steps are explicit derivations rather than re-labeling or self-referential fitting.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; the work rests on standard FSO channel statistics that are treated as given rather than derived here.

axioms (1)
  • domain assumption Atmospheric turbulence, ORIS-induced pointing errors, and geometric attenuation admit a joint statistical model that is tractable for closed-form outage analysis.
    Invoked to obtain the end-to-end channel model and subsequent OP expressions.

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discussion (0)

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