arxiv: 2601.20178 · v2 · submitted 2026-01-28 · 📡 eess.SP

Recognition: no theorem link

Coverage Performance Analysis of FAS-enhanced LoRa Wide Area Networks under both Co-SF and Inter-SF Interference

Gaoze Mu , Yanzhao Hou , Mingjie Chen , Yuanyu Hu , Yongan Zheng , Qimei Cui , Xiaofeng Tao

Authors on Pith no claims yet

Pith reviewed 2026-05-16 11:02 UTC · model grok-4.3

classification 📡 eess.SP

keywords fluid antenna systemLoRaWANcoverage probabilityco-SF interferenceinter-SF interferenceextreme-value theoremALOHA protocolIoT networks

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The pith

Fluid antenna systems with a 1x1 normalized aperture greatly increase end device numbers and coverage range in LoRa wide-area networks under co-SF and inter-SF interference.

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

This paper develops an analytical model to assess how fluid antenna systems improve coverage in LoRaWANs facing path loss, fading, and dense interference from ALOHA-based packet collisions. It accounts for both same-spreading-factor and different-spreading-factor interference, deriving simple approximations for the fluid antenna channel using the extreme-value theorem. The model shows that even a small normalized aperture of 1 by 1 yields substantial gains in supported devices and range. Readers care because LoRaWANs are widely used for IoT, and better coverage means fewer gateways and lower costs in real deployments.

Core claim

The paper derives the theoretical coverage probability for FAS-enhanced LoRaWANs by approximating the FAS channel envelope and power via the extreme-value theorem, then incorporating large-scale pathloss and both co-SF and inter-SF interference. This leads to the finding that a FAS with normalized aperture 1x1 greatly enhances network performance in terms of end device numbers and coverage range.

What carries the argument

Approximations of the fluid antenna system (FAS) channel envelope and power derived from the extreme-value theorem, which enable closed-form coverage probability expressions under combined interference.

Load-bearing premise

The statistical approximations of the FAS channel envelope and power derived via the extreme-value theorem remain accurate when plugged into the coverage probability expression under the combined co-SF and inter-SF interference model.

What would settle it

A Monte Carlo simulation comparing the derived coverage probability using the extreme-value approximations against the exact correlated FAS channel model under realistic interference conditions; significant deviation would falsify the accuracy claim.

Figures

Figures reproduced from arXiv: 2601.20178 by Gaoze Mu, Mingjie Chen, Qimei Cui, Xiaofeng Tao, Yanzhao Hou, Yongan Zheng, Yuanyu Hu.

**Figure 1.** Figure 1: LoRa receiver decision value. (a) Separated desired signal and interference, where the desired signal is characterized by {encoded symbol, SF} = {25, 8}, co-SF interference 1 by {125, 8}, co-SF interference 2 by {165, 8}, inter-SF interference 2 by {125, 7}), inter-SF interference 2 by {165, 9}). (b) Combined signal and interference [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: Approximations of envelope and power for the FAS channel. where SIR1 = S0 I (m) 1 , SIR2 = S0 P12 m˜ =7,m˜ ̸=m I (m,m˜ ) 2 and SNR = S0 σ2 . Dropping the inter-SF interference term, (9) is accord with [9, (3)]. Besides, σ 2 = −174 + NF + 10 log10(BW) in dBm is the variance of the additive white Gaussian noise (AWGN), and NF is the noise figure of the receiver. Additionally, the network necessitate SNR exce… view at source ↗

**Figure 3.** Figure 3: Coverage probability of the FAS-enhanced LoRa network under (a) varying numbers of EDs (SF = 9, R2 = 3000 m), and (b) varying network region radius (W1 × W2 = 1 × 1, Pt = 10 dBm). where xˆ = 4Pς β ln(R2)−ln(R1) R β 2 −R β 1 . By combining (14), (19), (20), (21) and (22), the coverage probability can be expressed as P (m) cov = Θ (m) (; R1) − Θ (m) (; R2), (23) where Θ(m) (; Rχ) = CL(m) 1 − C ⌊ Pϱ⌋ i=0 ci [… view at source ↗

read the original abstract

This paper presents an analytical framework for evaluating the coverage performance of the fluid antenna system (FAS)-enhanced LoRa wide-area networks (LoRaWANs). We investigate the effects of large-scale pathloss in LoRaWAN, small-scale fading characterized by FAS, and dense interference (i.e., packet collisions under the ALOHA protocol) arising from randomly deployed end devices (EDs). Both co-spreading factor (co-SF) interference (with the same SF) and inter-SF interference (with different SFs) are introduced into the network, and their differences in physical characteristics are also considered in the analysis. Additionally, simple yet accurate statistical approximations of the FAS channel envelope and power are derived using the extreme-value theorem. Based on the approximated channel expression, the theoretical coverage probability of the proposed FAS-enhanced LoRaWAN is derived. Numerical results validate our analytical approximations by exhibiting close agreement with the exact correlation model. Notably, it is revealed that a FAS with a normalized aperture of 1 times 1 can greatly enhance network performance, in terms of both ED numbers and coverage range.

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.

Desk Editor's Note private letter to a colleague

The paper builds a workable coverage formula for fluid-antenna LoRaWAN that folds in both co-SF and inter-SF ALOHA interference, but the numerical checks only confirm the channel approximations, not the full system model.

read the letter

The new piece is an analytical coverage probability for LoRaWAN when devices use fluid antennas, with both same-SF and cross-SF collisions treated explicitly through their different capture thresholds. They approximate the FAS envelope and power via the extreme-value theorem, then insert those into the success probability that already accounts for path loss and random ED locations. That combination is not in the earlier LoRa papers they cite, so the framework itself is fresh. The derivations look clean on paper and the abstract reports that the channel approximations track the exact correlation model closely in the plots they show. That is useful for anyone who needs a closed-form handle on FAS in this setting. The soft spot is exactly where the stress-test note points: the validation stops at the marginal channel statistics. There is no reported Monte-Carlo check of the complete coverage expression against full-system simulations that include random packet arrivals, the distinct co-SF versus inter-SF interference powers, and the resulting capture events. Because the claimed gains are large even for a normalized 1×1 aperture, any mismatch in the tail behavior of the approximated power could be magnified by the interference terms. The paper does not appear to contain error bars or sensitivity sweeps on that point. This work is aimed at researchers who model dense IoT networks and want an analytical shortcut for fluid-antenna variants of LoRa. It is narrow enough that it will not change general wireless theory, but the math is grounded and the problem is practical. I would send it to peer review; the framework is worth referee time even if the validation needs tightening.

Referee Report

1 major / 0 minor

Summary. The manuscript develops an analytical framework for the coverage probability of fluid antenna system (FAS)-enhanced LoRaWANs. It models large-scale path loss, small-scale FAS fading using extreme-value theorem approximations for the channel envelope and power, and both co-SF and inter-SF interference under the ALOHA protocol with random end-device deployments. The paper derives a theoretical coverage probability expression based on these approximations and presents numerical results claiming validation against the exact correlation model, while highlighting significant performance gains from a 1×1 normalized aperture FAS in terms of supported end devices and coverage range.

Significance. Should the central approximations hold under the full system model, this work offers a practical analytical tool for performance evaluation in interference-limited LoRa networks augmented by fluid antennas. It could inform the design of next-generation LPWANs by quantifying how FAS can mitigate fading and interference effects, potentially leading to denser deployments and extended ranges without increasing transmit power. The explicit treatment of both co-SF and inter-SF interference with distinct capture thresholds is a strength.

major comments (1)

[Numerical results section] Numerical results section: The validation shows close agreement between the approximated FAS channel envelope/power statistics and the exact correlation model. However, this comparison is limited to marginal channel statistics and does not include Monte Carlo simulations of the complete coverage probability expression that incorporates random ED locations, path-loss, ALOHA packet collisions, and the distinct SINR thresholds for co-SF versus inter-SF interference. Because the claimed performance gains (e.g., for normalized aperture 1×1) rely on the tail behavior of the approximated distribution under dense interference, this gap is load-bearing for the quantitative conclusions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We agree that direct Monte Carlo validation of the full coverage probability (incorporating random ED locations, path loss, ALOHA collisions, and distinct co-SF/inter-SF thresholds) would strengthen the quantitative claims, particularly for the tail behavior under dense interference. We will add these simulations in the revised manuscript.

read point-by-point responses

Referee: [Numerical results section] Numerical results section: The validation shows close agreement between the approximated FAS channel envelope/power statistics and the exact correlation model. However, this comparison is limited to marginal channel statistics and does not include Monte Carlo simulations of the complete coverage probability expression that incorporates random ED locations, path-loss, ALOHA packet collisions, and the distinct SINR thresholds for co-SF versus inter-SF interference. Because the claimed performance gains (e.g., for normalized aperture 1×1) rely on the tail behavior of the approximated distribution under dense interference, this gap is load-bearing for the quantitative conclusions.

Authors: We acknowledge the referee's point. Our current numerical section validates only the marginal FAS channel approximations (envelope and power) against the exact correlation model, while the coverage probability curves are obtained by substituting the approximations into the derived analytical expressions. To confirm accuracy under the full system model—including random ED deployments, large-scale path loss, ALOHA packet collisions, and the distinct capture thresholds for co-SF versus inter-SF interference—we will add Monte Carlo simulations of the complete coverage probability in the revised version. These will be plotted alongside the analytical results to directly validate the performance gains (e.g., for the 1×1 normalized aperture) and the tail behavior under interference. revision: yes

Circularity Check

0 steps flagged

No circularity: approximations derived from external theorem and inserted into independent coverage expression

full rationale

The paper derives statistical approximations for the FAS channel envelope and power via the extreme-value theorem (an external result from statistics) and substitutes them into a coverage probability expression that accounts for path loss, ALOHA interference, and distinct co-SF/inter-SF capture thresholds. Numerical results are presented as agreement between the approximated channel statistics and an exact correlation model; this is a validation step rather than a reduction of the final performance metrics to the inputs by construction. No self-citations are load-bearing for the central claim, no parameters are fitted to a data subset and then relabeled as predictions, and no uniqueness theorems or ansatzes are imported from the authors' prior work. The derivation chain remains forward and self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework rests on standard wireless propagation models, the extreme-value theorem for channel statistics, and ALOHA interference assumptions; no new physical entities are introduced.

free parameters (1)

normalized aperture size
Set to 1x1 to demonstrate performance gain; value chosen for the reported enhancement claim.

axioms (2)

domain assumption Extreme-value theorem provides accurate statistical approximation for FAS channel envelope and power
Invoked to derive simple closed-form expressions used in the coverage probability calculation.
domain assumption ALOHA protocol governs packet collisions for both co-SF and inter-SF interference
Used to model dense interference from randomly deployed end devices.

pith-pipeline@v0.9.0 · 5519 in / 1327 out tokens · 46783 ms · 2026-05-16T11:02:45.322603+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

[1]

A comprehensive survey on internet of things (IoT) toward 5G wireless systems,

L. Chettri and R. Bera, “A comprehensive survey on internet of things (IoT) toward 5G wireless systems,”IEEE Internet Things J., vol. 7, no. 1, pp. 16–32, Jan. 2020

work page 2020
[2]

Closed-form approximation of LoRa modulation BER performance,

T. Elshabrawy and J. Robert, “Closed-form approximation of LoRa modulation BER performance,”IEEE Commun. Lett., vol. 22, no. 9, pp. 1778–1781, Sep. 2018

work page 2018
[3]

RIS-Enabled Anti-Interference in LoRa Systems,

Z. Lianget al., “RIS-Enabled Anti-Interference in LoRa Systems,”IEEE Trans. Commun., vol. 72, no. 10, pp. 6599-6616, Oct. 2024

work page 2024
[4]

On Performance of LoRa Fluid Antenna Systems,

G. Muet al., “On Performance of LoRa Fluid Antenna Systems,”IEEE Trans. Wireless Commun., DOI:10.1109/TWC.2025.3614671, 2025

work page doi:10.1109/twc.2025.3614671 2025
[5]

Impact of LoRa Imperfect Orthogonality: Analysis of Link-Level Performance,

D. Croceet al., “Impact of LoRa Imperfect Orthogonality: Analysis of Link-Level Performance,”IEEE Commun. Lett., vol. 22, no. 4, pp. 796-799, Apr. 2018

work page 2018
[6]

Analysis of the Reliability of LoRa,

Q. M. Qadiret al., “Analysis of the Reliability of LoRa,”IEEE Commun. Lett., vol. 25, no. 3, pp. 1037-1040, Mar. 2021

work page 2021
[7]

On the Advantage of Coherent LoRa Detection in the Presence of Interference,

O. Afisiadiset al., “On the Advantage of Coherent LoRa Detection in the Presence of Interference,”IEEE Int. Things J., vol. 8, no. 14, pp. 11581-11593, Jul. 2021

work page 2021
[8]

Scalability Analysis of a LoRa Network Under Imperfect Orthogonality,

A. Mahmoodet al., “Scalability Analysis of a LoRa Network Under Imperfect Orthogonality,”IEEE Transactions Ind. Inf., vol. 15, no. 3, pp. 1425-1436, Mar. 2019

work page 2019
[9]

On the Spectral Efficiency of LoRa Networks: Perfor- mance Analysis, Trends and Optimal Points of Operation,

L. Tuet al., “On the Spectral Efficiency of LoRa Networks: Perfor- mance Analysis, Trends and Optimal Points of Operation,”IEEE Trans. Commun., vol. 70, no. 4, pp. 2788-2804, Apr. 2022

work page 2022
[10]

Toward LoRa-Based LEO Satellite IoT: A Stochastic Geometry Perspective,

Q. Yuet al., “Toward LoRa-Based LEO Satellite IoT: A Stochastic Geometry Perspective,”IEEE Internet Things J., vol. 12, no. 15, pp. 30725-30738, Aug. 2025

work page 2025
[11]

LoRa Beyond ALOHA: An Investigation of Alternative Random Access Protocols,

L. Beltramelliet al., “LoRa Beyond ALOHA: An Investigation of Alternative Random Access Protocols,”IEEE Trans. Ind. Inf., vol. 17, no. 5, pp. 3544-3554, May 2021

work page 2021
[12]

Design and Performance Analysis of MEC-Aided LoRa Networks With Power Control,

Q. Chenget al., “Design and Performance Analysis of MEC-Aided LoRa Networks With Power Control,”IEEE Trans. V eh. Technol., vol. 74, no. 1, pp. 1597-1609, Jan. 2025

work page 2025
[13]

Performance Analysis of Clustered LoRa Networks,

Z. Qinet al., “Performance Analysis of Clustered LoRa Networks,” IEEE Trans. V eh. Technol., vol. 68, no. 8, pp. 7616-7629, Aug. 2019

work page 2019
[14]

Power and spreading factor control in low power wide area networks,

B. Reynderset al., “Power and spreading factor control in low power wide area networks,” inProc. IEEE Int. Conf. Commun. (ICC), Paris, France, May, 2017, pp. 1-6

work page 2017
[15]

A new spatial block-correlation model for fluid antenna systems,

P. Ram ´ırez-Espinosaet al., “A new spatial block-correlation model for fluid antenna systems,”IEEE Trans. Wireless Commun., DOI:10.1109/ TWC.2024.3434509, 2024

work page arXiv 2024
[16]

Revisiting Spatial Block-Correlation Model for Fluid Antenna Systems: from Constant to Variable Correlations,

X. Laiet al., “Revisiting Spatial Block-Correlation Model for Fluid Antenna Systems: from Constant to Variable Correlations,”IEEE J. sel. Areas Commun., DOI:10.1109/JSAC.2025.3617021, 2025. [17]LoRa SX1272/73 Transceiver Datasheet, Semtech Co., Carmarillo, CA, USA, 2015. [Online]. Available

work page doi:10.1109/jsac.2025.3617021 2025
[17]

Limit theorems for random maximum of inde- pendent and non-identically distributed random vectors,

H. M. Barakatet al., “Limit theorems for random maximum of inde- pendent and non-identically distributed random vectors,”Statistics, vol. 47, no. 3, pp. 546-557, 2013

work page 2013
[18]

Coverage Probability and Average Rate Analysis of Hy- brid Cellular and Cell-free Network,

Z. Daiet al., “Coverage Probability and Average Rate Analysis of Hy- brid Cellular and Cell-free Network,”IEEE Trans. Wireless Commun., DOI:10.1109/TWC.2025.3616960, 2025

work page doi:10.1109/twc.2025.3616960 2025
[19]

The H-Function, Theory and Applications,

A.M. Mathaiet al., “The H-Function, Theory and Applications,”Springer Science & Business Media, 2009

work page 2009
[20]

Table of integrals, series, and products

I. S. Gradshteyn and I. M. Ryzhik. “Table of integrals, series, and products”, Academic press, 2014

work page 2014
[21]

Statistical distributions,

C. Forbes, et. al., “Statistical distributions,” John Wiley & Sons, 2011

work page 2011
[22]

Rayleigh Fading Modeling and Chan- nel Hardening for Reconfigurable Intelligent Surfaces,

E. Bj ¨ornson and L. Sanguinetti, “Rayleigh Fading Modeling and Chan- nel Hardening for Reconfigurable Intelligent Surfaces,”IEEE Wireless Commun. Lett., vol. 10, no. 4, pp. 830-834, Apr. 2021

work page 2021