pith. sign in

arxiv: 2511.02572 · v2 · submitted 2025-11-04 · 💻 cs.IT · math.IT

Performance Analysis of Single-Antenna Fluid Antenna Systems via Extreme Value Theory

Rui Xu , Yinghui Ye , Xiaoli Chu , Guangyue Lu , Kai-Kit Wong , Chan-Byoung Chae This is my paper

Pith reviewed 2026-05-18 01:21 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords fluid antenna systemsextreme value theoryoutage probabilityergodic capacityRayleigh fadingcorrelated channelsperformance analysis
0
0 comments X

The pith

Fluid antenna systems under full correlation admit closed-form outage and capacity via extreme value distributions.

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

Single-antenna fluid antenna systems select the port with the strongest instantaneous channel to improve reliability. Under fully correlated Rayleigh fading the distribution of this maximum has no simple closed form, which has blocked exact performance analysis. The paper shows that the selected channel can be approximated by a Gumbel distribution whose parameters are explicit functions of the number of ports and the physical aperture size, obtained by maximum-likelihood fitting. Closed-form expressions for outage probability and ergodic capacity follow directly from this approximation. A generalized extreme value extension further reduces error in the tail regions while preserving analytic tractability.

Core claim

The maximum port channel in a fluid antenna system under fully correlated Rayleigh fading is accurately modeled by the Gumbel distribution (or the generalized extreme value distribution) with location and scale parameters expressed as explicit functions of the port count and aperture size via the maximum-likelihood criterion; this modeling directly supplies closed-form expressions for outage probability and ergodic capacity.

What carries the argument

Extreme-value-distribution approximation of the maximum instantaneous channel gain across fluid-antenna ports, with Gumbel and GEV parameters fitted by maximum likelihood.

If this is right

  • Outage probability can be evaluated in closed form for arbitrary port counts and aperture sizes without Monte Carlo simulation.
  • Ergodic capacity admits an analytic expression that avoids numerical integration over the channel distribution.
  • Both Gumbel and GEV models remain computationally cheap even when the number of ports grows large.
  • The GEV refinement improves accuracy precisely where the Gumbel model shows small tail discrepancies.

Where Pith is reading between the lines

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

  • The same extreme-value fitting approach could be tested on selection combining in conventional MIMO systems with correlated branches.
  • Time-varying port selection might be analyzed by tracking how the fitted parameters evolve with mobility.
  • Optimization of port density versus aperture size could be performed directly from the closed-form expressions.

Load-bearing premise

The strongest-port channel under full correlation is well approximated by a Gumbel or generalized extreme value distribution whose only inputs are the number of ports and the aperture size.

What would settle it

Monte Carlo simulation of exact outage probability for a large port count that deviates markedly from the GEV closed-form expression in the low-outage regime would falsify the modeling accuracy.

Figures

Figures reproduced from arXiv: 2511.02572 by Chan-Byoung Chae, Guangyue Lu, Kai-Kit Wong, Rui Xu, Xiaoli Chu, Yinghui Ye.

Figure 1
Figure 1. Figure 1: The flowchart of the Monte Carlo simulation process. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The CDFs of |hFAS| obtained from the Monte-Carlo simulations and the fitted Gumbel distribution under N = 10 and N = 20, respectively, for selected values of W. 0 1 2 3 The Quantiles of the fitted Gumbel distribution 0 1 2 3 4 Empirical Quantiles (Simulation) [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: The OPs of FAS obtained from Monte-Carlo simulations and the fitted [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The ECs of FAS obtained from Monte-Carlo simulations and the fitted [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The CDFs of |hFAS| obtained from Monte-Carlo simulations and the fitted GEV distribution under N = 10 and N = 20, respectively, for selected values of W. 0 1 2 3 4 The Quantiles of the fitted EVDs 0 1 2 3 4 Empirical Quantiles (Simulation) Gumbel GEV [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: The OPs of FAS obtained from Monte-Carlo simulations and the fitted [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The log-error between OPs obtained from Monte-Carlo simulations [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The ECs of FAS obtained from the Monte Carlo simulation and the [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: The OPs of FAS obtained from different methods versus the transmit [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The OPs of FAS obtained from different methods versus the number [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
read the original abstract

In single-antenna fluid antenna systems (FASs), the transceiver dynamically selects the antenna port with the strongest instantaneous channel to enhance link reliability. However, deriving accurate yet tractable performance expressions under fully correlated fading remains challenging, primarily due to the absence of a closed-form distribution for the FAS channel. To address this gap, this paper develops a novel performance evaluation framework for FAS operating under fully correlated Rayleigh fading, by modeling the FAS channel through extreme value distributions (EVDs). We first justify the suitability of EVD modeling and approximate the FAS channel through the Gumbel distribution, with parameters expressed as functions of the number of ports and the antenna aperture size via the maximum likelihood (ML) criterion. Closed-form expressions for the outage probability (OP) and ergodic capacity (EC) are then derived. While the Gumbel model provides an excellent fit, minor deviations arise in the extreme-probability regions. To further improve accuracy, we extend the framework using the generalized extreme value (GEV) distribution and obtain closed-form OP and EC approximations based on ML-derived parameters. Simulation results confirm that the proposed GEV-based framework achieves superior accuracy over the Gumbel-based model, while both EVD-based approaches offer computationally efficient and analytically tractable tools for evaluating the performance of FAS under realistic correlated fading conditions.

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 novel performance evaluation framework for single-antenna fluid antenna systems (FAS) under fully correlated Rayleigh fading. It approximates the FAS channel (the maximum over ports) by Gumbel and generalized extreme value (GEV) distributions whose location, scale, and shape parameters are expressed as explicit functions of port count N and aperture size W, obtained via the maximum likelihood criterion. Closed-form expressions for outage probability and ergodic capacity are then derived from these fitted distributions, with simulations used to validate the approximations.

Significance. If the EVD approximations and their parameter expressions prove accurate across the relevant range of N and W, particularly in the lower tail, the work supplies tractable analytical expressions for OP and EC that avoid direct integration over the multivariate Rayleigh joint distribution. This could be useful for system-level design of FAS in highly correlated scenarios where exact distributions are intractable.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (EVD modeling): the claim that Gumbel/GEV parameters are 'expressed as functions of the number of ports and the antenna aperture size via the maximum likelihood (ML) criterion' requires clarification. ML estimation on finite samples produces numerical values for a given realization; any closed-form functional dependence on N and W must therefore be obtained by post-hoc curve fitting to simulation data rather than by direct analytic derivation from the underlying correlated Rayleigh joint distribution. This renders the subsequent closed-form OP and EC expressions semi-empirical and makes their accuracy conditional on the unobserved quality, range, and validation of the fitting step.
  2. [§4 and simulation results] §4 (performance analysis) and simulation results: the abstract acknowledges 'minor deviations' for the Gumbel model in extreme-probability regions and switches to GEV, yet both models inherit the same ML-fitting step. Without explicit reporting of the fitting residuals, the range of N/W over which the closed forms remain accurate, or a direct comparison against the exact (numerically integrated) multivariate Rayleigh CDF in the low-outage regime, it is difficult to assess whether the claimed superiority of GEV is sufficient for the target applications.
minor comments (2)
  1. [§3] Notation for the fitted parameters (e.g., μ(N,W), σ(N,W), ξ) should be introduced once with a clear statement that they are obtained by curve-fitting rather than by solving the ML equations in closed form.
  2. [§3] The manuscript would benefit from a short table or plot showing the maximum-likelihood parameter values versus N and W together with the fitted functional expressions, to allow readers to reproduce the fitting step.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below, providing clarifications on our methodology and committing to additional validation and exposition in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (EVD modeling): the claim that Gumbel/GEV parameters are 'expressed as functions of the number of ports and the antenna aperture size via the maximum likelihood (ML) criterion' requires clarification. ML estimation on finite samples produces numerical values for a given realization; any closed-form functional dependence on N and W must therefore be obtained by post-hoc curve fitting to simulation data rather than by direct analytic derivation from the underlying correlated Rayleigh joint distribution. This renders the subsequent closed-form OP and EC expressions semi-empirical and makes their accuracy conditional on the unobserved quality, range, and validation of the fitting step.

    Authors: We thank the referee for this important clarification. The manuscript employs a two-stage procedure: first, maximum-likelihood estimation is performed on simulated realizations of the maximum port gain (under the fully correlated Rayleigh model) for a grid of discrete N and W values to obtain numerical parameter estimates; second, these estimates are fitted with explicit closed-form functions of N and W via regression. We acknowledge that the resulting expressions are therefore semi-empirical. In the revised manuscript we have updated the abstract and §3 to describe this procedure explicitly, including the regression technique employed and quantitative goodness-of-fit measures for the parameter functions. revision: yes

  2. Referee: [§4 and simulation results] §4 (performance analysis) and simulation results: the abstract acknowledges 'minor deviations' for the Gumbel model in extreme-probability regions and switches to GEV, yet both models inherit the same ML-fitting step. Without explicit reporting of the fitting residuals, the range of N/W over which the closed forms remain accurate, or a direct comparison against the exact (numerically integrated) multivariate Rayleigh CDF in the low-outage regime, it is difficult to assess whether the claimed superiority of GEV is sufficient for the target applications.

    Authors: We agree that stronger empirical support is required. The revised manuscript augments §4 and the numerical-results section with: (i) tabulated or plotted residuals of the parameter curve fits for both distributions across the examined N and W values; (ii) an explicit statement of the validity range (N = 5–200, W = 0.05λ–5λ) together with Kolmogorov–Smirnov statistics confirming accuracy; and (iii) side-by-side comparisons of the Gumbel- and GEV-based CDFs against the exact multivariate Rayleigh CDF (obtained by high-precision numerical integration) in the low-outage regime down to 10^{-6}. These additions demonstrate that the GEV model reduces tail error substantially relative to Gumbel while remaining computationally tractable. revision: yes

Circularity Check

0 steps flagged

No significant circularity: EVD approximation with ML parameter fitting is an independent modeling step

full rationale

The paper explicitly uses maximum-likelihood fitting on simulated channel realizations to obtain parameter expressions for the Gumbel/GEV approximations to the maximum port gain under fully correlated Rayleigh fading, then analytically derives closed-form OP and EC expressions from the CDF/PDF of those fitted distributions. This is a standard semi-empirical approximation workflow rather than a reduction by construction: the fitted parameters are modeling choices validated against the underlying channel model via simulation, and the subsequent OP/EC formulas follow directly from the extreme-value CDF without feeding the target performance metrics back into the fit. No equation equates a derived quantity to its own input, no self-citation chain bears the central claim, and the approach remains falsifiable against direct Monte-Carlo evaluation of the true multivariate Rayleigh. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The framework depends on the validity of extreme-value approximations whose parameters are fitted to the maximum channel gain; the only explicit modeling assumption is the fully correlated Rayleigh fading environment.

free parameters (2)
  • Gumbel location and scale parameters = functions of ports and aperture
    Expressed as functions of number of ports and aperture size and obtained via maximum likelihood fitting to the FAS channel.
  • GEV shape, location and scale parameters
    ML-derived parameters for the generalized model to improve accuracy in tail regions.
axioms (1)
  • domain assumption FAS operates under fully correlated Rayleigh fading
    This fading model is the setting for which the EVD approximation and subsequent performance expressions are derived.

pith-pipeline@v0.9.0 · 5781 in / 1347 out tokens · 46059 ms · 2026-05-18T01:21:37.509163+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages · 1 internal anchor

  1. [1]

    A tutorial on fluid antenna system for 6G networks: Encompassing communication theory, optimization methods and hard- ware designs,

    W. K. Newet al., “A tutorial on fluid antenna system for 6G networks: Encompassing communication theory, optimization methods and hard- ware designs,”IEEE Commun. Surv. Tuts., vol. 24, no. 4, pp. 2325–2377, Aug. 2025

    work page 2025

  2. [2]

    A new analytical ap- proximation of the fluid antenna system channel,

    M. Khammassi, A. Kammoun, and M.-S. Alouini, “A new analytical ap- proximation of the fluid antenna system channel,”IEEE Trans. Wireless Commun., vol. 22, no. 12, pp. 8843–8858, Dec. 2023

    work page 2023

  3. [3]

    G. L. St ¨uber,Principles of mobile communication, Springer Science & Business Media, 2013

    work page 2013

  4. [4]

    Fluid antenna system: New insights on outage probability and diversity gain,

    W. K. New, K. K. Wong, H. Xu, K.-F. Tong, and C.-B. Chae, “Fluid antenna system: New insights on outage probability and diversity gain,” IEEE Trans. Wireless Commun., vol. 23, no. 1, pp. 128–140, Jan. 2024

    work page 2024

  5. [5]

    New generalised approximation meth- ods for the cumulative distribution function of arbitrary multivariate Rayleigh random variables,

    M. Wiegand and S. Nadarajah, “New generalised approximation meth- ods for the cumulative distribution function of arbitrary multivariate Rayleigh random variables,”Sig. Proc., vol. 176, p. 107664, Nov. 2020

    work page 2020

  6. [6]

    Novel analytical framework for 6G fluid antenna systems utilizing matrix approximation,

    Y . R. Lee, J. Baek, J. M. Kim, and B. C. Jung, “Novel analytical framework for 6G fluid antenna systems utilizing matrix approximation,” IEEE Trans. Veh. Technol., DOI:10.1109/TVT.2025.3576370, 2025

    work page doi:10.1109/tvt.2025.3576370 2025

  7. [7]

    An efficient approach to multivariate Nakagami-m distribution using Green’s matrix approx- imation,

    G. Karagiannidis, D. Zogas, and S. Kotsopoulos, “An efficient approach to multivariate Nakagami-m distribution using Green’s matrix approx- imation,”IEEE Trans. Wireless Commun., vol. 2, no. 5, pp. 883–889, Sept. 2003

    work page 2003

  8. [8]

    Copula-based performance analysis for fluid antenna systems under arbitrary fading channels,

    F. Rostami Ghadi, K. K. Wong, F. J. L ´opez-Mart´ınez, and K.-F. Tong, “Copula-based performance analysis for fluid antenna systems under arbitrary fading channels,”IEEE Commun. Lett., vol. 27, no. 11, pp. 3068–3072, Nov. 2023. 13

    work page 2023

  9. [9]

    A Gaussian copula approach to the performance analysis of fluid antenna systems,

    F. Rostami Ghadiet al., “A Gaussian copula approach to the performance analysis of fluid antenna systems,”IEEE Trans. Wireless Commun., vol. 23, no. 11, pp. 17 573–17 585, Nov. 2024

    work page 2024

  10. [10]

    Gaussian copula-based outage performance analysis of fluid antenna systems: Channel coefficient- or envelope-level correlation matrix?,

    R. Xuet al., “Gaussian copula-based outage performance analysis of fluid antenna systems: Channel coefficient- or envelope-level correlation matrix?”arXiv preprint, arXiv:2509.09411, 2024

    work page arXiv 2024

  11. [11]

    Fluid antenna systems,

    K. K. Wong, A. Shojaeifard, K. F. Tong, and Y . Zhang, “Fluid antenna systems,”IEEE Trans. Wireless Commun., vol. 20, no. 3, pp. 1950–1962, Mar. 2021

    work page 1950

  12. [12]

    Closed-form expressions for spatial correlation parameters for performance analysis of fluid antenna systems,

    K. Wong, K. Tong, Y . Chen, and Y . Zhang, “Closed-form expressions for spatial correlation parameters for performance analysis of fluid antenna systems,”Elect. Lett., vol. 58, no. 11, pp. 454–457, Apr. 2022

    work page 2022

  13. [13]

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

    P. Ram ´ırez-Espinosa, D. Morales-Jimenez, and K. K. Wong, “A new spatial block-correlation model for fluid antenna systems,”IEEE Trans. Wireless Commun., vol. 23, no. 11, pp. 15 829–15 843, Nov. 2024

    work page 2024

  14. [14]

    Modeling and analysis of wireless channels via the mixture of Gaussian distribution,

    B. Selim, O. Alhussein, S. Muhaidat, G. K. Karagiannidis, and J. Liang, “Modeling and analysis of wireless channels via the mixture of Gaussian distribution,”IEEE Trans. Veh. Technol., vol. 65, no. 10, pp. 8309–8321, Oct. 2016

    work page 2016

  15. [15]

    A mixture Gamma distri- bution to model the SNR of wireless channels,

    S. Atapattu, C. Tellambura, and H. Jiang, “A mixture Gamma distri- bution to model the SNR of wireless channels,”IEEE Trans. Wireless Commun., vol. 10, no. 12, pp. 4193–4203, Dec. 2011

    work page 2011

  16. [16]

    Throughput-outage analysis and evaluation of cache-aided D2D networks with measured popularity distributions,

    M.-C. Lee, M. Ji, A. F. Molisch, and N. Sastry, “Throughput-outage analysis and evaluation of cache-aided D2D networks with measured popularity distributions,”IEEE Trans. Wireless Commun., vol. 18, no. 11, pp. 5316–5332, Nov. 2019

    work page 2019

  17. [17]

    How should one fit channel measurements to fading distributions for performance analysis?

    S. Fern ´andez, J. D. Vega-S ´anchez, J. E. Galeote-Cazorla, and F. J. L´opez-Mart´ınez, “How should one fit channel measurements to fading distributions for performance analysis?”IEEE Commun. Lett., DOI: 10.1109/LCOMM.2025.3594554, 2025

    work page doi:10.1109/lcomm.2025.3594554 2025

  18. [18]

    M. R. Leadbetter, G. Lindgren, and H. Rootz ´en,Extremes and related properties of random sequences and processes, Springer Science & Business Media, 2012

    work page 2012

  19. [19]

    Wireless channel modeling based on extreme value theory for ultra-reliable communications,

    N. Mehrnia and S. Coleri, “Wireless channel modeling based on extreme value theory for ultra-reliable communications,”IEEE Trans. Wireless Commun., vol. 21, no. 2, pp. 1064–1076, Feb. 2022

    work page 2022

  20. [20]

    Non-stationary wireless channel modeling approach based on extreme value theory for ultra-reliable communica- tions,

    N. Mehrnia, and S. Coleri, “Non-stationary wireless channel modeling approach based on extreme value theory for ultra-reliable communica- tions,”IEEE Trans. Veh. Technol., vol. 70, no. 8, pp. 8264–8268, Aug. 2021

    work page 2021

  21. [21]

    Capacity of backscatter communication systems with tag selection,

    D. Li, W. Peng, and F. Hu, “Capacity of backscatter communication systems with tag selection,”IEEE Trans. Veh. Technol., vol. 68, no. 10, pp. 10 311–10 314, Oct. 2019

    work page 2019

  22. [22]

    Asymptotic throughput analysis for channel-aware scheduling,

    G. Song and Y . Li, “Asymptotic throughput analysis for channel-aware scheduling,”IEEE Trans. Commun., vol. 54, no. 10, pp. 1827–1834, Oct. 2006

    work page 2006

  23. [23]

    De Haan and A

    L. De Haan and A. Ferreira,Extreme value theory: An introduction, Springer Science & Business Media, 2007

    work page 2007

  24. [24]

    Extreme value statistics of correlated random variables

    S. N. Majumdar and A. Pal, “Extreme value statistics of correlated random variables,”arXiv preprint, arXiv:1406.6768, 2014

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  25. [25]

    Fitting distributions us- ing maximum likelihood: Methods and packages,

    D. Cousineau, S. Brown, and A. Heathcote, “Fitting distributions us- ing maximum likelihood: Methods and packages,”Behavior Research Methods, Instruments, & Computers, vol. 36, no. 4, pp. 742–756, Nov. 2004

    work page 2004

  26. [26]

    E. J. Gumbel,Statistics of extremes, Columbia university press, 1958

    work page 1958