pith. machine review for the scientific record. sign in

arxiv: 2605.06823 · v1 · submitted 2026-05-07 · 📡 eess.SP

Recognition: 2 theorem links

· Lean Theorem

Performance Analysis of Fluid Antenna-Assisted Over-the-Air Federated Learning Under Spatially Correlated Fading

Ghosheh Abed Hodtani, Ji Wang, Ming Zeng, Mohsen Ahmadzadeh, Saeid Pakravan, Wessam Ajib

Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:11 UTC · model grok-4.3

classification 📡 eess.SP
keywords fluid antennaover-the-air federated learningspatially correlated fadingClayton copulaaggregation error outageuser participationperformance analysis
0
0 comments X

The pith

Fluid antennas let over-the-air federated learning users pick positions that reduce aggregation errors under correlated fading.

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

This paper shows that fluid-antenna users in an uplink OTA-FL system can dynamically choose port positions to obtain more favorable channels, raising the chance each user contributes successfully to the wireless aggregation step. It derives closed-form expressions for the aggregation-error outage probability and the expected number of active users per round, modeling the spatial correlation across ports with the Clayton copula to capture worst-case lower-tail dependence. If these expressions hold, the scheme delivers higher reliability and participation than fixed-antenna baselines without extra transmit power or bandwidth. A reader would care because federated learning over wireless links is limited by channel-induced aggregation failures; position reconfigurability offers a low-overhead way to mitigate them.

Core claim

The paper establishes a tractable analytical framework for fluid-antenna-assisted over-the-air federated learning over spatially correlated fading. Closed-form expressions are obtained for the aggregation error outage probability and the expected number of participating users per communication round. The framework employs the Clayton copula to model the lower-tail dependence between fluid-antenna ports, and numerical evaluation shows that the resulting performance exceeds that of conventional fixed-antenna OTA-FL under the same conditions.

What carries the argument

The Clayton-copula model of spatial correlation across fluid-antenna ports, which supplies the joint fading statistics needed to compute closed-form outage and participation metrics for the OTA aggregation step.

If this is right

  • Closed-form outage probability lets system designers set power and participation thresholds without Monte-Carlo simulation.
  • The expected number of active users per round rises because more users can avoid deep fades by repositioning.
  • Performance advantage over fixed antennas grows with the number of available fluid-antenna ports.
  • The same analytical approach applies to other performance metrics such as convergence speed of the global model.

Where Pith is reading between the lines

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

  • The framework could be extended to joint optimization of user scheduling and fluid-antenna positions in a single round.
  • Similar copula-based modeling might apply to fluid-antenna performance in non-OTA federated learning or in cell-free massive MIMO.
  • Hardware prototypes with real-time position control would test whether the analytical gains survive calibration errors and mobility constraints.

Load-bearing premise

The spatial correlation between fluid-antenna ports is accurately described by the Clayton copula's lower-tail dependence under worst-case fading.

What would settle it

A direct comparison of measured aggregation-error rates in a hardware testbed using movable antennas versus fixed antennas, under channel conditions whose empirical correlation matches the Clayton-copula assumption, would confirm or refute the claimed closed-form gains.

Figures

Figures reproduced from arXiv: 2605.06823 by Ghosheh Abed Hodtani, Ji Wang, Ming Zeng, Mohsen Ahmadzadeh, Saeid Pakravan, Wessam Ajib.

Figure 1
Figure 1. Figure 1: An illustration of the proposed FA-assisted OTA-FL system. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The CDF of the normalized MSE for |S| = 15. demonstrating the critical role of FA-enabled spatial diversity in enhancing user participation. As spatial correlation increases, i.e., from β = 0 to β = 2, the PMF gradually shifts toward smaller values of |S|, reflecting reduced diversity. Nonetheless, even under correlated FA conditions, the achievable participa￾tion level remains markedly superior to that of… view at source ↗
Figure 3
Figure 3. Figure 3: The PMF of the number of participating devices for [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The PMF of full-participation OTA-FL for [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Learning performance of FA-assisted OTA-FL on the MNIST dataset [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

Fluid antenna (FA) technology has recently emerged as an effective means of exploiting spatial diversity through position-domain reconfigurability. This paper investigates the integration of FA into over-the-air federated learning (OTA-FL) systems with the aim of improving aggregation reliability and user participation under realistic channel conditions. By dynamically selecting antenna positions, FA-equipped users can exploit additional spatial degrees of freedom to realize more favorable channel conditions, thereby increasing the probability of successful contribution to the OTA aggregation process in each communication round. We consider an uplink OTA-FL framework consisting of a single fixed-antenna access point and multiple FA-enabled users operating over spatially correlated fading channels. Unlike existing studies that primarily rely on optimization-based designs or numerical evaluations, we develop a tractable analytical framework that enables a rigorous performance characterization of FA-assisted OTA-FL. In particular, closed-form expressions are derived for the aggregation error outage probability and the expected number of participating users per round. Spatial channel correlation across FA ports is modeled using a copula-based approach, where the Clayton copula is adopted to capture lower-tail dependence relevant to worst-case fading conditions. Numerical results validate the analytical findings and demonstrate that FA-assisted OTA-FL significantly outperforms conventional fixed-antenna schemes in terms of aggregation reliability and participation efficiency, while providing insights under practical system considerations.

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 manuscript develops a tractable analytical framework for fluid antenna (FA)-assisted over-the-air federated learning (OTA-FL) under spatially correlated fading. It derives closed-form expressions for the aggregation error outage probability and the expected number of participating users per round, modeling spatial correlation across FA ports via the Clayton copula to capture lower-tail dependence. Numerical results are used to claim that FA-assisted OTA-FL significantly outperforms conventional fixed-antenna schemes in aggregation reliability and participation efficiency.

Significance. If the derivations hold under the stated assumptions, the work supplies closed-form performance metrics that could aid design of position-reconfigurable OTA-FL systems. The focus on analytical characterization rather than purely numerical optimization is a strength, as are the explicit incorporation of practical considerations such as spatial correlation and user participation.

major comments (2)
  1. [§II (Channel Model)] §II (Channel Model): The Clayton copula is selected solely for its lower-tail dependence to represent worst-case fading, yet no justification, sensitivity analysis, or comparison is provided against geometry-based alternatives (e.g., exponential decay with port separation) or other copulas. Because the closed-form outage probability and expected participation expressions are derived directly from the joint distribution induced by this copula, the central outperformance claims over fixed-antenna baselines rest on an unvalidated modeling choice.
  2. [§III (Performance Analysis)] §III (Performance Analysis): The derivations of the closed-form outage probability and participation count are stated to be tractable, but the manuscript provides insufficient intermediate steps or explicit dependence on the copula parameter to allow independent verification. This is load-bearing, as the numerical validation of FA gains relies on these expressions being accurate under the chosen dependence structure.
minor comments (2)
  1. [Abstract] The abstract and introduction could more explicitly list the system parameters (e.g., number of users, FA port count, copula parameter range) used in the numerical results to improve reproducibility.
  2. [Numerical Results] Figure captions should indicate the specific values of the Clayton copula dependence parameter and the correlation scenarios plotted, rather than leaving them implicit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help improve the clarity and rigor of our manuscript. We address each major comment below and will make the indicated revisions to strengthen the presentation of the channel model and derivations.

read point-by-point responses

  1. Referee: [§II (Channel Model)] §II (Channel Model): The Clayton copula is selected solely for its lower-tail dependence to represent worst-case fading, yet no justification, sensitivity analysis, or comparison is provided against geometry-based alternatives (e.g., exponential decay with port separation) or other copulas. Because the closed-form outage probability and expected participation expressions are derived directly from the joint distribution induced by this copula, the central outperformance claims over fixed-antenna baselines rest on an unvalidated modeling choice.

    Authors: We thank the referee for this observation. The Clayton copula was adopted specifically because it exhibits strong lower-tail dependence, which is essential for modeling the joint deep-fade events that dominate aggregation error outage in OTA-FL under worst-case conditions. The manuscript notes this motivation in the context of practical fading, but we agree that a more explicit justification, sensitivity analysis over the dependence parameter, and comparison to alternatives (e.g., exponential correlation models or Gumbel copula) would better support the choice. In the revised manuscript we will expand Section II accordingly, including these elements to validate the modeling decision and its influence on the derived metrics. revision: yes

  2. Referee: [§III (Performance Analysis)] §III (Performance Analysis): The derivations of the closed-form outage probability and participation count are stated to be tractable, but the manuscript provides insufficient intermediate steps or explicit dependence on the copula parameter to allow independent verification. This is load-bearing, as the numerical validation of FA gains relies on these expressions being accurate under the chosen dependence structure.

    Authors: We acknowledge the referee's point on the need for greater transparency. While the closed-form expressions are obtained from the copula-based joint distribution, additional intermediate steps would facilitate verification. In the revised version we will expand the derivations in Section III (with key steps moved to an appendix if needed), explicitly tracing the dependence on the copula parameter from the joint CDF through to the final outage probability and expected participation expressions. This will allow independent confirmation of the results under the chosen dependence structure. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations are model-based and self-contained

full rationale

The paper constructs closed-form expressions for aggregation error outage probability and expected number of participating users directly from the joint distribution of effective channel gains under the chosen Clayton copula model for spatial correlation. These expressions follow standard probabilistic derivations (e.g., integrating over the copula-induced CDFs) without any fitted parameters being renamed as predictions, without self-citations serving as load-bearing uniqueness theorems, and without the central outperformance claim reducing tautologically to the inputs. Numerical validation compares FA vs. fixed-antenna cases under the same model assumptions, providing independent content rather than circular confirmation. The copula selection is an explicit modeling choice justified by tail-dependence properties, not smuggled via self-citation or self-definition.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard wireless fading assumptions plus the specific choice of Clayton copula to represent spatial dependence; no free parameters are explicitly named in the abstract, but the copula parameter itself functions as a modeling choice.

free parameters (1)
  • Clayton copula dependence parameter
    Controls the strength of lower-tail dependence between antenna ports; chosen or fitted to represent worst-case fading correlation.
axioms (1)
  • domain assumption Spatially correlated fading across fluid-antenna ports can be represented by the Clayton copula to capture lower-tail dependence in worst-case conditions
    Invoked to enable tractable closed-form outage expressions under realistic channel conditions.

pith-pipeline@v0.9.0 · 5554 in / 1330 out tokens · 33788 ms · 2026-05-11T01:11:13.891502+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Reference graph

Works this paper leans on

47 extracted references · 47 canonical work pages

  1. [1]

    Aerial access networks for federated learning: Applications and challenges,

    Q.-V . Pham, M. Zeng, T. Huynh-The, Z. Han, and W.-J. Hwang, “Aerial access networks for federated learning: Applications and challenges,” IEEE Network, vol. 36, no. 3, pp. 159–166, Jul. 2022. 11

    work page 2022

  2. [2]

    Connectivity enrich- ment for decentralized federated learning networks with teleportation,

    X. Wang, Y . Chen, Q. Ye, and O. A. Dobre, “Connectivity enrich- ment for decentralized federated learning networks with teleportation,” inProc. IEEE International Conference on Computer Communications (INFOCOM WKSHPS), London, United Kingdom, pp. 1–6, May. 2025

    work page 2025

  3. [3]

    Federated learning for wireless communications: Motivation, opportunities, and challenges,

    S. Niknam, H. S. Dhillon, and J. H. Reed, “Federated learning for wireless communications: Motivation, opportunities, and challenges,” IEEE Communications Magazine, vol. 58, no. 6, pp. 46–51, Jun. 2020

    work page 2020

  4. [4]

    Energy efficient federated learning over wireless communication networks,

    Z. Yang, M. Chen, W. Saad, C. S. Hong, and M. Shikh-Bahaei, “Energy efficient federated learning over wireless communication networks,”IEEE Transactions on Wireless Communications, vol. 20, no. 3, pp. 1935–1949, Nov. 2021

    work page 1935

  5. [5]

    Over- the-air computation for 6G: Foundations, technologies, and applications,

    Z. Wang, Y . Zhao, Y . Zhou, Y . Shi, C. Jiang, and K. B. Letaief, “Over- the-air computation for 6G: Foundations, technologies, and applications,” IEEE Internet of Things Journal, vol. 11, no. 14, pp. 24 634–24 658, May. 2024

    work page 2024

  6. [6]

    A survey on over-the-air computation,

    A. S ¸ahin and R. Yang, “A survey on over-the-air computation,”IEEE Communications Surveys & Tutorials, vol. 25, no. 3, pp. 1877–1908, Apr. 2023

    work page 1908

  7. [7]

    Over-the- air federated learning and optimization,

    J. Zhu, Y . Shi, Y . Zhou, C. Jiang, W. Chen, and K. B. Letaief, “Over-the- air federated learning and optimization,”IEEE Internet of Things Journal, vol. 11, no. 10, pp. 16 996–17 020, Jan. 2024

    work page 2024

  8. [8]

    Federated learning via over- the-air computation,

    K. Yang, T. Jiang, Y . Shi, and Z. Ding, “Federated learning via over- the-air computation,”IEEE Transactions on Wireless Communications, vol. 19, no. 3, pp. 2022–2035, Jan. 2020

    work page 2022

  9. [9]

    Over- the-air fair federated learning via multi-objective optimization,

    S. Mohajer Hamidi, A. Bereyhi, S. Asaad, and H. Vincent Poor, “Over- the-air fair federated learning via multi-objective optimization,”IEEE Communications Letters, vol. 29, no. 7, pp. 1549–1553, May. 2025

    work page 2025

  10. [10]

    Secure and private over-the-air federated learning: Biased and unbiased aggregation design,

    N. Yan, K. Wang, K. Zhi, C. Pan, K. K. Chai, and H. V . Poor, “Secure and private over-the-air federated learning: Biased and unbiased aggregation design,”IEEE Transactions on Wireless Communications, vol. 24, no. 7, pp. 5901–5916, Mar. 2025

    work page 2025

  11. [11]

    Data aggregation in regular large-scale IoT networks: Granularity, reliability, and delay tradeoffs,

    Y . Nabil, H. ElSawy, S. Al-Dharrab, H. Mostafa, and H. Attia, “Data aggregation in regular large-scale IoT networks: Granularity, reliability, and delay tradeoffs,”IEEE Internet of Things Journal, vol. 9, no. 18, pp. 17 767–17 784, Mar. 2022

    work page 2022

  12. [12]

    Over-the-air federated learning over scalable cell- free massive MIMO,

    H. Sifaou and G. Y . Li, “Over-the-air federated learning over scalable cell- free massive MIMO,”IEEE Transactions on Wireless Communications, vol. 23, no. 5, pp. 4214–4227, Sep. 2024

    work page 2024

  13. [13]

    Joint antenna selection and beamforming for massive MIMO-enabled over-the-air federated learning,

    S. Asaad, H. Tabassum, C. Ouyang, and P. Wang, “Joint antenna selection and beamforming for massive MIMO-enabled over-the-air federated learning,”IEEE Transactions on Wireless Communications, vol. 23, no. 8, pp. 8603–8618, Feb. 2024

    work page 2024

  14. [14]

    Differentially private over-the-air federated learning over MIMO fading channels,

    H. Liu, J. Yan, and Y .-J. A. Zhang, “Differentially private over-the-air federated learning over MIMO fading channels,”IEEE Transactions on Wireless Communications, vol. 23, no. 8, pp. 8232–8247, Jan. 2024

    work page 2024

  15. [15]

    Directional antennas for sub-THz and THz MIMO systems: Bridging the gap between theory and implementation,

    D. M. Bodet and J. M. Jornet, “Directional antennas for sub-THz and THz MIMO systems: Bridging the gap between theory and implementation,” IEEE Open Journal of the Communications Society, vol. 4, pp. 2261– 2273, Sep. 2023

    work page 2023

  16. [16]

    Directional antennas modeling and coverage analysis of UA V-assisted networks,

    J. Peng, W. Tang, and H. Zhang, “Directional antennas modeling and coverage analysis of UA V-assisted networks,”IEEE Wireless Communi- cations Letters, vol. 11, no. 10, pp. 2175–2179, Aug. 2022

    work page 2022

  17. [17]

    A tutorial on movable antennas for wireless networks,

    L. Zhu, W. Ma, W. Mei, Y . Zeng, Q. Wu, B. Ning, Z. Xiao, X. Shao, J. Zhang, and R. Zhang, “A tutorial on movable antennas for wireless networks,”IEEE Communications Surveys & Tutorials, vol. 28, pp. 3002– 3054, Feb. 2025

    work page 2025

  18. [18]

    Balancing accuracy and integrity for reconfigurable intelligent surface-aided over-the-air federated learning,

    J. Zheng, H. Tian, W. Ni, W. Ni, and P. Zhang, “Balancing accuracy and integrity for reconfigurable intelligent surface-aided over-the-air federated learning,”IEEE Transactions on Wireless Communications, vol. 21, no. 12, pp. 10 964–10 980, Jul. 2022

    work page 2022

  19. [19]

    Physical-layer security of RIS-assisted networks over correlated fisher- snedecor F fading channels,

    S. Pakravan, J.-Y . Chouinard, M. Zeng, X. Li, W. Hao, and O. A. Dobre, “Physical-layer security of RIS-assisted networks over correlated fisher- snedecor F fading channels,”IEEE Internet of Things Journal, vol. 11, no. 9, pp. 15 152–15 165, May. 2024

    work page 2024

  20. [20]

    Joint beamforming design for multifunctional RIS-aided over-the-air federated learning,

    X. Zhang, H. Tian, W. Ni, and Z. Yang, “Joint beamforming design for multifunctional RIS-aided over-the-air federated learning,”IEEE Internet of Things Journal, vol. 12, no. 12, pp. 21 720–21 739, Jun. 2025

    work page 2025

  21. [21]

    AI-enhanced RIS-aided cognitive radio network: Integrating communication and over-the-air federated learning users,

    M. Ahmadzadeh, S. Pakravan, G. A. Hodtani, M. Zeng, X. Li, N. Zhang, and J.-Y . Chouinard, “AI-enhanced RIS-aided cognitive radio network: Integrating communication and over-the-air federated learning users,” IEEE Transactions on Vehicular Technology, pp. 1–14, Jan. 2026

    work page 2026

  22. [22]

    Reconfigurable intelligent surfaces-aided federated learning in over-the-air computation,

    M. Kim and D. Park, “Reconfigurable intelligent surfaces-aided federated learning in over-the-air computation,”IEEE Wireless Communications Letters, vol. 13, no. 7, pp. 1983–1987, May. 2024

    work page 1983

  23. [23]

    Deep reinforcement learning for robust RIS-aided over-the- air federated learning in cognitive radio,

    M. Ahmadzadeh, S. Pakravan, G. A. Hodtani, M. Zeng, and J.-Y . Chouinard, “Deep reinforcement learning for robust RIS-aided over-the- air federated learning in cognitive radio,” inProc. of IEEE Middle East Conference on Communications and Networking (MECOM), Abu Dhabi, United Arab Emirates, pp. 368-373, Nov. 2024

    work page 2024

  24. [24]

    Port selection for fluid antenna systems,

    Z. Chai, K.-K. Wong, K.-F. Tong, Y . Chen, and Y . Zhang, “Port selection for fluid antenna systems,”IEEE Communications Letters, vol. 26, no. 5, pp. 1180–1184, Feb. 2022

    work page 2022

  25. [25]

    Fluid antenna system—part I: Preliminaries,

    K.-K. Wong, W. K. New, X. Hao, K.-F. Tong, and C.-B. Chae, “Fluid antenna system—part I: Preliminaries,”IEEE Communications Letters, vol. 27, no. 8, pp. 1919–1923, Jul. 2023

    work page 1919

  26. [26]

    A contemporary survey on fluid antenna systems: Fundamentals and networking perspectives,

    H. Hong, K.-K. Wong, C.-B. Chae, H. Xu, X. Guo, F. R. Ghadi, Y . Chen, Y . Xu, B. Liu, K.-F. Tong, and Y . Zhang, “A contemporary survey on fluid antenna systems: Fundamentals and networking perspectives,”IEEE Transactions on Network Science and Engineering, vol. 13, pp. 2305– 2328, Sep. 2025

    work page 2025

  27. [27]

    Fluid antenna-assisted uplink NOMA net- works under imperfect SIC,

    S. Pakravan, M. Ahmadzadeh, M. Zeng, Z. Yang, G. A. Hodtani, J.-Y . Chouinard, and Q.-V . Pham, “Fluid antenna-assisted uplink NOMA net- works under imperfect SIC,”IEEE Transactions on Vehicular Technology, vol. 75, no. 1, pp. 1689–1694, Aug. 2025

    work page 2025

  28. [28]

    Fluid antenna systems under channel uncertainty and hardware impairments: Trends, challenges, and future research directions,

    S. Pakravan, M. Ahmadzadeh, M. Zeng, W. Ajib, J. Wang, and X. Li, “Fluid antenna systems under channel uncertainty and hardware impair- ments: Trends, challenges, and future research directions,”arXiv preprint arXiv:2601.22989, Jan. 2026

    work page arXiv 2026

  29. [29]

    A tutorial on fluid antenna system for 6G networks: En- compassing communication theory, optimization methods and hardware designs,

    W. K. New, K.-K. Wong, H. Xu, C. Wang, F. R. Ghadi, J. Zhang, J. Rao, R. Murch, P. Ram ´ırez-Espinosa, D. Morales-Jimenez, C.-B. Chae, and K.-F. Tong, “A tutorial on fluid antenna system for 6G networks: En- compassing communication theory, optimization methods and hardware designs,”IEEE Communications Surveys & Tutorials, vol. 27, no. 4, pp. 2325–2377, Nov. 2025

    work page 2025

  30. [30]

    SWIPT in FA-enabled cellular networks: A stochastic geometry copula-based approach,

    C. Skouroumounis and I. Krikidis, “SWIPT in FA-enabled cellular networks: A stochastic geometry copula-based approach,” inProc. IEEE International Conference on Communications (ICC), Denver, USA, pp. 2360-2365, Aug. 2024

    work page 2024

  31. [31]

    Enhanced over-the-air federated learning using AI-based fluid antenna system,

    M. Ahmadzadeh, S. Pakravan, G. Abed Hodtani, M. Zeng, J.-Y . Chouinard, and L. A. Rusch, “Enhanced over-the-air federated learning using AI-based fluid antenna system,” inProc. IEEE Wireless Communi- cations and Networking Conference (WCNC), Milan, Italy, pp. 1–6, Mar. 2025

    work page 2025

  32. [32]

    AI-based fluid antenna design for client selection in over-the-air federated learning,

    M. Ahmadzadeh, S. Pakravan, G. A. Hodtani, M. Zeng, Q. J. Ye, J.-Y . Chouinard, and L. A. Rusch, “AI-based fluid antenna design for client selection in over-the-air federated learning,”IEEE Internet of Things Journal, vol. 12, no. 20, pp. 42 549–42 558, Oct. 2025

    work page 2025

  33. [33]

    Advancing over- the-air federated learning through deep reinforcement learning in UA V- assisted networks with movable antennas,

    M. Ahmadzadeh, S. Pakravan, and G. A. Hodtani, “Advancing over- the-air federated learning through deep reinforcement learning in UA V- assisted networks with movable antennas,”Computer and Knowledge Engineering, vol. 8, no. 2, pp. 1–10, May. 2025

    work page 2025

  34. [34]

    Robust resource allocation for over-the-air computation networks with fluid antenna array,

    S. Pakravan, M. Ahmadzadeh, M. Zeng, G. Abed Hodtani, J.-Y . Chouinard, and L. A. Rusch, “Robust resource allocation for over-the-air computation networks with fluid antenna array,” inProc. IEEE Globecom Workshops (GC Wkshps), Cape Town, South Africa, pp. 1–6, Sep. 2024

    work page 2024

  35. [35]

    Fluid antenna enabled over-the- air federated learning: Joint optimization of positioning, beamforming, and user selection,

    Y . Zhao, M. Xu, P. Wang, and D. Niyato, “Fluid antenna enabled over-the- air federated learning: Joint optimization of positioning, beamforming, and user selection,”arXiv preprint arXiv:2503.00011, Feb. 2025

    work page arXiv 2025

  36. [36]

    Physical layer security over fluid antenna systems: Secrecy performance analysis,

    F. Rostami Ghadi, K.-K. Wong, F. Javier L ´opez-Mart´ınez, W. Kiat New, H. Xu, and C.-B. Chae, “Physical layer security over fluid antenna systems: Secrecy performance analysis,”IEEE Transactions on Wireless Communications, vol. 23, no. 12, pp. 18 201–18 213, Sep. 2024

    work page 2024

  37. [37]

    Space-terrestrial cooperation over spatially correlated chan- nels relying on imperfect channel estimates: Uplink performance analysis and optimization,

    T. Van Chien, E. Lagunas, T. M. Hoang, S. Chatzinotas, B. Ottersten, and L. Hanzo, “Space-terrestrial cooperation over spatially correlated chan- nels relying on imperfect channel estimates: Uplink performance analysis and optimization,”IEEE Transactions on Communications, vol. 71, no. 2, pp. 773–791, Dec. 2023

    work page 2023

  38. [38]

    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- actions on Wireless Communications, vol. 23, no. 11, pp. 15 829–15 843, Aug. 2024

    work page 2024

  39. [39]

    FAS-RIS: A block-correlation model analysis,

    X. Lai, J. Yao, K. Zhi, T. Wu, D. Morales-Jimenez, and K.-K. Wong, “FAS-RIS: A block-correlation model analysis,”IEEE Transactions on Vehicular Technology, vol. 74, no. 2, pp. 3412–3417, Oct. 2025

    work page 2025

  40. [40]

    Federated learning for channel estimation in conventional and RIS-assisted massive MIMO,

    A. M. Elbir and S. Coleri, “Federated learning for channel estimation in conventional and RIS-assisted massive MIMO,”IEEE Transactions on Wireless Communications, vol. 21, no. 6, pp. 4255–4268, Nov. 2022. 12

    work page 2022

  41. [41]

    Federated learning in multi-RIS-aided systems,

    W. Ni, Y . Liu, Z. Yang, H. Tian, and X. Shen, “Federated learning in multi-RIS-aided systems,”IEEE Internet of Things Journal, vol. 9, no. 12, pp. 9608–9624, Nov. 2022

    work page 2022

  42. [42]

    Reconfigurable intelligent surface-assisted wireless federated learning with imperfect aggregation,

    P. Sun, E. Liu, W. Ni, R. Wang, Z. Xing, B. Li, and A. Jamalipour, “Reconfigurable intelligent surface-assisted wireless federated learning with imperfect aggregation,”IEEE Transactions on Communications, vol. 73, no. 2, pp. 1058–1071, Feb. 2025

    work page 2025

  43. [43]

    Fluid antenna-assisted dirty multiple access channels over composite fading,

    F. R. Ghadi, K.-K. Wong, F. J. L ´opez-Mart´ınez, C.-B. Chae, K.-F. Tong, and Y . Zhang, “Fluid antenna-assisted dirty multiple access channels over composite fading,”IEEE Communications Letters, vol. 28, no. 2, pp. 382– 386, Dec. 2023

    work page 2023

  44. [44]

    Joint client selection and receive beamforming for over-the-air federated learning with energy harvesting,

    C. Chen, Y .-H. Chiang, H. Lin, J. C. Lui, and Y . Ji, “Joint client selection and receive beamforming for over-the-air federated learning with energy harvesting,”IEEE Open Journal of the Communications Society, vol. 4, pp. 1127–1140, May. 2023

    work page 2023

  45. [45]

    R. B. Nelsen,An introduction to copulas. Springer, 2006

    work page 2006

  46. [46]

    Copula, marginal distributions and model selection: A bayesian note,

    R. d. S. Silva and H. F. Lopes, “Copula, marginal distributions and model selection: A bayesian note,”Statistics and Computing, vol. 18, no. 3, pp. 313–320, Mar. 2008

    work page 2008

  47. [47]

    Copula-based bounds for multi-user communications–part II: Outage performance,

    K.-L. Besser and E. A. Jorswieck, “Copula-based bounds for multi-user communications–part II: Outage performance,”IEEE Communications Letters, vol. 25, no. 1, pp. 8–12, Jan. 2021

    work page 2021