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REVIEW 5 major objections 5 minor 36 references

A closed-loop framework of GRU-based CSI prediction, personalization, RIS optimization, and user grouping makes RIS-assisted over-the-air federated learning reliable under imperfect, time-varying channels.

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2026-08-01 18:48 UTC pith:2EXEHDJT

load-bearing objection A credible integration of GRU-based CSI prediction, Reptile personalization, and RIS-aware grouping for OTA-FL; the gains are demonstrated only in simulation, and the low-pilot channel recovery deserves a closer identifiability check. the 5 major comments →

arxiv 2607.17169 v1 pith:2EXEHDJT submitted 2026-07-19 cs.IT math.IT

Joint Channel Estimation and Dynamics-Aware Grouping for Time-Varying RIS-Assisted OTA Federated Learning

Ziqi Li , Shuangzhi Li , Uchechukwu Awada , Jiankang Zhang This is my paper
classification cs.IT math.IT
keywords over-the-air federated learningreconfigurable intelligent surfacescascaded channel estimationgated recurrent unitsuser groupingtime-varying channelspersonalized federated learningimperfect CSI
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper aims to solve a coupled problem: in over-the-air federated learning with a reconfigurable intelligent surface, channel estimation, RIS configuration, and model aggregation are tightly linked, yet existing designs treat them separately. It proposes a unified closed-loop framework where a gated recurrent unit learns to predict the time-varying cascaded channel from very few pilots, a personalized Reptile-style update keeps the shared model robust across heterogeneous users, and a dynamics-aware grouping separates users by path-loss and short-term channel fluctuations to prevent update cancellation. The paper argues that this joint design substantially reduces channel estimation error and aggregation distortion in low-pilot and high-mobility regimes, while preserving weak users in training. If true, it would make distributed learning over wireless links practical in mobile, resource-constrained settings.

Core claim

The central claim is that the entangled problems of frequency-selective CSI acquisition, RIS phase control, and OTA aggregation distortion in RIS-assisted OTA-FL can be jointly addressed by a single closed-loop pipeline. The key is a GRU-based temporal estimator that, using only P=8 beam-combined pilot observations and a sliding window of W=8 rounds, predicts both the current channel and the uplink-instant channel under a Jakes AR(1) model, feeding the predicted CSI into the AirComp pre-equalizer and the grouping proxies. Combined with a shared-backbone personalized update and an RIS-aware max-min optimization, the framework is shown in simulation to achieve lower uplink NMSE and aggregation

What carries the argument

The load-bearing mechanism is the GRU-based channel estimator F(x; φ, ψ, q): a shared Conv1D–GRU backbone plus a user-specific head that maps low-dimensional real/imaginary pilot observations to the cascaded channel estimate ĥ, an uplink-instant offset Δĥ, and a path-loss proxy β̂. This one function simultaneously drives three downstream components: the transmit equalization factor via the effective channel ĉ_k, the RIS/beamforming optimization through the distortion proxy NMSE_proxy, and the dynamics-aware grouping through the features (β̂, δ̂). The temporal recurrence is what allows recovery from few pilots, and the AR(1) Jakes model is what makes the temporal correlation learnable in simu

Load-bearing premise

The main gains rest on the assumption that an N=64-dimensional cascaded channel can be recovered from only P=8 pilots per round by exploiting temporal history and a first-order AR(1) Jakes dynamics model; if real channels do not follow that model, the estimated CSI feeding the aggregation can be badly biased and the reported gains collapse.

What would settle it

Run the GRU-based pipeline with P=8, W=8 on a measured or simulated channel trace whose temporal correlation is not AR(1) Jakes (for example, an indoor measured channel or a two-ray mobile channel), and compare the uplink NMSE and aggregation NMSE against the LMMSE 64-pilot baseline; if the GRU does not stay below LMMSE, the central claim of low-pilot robustness is contradicted.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Deployed RIS-assisted OTA-FL systems could cut pilot overhead dramatically, operating with as few as 8 pilots per round instead of the 64-pilot LMMSE reference, without sacrificing aggregation quality.
  • The OTA distortion is bounded by a proxy that scales inversely with the worst-user receive reliability η_r; any mechanism that improves worst-user channel estimates (e.g., better temporal prediction) directly tightens the steady-state convergence neighborhood of the learning algorithm.
  • Dynamics-aware grouping is provably no worse than global aggregation because the grouped problem contains global aggregation as a feasible point, and it avoids the fairness penalty of device selection by retaining weak users in a high-risk group.
  • The GRU's temporal memory provides the largest gains exactly where pilots are scarce, suggesting that learning-based channel prediction is a viable substitute for pilot-hungry classical estimation in mobile environments.
  • Under strong user heterogeneity, grouping into two risk classes reduces cross-user update cancellation and improves convergence speed, with the high-risk group still making partial progress rather than being excluded.

Where Pith is reading between the lines

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

  • Because the simulated channels follow an AR(1) Jakes model, a natural stress test is to run the same pipeline on measured channel traces with different Doppler spectra (e.g., two-ray or non-Jakes scattering); if the GRU's predictive edge disappears, the temporal-memory assumption is the real load-bearing element.
  • The separation of users by long-term path-loss and short-term dynamics could be lifted out of this paper and applied to other RIS-aided multi-user problems, such as scheduling, rate splitting, or beamforming group design, where the pairwise signature-correlation ρ_ij is a ready-made structural prior.
  • The closed-loop idea suggests a further extension: train the GRU with a loss that directly includes the aggregation NMSE (or the max-min η_r) instead of pure CSI reconstruction error, which might create an even tighter coupling between communication reliability and learning performance.
  • If the identifiability assumption fails in deployment — for instance if temporal diversity is insufficient because the channel changes too slowly or too quickly relative to the round interval — the same framework could be adapted to incorporate compressed sensing or side information about the RIS phase codebook to stabilize the estimate.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes a closed-loop framework for RIS-assisted over-the-air federated learning (OTA-FL) under time-varying channels and imperfect CSI. The framework combines a GRU-based temporal channel estimator, a Reptile-style personalized FL backbone, RIS/beamforming optimization driven by the estimated CSI, and a dynamics-aware two-group user grouping strategy. The analytical part gives a perturbation bound (Lemma 1) and a qualitative stationarity bound (Theorem 1) for the FL recursion under OTA distortion, plus convergence claims for the SCA grouping solver. Simulations on synthetic AR(1)-Jakes channels compare the GRU estimator against CNN and LMMSE baselines, reporting lower CSI NMSE and aggregation NMSE, and show that grouping reduces NMSE for low-risk users under mobility and heterogeneity.

Significance. If the claims are substantiated, the framework addresses a relevant and difficult coupling: imperfect time-varying cascaded CSI, OTA aggregation distortion, and user heterogeneity. The paper releases code, which aids reproducibility, and its theoretical results are honestly framed as perturbation/stationarity bounds rather than overclaimed convergence rates. The low-pilot and high-mobility operating regime is practically important. However, the current evidence is conditional: the key low-pilot gain rests on an unproven identifiability assumption, the numerical evaluation lacks statistical confidence measures and end-to-end FL accuracy curves, and the grouping benefit is argued from a flawed feasible-set comparison. The central idea remains plausible and worth further development, but the paper needs substantial revision to support its headline claims.

major comments (5)
  1. [§II-B, Eq. (12), and §V.A] The claimed low-pilot gain (P=8 pilots for N=64 cascaded channel coefficients) is not supported by an identifiability or observability analysis. Eq. (8) is an AR(1) model with scalar-multiple state transition, so if the RIS pilot phase matrix Θ^r is fixed or low-rank across rounds, stacking time history does not add new spatial measurement directions. If Θ^r is varied across rounds, the paper states no persistent-excitation condition. The GRU is trained offline on LMMSE labels generated with P_ref=64 pilots, a different, better-conditioned sensing model; no distribution-shift or model-mismatch test is reported. A biased ĉ^r entering Eqs. (21)-(22) would inflate Ξ^r_CSI in Lemma 1, yet the paper's robustness claims do not address this failure mode.
  2. [§V.C, Figs. 5–12, Table I] No error bars, multiple-seed statistics, or significance tests are reported; all conclusions are based on single simulation traces. The abstract claims 'improving convergence speed' of federated learning, but no end-to-end FL loss or test-accuracy curves are shown anywhere. Figs. 5–8 report CSI NMSE and aggregation NMSE, which are physical-layer proxies, not learning performance. The 'warmup-then-group' convergence-speed claim in §III-D is therefore not directly measured. The authors should add multi-seed statistics and FL learning curves, or temper the convergence-speed claim.
  3. [§V.D, 'From a mathematical perspective...'] The argument that grouping cannot be worse because 'the grouped problem contains single global aggregation as a special case' is incorrect as stated. In the grouped procedure, each group runs its own independent OTA-FL chain with its own shared backbone; a single global model is not a feasible point unless the two group models are constrained to be equal, which the algorithm does not do. The feasible-set inclusion is therefore not established. Either provide a formal reduction with explicit shared constraints or replace this justification with empirical evidence.
  4. [§III-D and §V.A] The grouping module depends on many hyperparameters — ζ_1..ζ_4, γ_β, γ_δ, λ, λ_φ, ς_i, K_min — and on an activation rule ('several consecutive rounds after a prescribed minimum round index') whose values are never specified in the simulation settings. The paper also does not report the SCA iteration counts or tolerances used for the grouping solver. Since grouping is a core contribution, the missing hyperparameters and activation threshold prevent independent reproduction and sensitivity analysis. The available code helps, but the paper should state the values.
  5. [§IV-A, Appendix B, Theorem 1] The proof of Theorem 1 uses E[e^r_OTA | φ^r] = 0, but Lemma 1 only establishes a second-moment bound for e^r_OTA; zero conditional mean is neither stated in Assumption A3 nor proved. Without zero mean, the −c_1∥∇F∥² descent term may be contaminated by a first-order bias, and the stationarity-neighborhood interpretation changes. The authors should add an explicit zero-mean assumption or prove it from the AirComp model. Additionally, Theorem 1 yields only a bounded neighborhood, not convergence speed, so the abstract's 'convergence speed' wording should be softened.
minor comments (5)
  1. [Eqs. (4)–(5)] The definition of ω^r_k is inconsistent with the denominator in Eq. (5). As defined, Σ_k ω^r_k = K, making 1/Σω^r_k a factor 1/K; if normalized weights are intended, define them accordingly.
  2. [§IV-B] The subsection is titled 'Statistical Convergence' but the evidence is a single run of proxy trajectories (Fig. 3) with no statistical measures. Consider renaming it 'Empirical stabilization' or adding confidence regions.
  3. [Figs. 6–7 captions] The captions state that 11-round rolling medians are overlaid, while the text says mean values are computed from round 50 onward. Clarify which quantity is plotted and which is averaged.
  4. [Notation] C is used both to denote the complex numbers and the constant in Lemma 1/Theorem 1. This can confuse readers; use a distinct symbol, e.g., C_0, for the bound constant.
  5. [Conclusion] The conclusion says theoretical analysis shows 'convergence of the Reptile-based shared backbone', but Theorem 1 only establishes a bounded stationarity neighborhood under bounded disturbances. Reword to avoid overclaiming.

Circularity Check

0 steps flagged

No significant circularity: Lemma 1 is a derived bound, the GRU gains are external simulation results against true channels, and the self-citations are background only.

full rationale

The claimed derivation chain is not circular. The low-pilot GRU result is an empirical simulation claim: the estimator is trained offline on LMMSE reference labels generated with P_ref=64 pilots (Sec. V-A), but the reported metric is the round-wise uplink true NMSE against the simulated true channels, so the 'prediction' is not the fitted label by construction. Lemma 1, although it bounds the OTA perturbation by NMSE_proxy, is derived algebraically in Appendix A from the pre-equalizer (21)-(22), Cauchy-Schwarz, and the pilot/aggregation model; NMSE_proxy is not assumed to be the error, it is an analytically related design proxy. Theorem 1 is a standard smooth-descent argument with the Lemma-1 bound as a perturbation term; it does not fold the conclusion into an assumption. The coupling between CSI accuracy and aggregation reliability is a consequence of the definitions, not a self-definitional prediction. The grouping benefit is justified by feasible-set inclusion, a valid inequality, and is also empirically tested against non-grouping baselines. The self-citations ([10], [16], [17]) appear in background/related-work sentences and are not used to justify the main claims; no uniqueness theorem or modeling ansatz is imported from those papers. The identifiability concern raised by the skeptical reading (recovering an N=64 cascaded channel from P=8 pilots) is a real correctness/robustness risk, but it is not circularity: the simulator's channel is generated by the AR(1)-Jakes model (Eq. 8), not by the GRU's own prior, and the test metric is the true channel NMSE. Hence no fitted value is renamed as a prediction and no derivation step reduces to its own input. Score 2 reflects only the presence of minor, non-load-bearing self-citations.

Axiom & Free-Parameter Ledger

4 free parameters · 8 axioms · 0 invented entities

The framework rests on standard smoothness assumptions for the convergence theorem, an idealized AR(1)-Jakes channel model for simulations, an implicit identifiability assumption for the low-pilot channel estimator, and several hand-tuned objective weights that are not fully reported. No new physical entities are introduced.

free parameters (4)
  • Reptile outer step size \beta_R = 0.2
    Chosen by hand in Section V-A; the theory only gives an upper bound 0<\beta_R<(1-\kappa/2)/(L G_1), not a specific value.
  • Estimation loss weights \lambda_\beta and \lambda_{\alpha,k}^r
    Introduced in Eq. (17) to balance fast-fading, slow-fading, and path-loss terms; numerical values are not reported.
  • Grouping objective hyperparameters \zeta_1..\zeta_4, \gamma_\beta, \gamma_\delta, \lambda, \lambda_\phi, \varsigma_i, K_
    Introduced in Eqs. (28)-(32) and never assigned values or given a sensitivity study; the grouping gain in Fig. 8 could depend on these choices.
  • Per-method best learning rates = GRU 1.05e-3, CNN-arch 1.05e-3, CNN-base 9.60e-3
    Table I reports steady-state NMSE under individually tuned learning rates; this is a per-method fit to the data, though the authors use it to argue the GRU gain is not solely learning-rate selection.
axioms (8)
  • standard math A1: F(\phi) is L-smooth.
    Imposed in Section IV-A for the Reptile descent analysis; standard in FL convergence proofs.
  • domain assumption A2: The ideal Reptile update satisfies a descent alignment condition with bounded heterogeneity bias B_het.
    Stated as an assumption in Section IV-A; not derived from the personalized FL objective or data heterogeneity.
  • domain assumption A3: The OTA perturbation e_OTA has bounded second moment.
    Stated in Section IV-A and made concrete by Lemma 1 under bounded \sum|\hat c_k|^2 and \sum|\vartheta_k|^2; boundedness of these is assumed.
  • domain assumption Small-scale fading follows the AR(1) Jakes model in Eq. (8).
    Used to generate all simulated channels and to construct temporal correlation exploited by the GRU; if real channels deviate, simulated gains may not transfer.
  • domain assumption The direct BS-user link is weak or blocked (\chi_d=0 in the default setting).
    Section II-B and Section V-A set 'only the reflected link is enabled'; the paper argues the direct link is negligible under its settings.
  • domain assumption LMMSE reference labels with P_ref=64 pilots are accurate enough to supervise GRU training.
    Section III-A uses LMMSE as the teacher for offline calibration; the GRU cannot be better than this teacher in deployment, and label error is acknowledged as the remaining gap in Fig. 11.
  • ad hoc to paper The P=8 beam-combined pilot observation plus temporal history is sufficient to recover the N=64 cascaded channel.
    Implicit in Eq. (12) and the simulation settings; no identifiability or rank analysis is provided, and the claim depends on the AR(1) temporal prior making the inverse well-posed.
  • ad hoc to paper Dynamic proxies stabilize after approximately 20 rounds, making grouping activation reliable.
    Section IV-B states 'all proxies converge after approximately 20 rounds' based on Fig. 3; this is empirical and not guaranteed across environments.

pith-pipeline@v1.3.0-alltime-deepseek · 17006 in / 12891 out tokens · 123709 ms · 2026-08-01T18:48:16.584190+00:00 · methodology

0 comments
read the original abstract

Reconfigurable intelligent surface (RIS)-assisted over-the-air federated learning (OTA-FL) enables efficient distributed intelligence but suffers from time-varying channels, imperfect channel state information (CSI), and strong user heterogeneity, which jointly degrade aggregation accuracy and cause severe model update cancellation. To address these issues, we propose a unified framework for joint channel estimation and dynamics-aware user grouping in RIS-assisted OTA-FL systems, enabling reliable learning under imperfect CSI and heterogeneous dynamics. The framework integrates gated recurrent unit (GRU) for temporal modeling to capture time-varying CSI evolution, OTA-based federated aggregation with personalization, and RIS-aware physical-layer optimization in a closed loop. In addition, we design a dynamics-aware grouping strategy based on long-term path-loss and short-term channel dynamics to reduce inter-user conflicts under heterogeneous conditions. Simulation results show that the proposed method achieves substantial gains in CSI estimation accuracy and OTA aggregation performance in low-pilot and high-mobility regimes, while improving convergence speed and robustness under strong user heterogeneity.

Figures

Figures reproduced from arXiv: 2607.17169 by Jiankang Zhang, Shuangzhi Li, Uchechukwu Awada, Ziqi Li.

Figure 1
Figure 1. Figure 1: RIS-assisted cascaded-channel OTA-FL system model and per-round [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Structure of the adopted GRU-based estimator. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dynamic/physical proxies across users. (a) Path-loss proxy heatmap. (b) Short-range dynamics proxy norm heatmap. (c) Converged short-range [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Scene-distribution designs. We evaluate the uplink channel prediction accuracy using the round-wise uplink NMSEr up = PK k=1∥hˆ r,τ RU,k−h r,τ RU,k∥ 2 P 2 K k=1∥h r,τ RU,k∥ 2 2 , and aggregation quality using NMSEr agg and proxy distortion NMSEr proxy. We apply a common-reference normalization for the proxy distortion to ensure fair comparison. B. Compared Methods We compare the following baselines: • GRU … view at source ↗
Figure 5
Figure 5. Figure 5: Round-wise uplink true NMSE in Scene 1 with Setting 1 and Scene 2 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Round-wise proxy-distortion gap after physical-layer optimization in [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: Round-wise uplink true NMSE in the extreme pilot case [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: GRU uplink true NMSE under different supervision-label qualities [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: DC-AO versus SCA in Scene 1 with all users static and Scene 2 [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗

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Reference graph

Works this paper leans on

36 extracted references · 2 canonical work pages

  1. [1]

    A survey on mobile edge computing: The communication perspective,

    Y . Mao, C. You, J. Zhang, K. Huang, and K. B. Letaief, “A survey on mobile edge computing: The communication perspective,”IEEE Communications Surveys & Tutorials, vol. 19, no. 4, pp. 2322–2358, 2017

    2017

  2. [2]

    Mobile edge computing: A survey,

    N. Abbas, Y . Zhang, A. Taherkordi, and T. Skeie, “Mobile edge computing: A survey,”IEEE Internet of Things Journal, vol. 5, no. 1, pp. 450–465, 2018

    2018

  3. [3]

    A survey on federated learning systems: Vision, hype and reality for data privacy and protection,

    Q. Li, Z. Wen, Z. Wu, S. Hu, N. Wang, Y . Li, X. Liu, and B. He, “A survey on federated learning systems: Vision, hype and reality for data privacy and protection,”IEEE Transactions on Knowledge and Data Engineering, vol. 35, no. 4, pp. 3347–3366, 2023

    2023

  4. [4]

    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, 2022

    2022

  5. [5]

    Communication-Efficient Learning of Deep Networks from Decentralized Data,

    H. B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. Ag ¨uera y Arcas, “Communication-Efficient Learning of Deep Networks from Decentralized Data,”arXiv e-prints, p. arXiv:1602.05629, Feb. 2016

    Pith/arXiv arXiv 2016

  6. [6]

    Advances and Open Problems in Federated Learning,

    P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis, A. Nitin Bhagoji, K. Bonawitz, Z. Charles, G. Cormode, R. Cummings, R. G. L. D’Oliveira, H. Eichner, S. El Rouayheb, D. Evans, J. Gardner, Z. Garrett, A. Gasc ´on, B. Ghazi, P. B. Gibbons, M. Gruteser, Z. Harchaoui, C. He, L. He, Z. Huo, B. Hutchinson, J. Hsu, M. Jaggi, T. Javidi, G. Joshi, M. Kho...

    Pith/arXiv arXiv 1912

  7. [7]

    Federated Optimization: Distributed Machine Learning for On-Device Intelli- gence,

    J. Kone ˇcn´y, H. B. McMahan, D. Ramage, and P. Richt ´arik, “Federated Optimization: Distributed Machine Learning for On-Device Intelli- gence,”arXiv e-prints, p. arXiv:1610.02527, Oct. 2016

    Pith/arXiv arXiv 2016

  8. [8]

    Broadband analog aggregation for low-latency federated edge learning,

    G. Zhu, Y . Wang, and K. Huang, “Broadband analog aggregation for low-latency federated edge learning,”IEEE Transactions on Wireless Communications, vol. 19, no. 1, pp. 491–506, 2020

    2020

  9. [9]

    Machine learning at the wireless edge: Distributed stochastic gradient descent over-the-air,

    M. Mohammadi Amiri and D. G ¨und¨uz, “Machine learning at the wireless edge: Distributed stochastic gradient descent over-the-air,”IEEE Transactions on Signal Processing, vol. 68, pp. 2155–2169, 2020

    2020

  10. [10]

    Airedge: A dependency- aware multi-task orchestration in federated aerial computing,

    U. Awada, J. Zhang, S. Chen, and S. Li, “Airedge: A dependency- aware multi-task orchestration in federated aerial computing,”IEEE Transactions on V ehicular Technology, vol. 71, no. 1, pp. 805–819, 2022

    2022

  11. [11]

    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, 2020

    2022

  12. [12]

    Imperfect csi: A key factor of uncertainty to over-the-air federated learning,

    J. Yao, Z. Yang, W. Xu, D. Niyato, and X. You, “Imperfect csi: A key factor of uncertainty to over-the-air federated learning,”IEEE Wireless Communications Letters, vol. 12, no. 12, pp. 2273–2277, 2023

    2023

  13. [13]

    Intelligent reflecting surface enhanced wireless network via joint active and passive beamforming,

    Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless network via joint active and passive beamforming,”IEEE Transactions on Wireless Communications, vol. 18, no. 11, pp. 5394–5409, 2019

    2019

  14. [14]

    Over-the-air computation via intelligent reflecting surfaces,

    T. Jiang and Y . Shi, “Over-the-air computation via intelligent reflecting surfaces,” in2019 IEEE Global Communications Conference (GLOBE- COM), 2019, pp. 1–6

    2019

  15. [15]

    Federated ma- chine learning for intelligent iot via reconfigurable intelligent surface,

    K. Yang, Y . Shi, Y . Zhou, Z. Yang, L. Fu, and W. Chen, “Federated ma- chine learning for intelligent iot via reconfigurable intelligent surface,” IEEE Network, vol. 34, no. 5, pp. 16–22, 2020

    2020

  16. [16]

    Joint channel estimation and blockage diagnosis in RIS-assisted mmwave MIMO-OFDM sys- tems,

    S. Li, C. Liu, H. Lei, N. Wang, and X. Guo, “Joint channel estimation and blockage diagnosis in RIS-assisted mmwave MIMO-OFDM sys- tems,”IEEE Transactions on V ehicular Technology, vol. 75, no. 5, pp. 8018–8029, 2026

    2026

  17. [17]

    Parametric channel estimation for RIS-assisted mmwave MIMO-OFDM systems with low pilot overhead,

    S. Li, R. Yang, X. Guo, G. Han, and J. Zhang, “Parametric channel estimation for RIS-assisted mmwave MIMO-OFDM systems with low pilot overhead,”Signal Processing, vol. 225, p. 109611, 2024. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S0165168424002305

    2024

  18. [18]

    Performance-oriented design for intelligent reflecting surface-assisted federated learning,

    Y . Zhao, Q. Wu, W. Chen, C. Wu, and H. V . Poor, “Performance-oriented design for intelligent reflecting surface-assisted federated learning,” IEEE Transactions on Communications, vol. 71, no. 9, pp. 5228–5243, 2023

    2023

  19. [19]

    Channel esti- mation with reconfigurable intelligent surfaces—a general framework,

    A. L. Swindlehurst, G. Zhou, R. Liu, C. Pan, and M. Li, “Channel esti- mation with reconfigurable intelligent surfaces—a general framework,” Proceedings of the IEEE, vol. 110, no. 9, pp. 1312–1338, 2022

    2022

  20. [20]

    A survey on channel estima- tion and practical passive beamforming design for intelligent reflecting surface aided wireless communications,

    B. Zheng, C. You, W. Mei, and R. Zhang, “A survey on channel estima- tion and practical passive beamforming design for intelligent reflecting surface aided wireless communications,”IEEE Communications Surveys & Tutorials, vol. 24, no. 2, pp. 1035–1071, 2022

    2022

  21. [21]

    Csi acquisition in ris-assisted mobile communication systems,

    Y . Han, W. Tang, X. Li, M. Matthaiou, and S. Jin, “Csi acquisition in ris-assisted mobile communication systems,”National Science Review, vol. 10, no. 8, p. nwad127, 05 2023. [Online]. Available: https://doi.org/10.1093/nsr/nwad127

    work page doi:10.1093/nsr/nwad127 2023

  22. [22]

    Two-timescale channel estimation for reconfigurable intelligent surface aided wireless communications,

    C. Hu, L. Dai, S. Han, and X. Wang, “Two-timescale channel estimation for reconfigurable intelligent surface aided wireless communications,” IEEE Transactions on Communications, vol. 69, no. 11, pp. 7736–7747, 2021

    2021

  23. [23]

    Reconfigurable intelligent surface enabled federated learning: A unified communication-learning design approach,

    H. Liu, X. Yuan, and Y .-J. A. Zhang, “Reconfigurable intelligent surface enabled federated learning: A unified communication-learning design approach,”IEEE Transactions on Wireless Communications, vol. 20, no. 11, pp. 7595–7609, 2021

    2021

  24. [24]

    Channel estimation in ris-aided heterogeneous wireless networks via federated learning,

    M. Asaad Cheema, A. Chawla, V . Chakravarthi Gogineni, and P. Salvo Rossi, “Channel estimation in ris-aided heterogeneous wireless networks via federated learning,”IEEE Communications Letters, vol. 29, no. 4, pp. 709–713, April 2025

    2025

  25. [25]

    Multi-center federated learning: clients clustering for better personalization,

    G. Long, M. Xie, T. Shen, T. Zhou, X. Wang, and J. Jiang, “Multi-center federated learning: clients clustering for better personalization,”World Wide Web, vol. 26, no. 1, pp. 481–500, 2023. [Online]. Available: https://doi.org/10.1007/s11280-022-01046-x

    work page doi:10.1007/s11280-022-01046-x 2023

  26. [26]

    Clustered federated learning: Model-agnostic distributed multitask optimization under privacy con- straints,

    F. Sattler, K.-R. M ¨uller, and W. Samek, “Clustered federated learning: Model-agnostic distributed multitask optimization under privacy con- straints,”IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 8, pp. 3710–3722, 2021

    2021

  27. [27]

    An efficient framework for clustered federated learning,

    A. Ghosh, J. Chung, D. Yin, and K. Ramchandran, “An efficient framework for clustered federated learning,”IEEE Transactions on Information Theory, vol. 68, no. 12, pp. 8076–8091, 2022

    2022

  28. [28]

    Federated multi-task learning,

    V . Smith, C.-K. Chiang, M. Sanjabi, and A. Talwalkar, “Federated multi-task learning,” inAdvances in Neural Information Processing Systems, I. Guyon, U. V . Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, Eds., vol. 30. Curran Associates, Inc., 2017. [Online]. Available: https://proceedings.neurips.cc/paper files/paper/2017/fi...

    arXiv 2017

  29. [29]

    Personalized Fed- erated Learning: A Meta-Learning Approach,

    A. Fallah, A. Mokhtari, and A. Ozdaglar, “Personalized Fed- erated Learning: A Meta-Learning Approach,”arXiv e-prints, p. arXiv:2002.07948, Feb. 2020

    Pith/arXiv arXiv 2002

  30. [30]

    Federated Meta-Learning with Fast Convergence and Efficient Communication,

    F. Chen, M. Luo, Z. Dong, Z. Li, and X. He, “Federated Meta-Learning with Fast Convergence and Efficient Communication,”arXiv e-prints, p. arXiv:1802.07876, Feb. 2018

    Pith/arXiv arXiv 2018

  31. [31]

    Personalized Federated Learning with Moreau Envelopes,

    C. T. Dinh, N. H. Tran, and T. Dung Nguyen, “Personalized Federated Learning with Moreau Envelopes,”arXiv e-prints, p. arXiv:2006.08848, Jun. 2020

    Pith/arXiv arXiv 2006

  32. [32]

    Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation,

    K. Cho, B. van Merrienboer, C. Gulcehre, D. Bahdanau, F. Bougares, H. Schwenk, and Y . Bengio, “Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation,”arXiv e- prints, p. arXiv:1406.1078, Jun. 2014

    Pith/arXiv arXiv 2014

  33. [33]

    Wiener,Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications

    N. Wiener,Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications. The MIT Press, 08 1949. [Online]. Available: https://doi.org/10.7551/mitpress/2946.001.0001

    doi:10.7551/mitpress/2946.001.0001 1949

  34. [34]

    Intelligent reflecting surface enhanced wireless network: Joint active and passive beamforming design,

    Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless network: Joint active and passive beamforming design,” in2018 IEEE Global Communications Conference (GLOBECOM), 2018, pp. 1–6

    2018

  35. [35]

    A unified convergence analysis of block successive minimization methods for nonsmooth optimization,

    M. Razaviyayn, M. Hong, and Z.-Q. Luo, “A unified convergence analysis of block successive minimization methods for nonsmooth optimization,”SIAM Journal on Optimization, vol. 23, no. 2, pp. 1126– 1153, 2013. [Online]. Available: https://doi.org/10.1137/120891009

    doi:10.1137/120891009 2013

  36. [36]

    Parallel and distributed methods for constrained nonconvex optimization—part i: Theory,

    G. Scutari, F. Facchinei, and L. Lampariello, “Parallel and distributed methods for constrained nonconvex optimization—part i: Theory,”IEEE Transactions on Signal Processing, vol. 65, no. 8, pp. 1929–1944, 2017

    1929