cs.LGMar 25, 2025

Unified Robust and Convergent Over-The-Air Federated Learning under Channel Noise and Heterogeneity

Authors: Zubair Shaban, Nazreen Shah, Ranjitha Prasad

Organizations: ECE dept., IIIT Delhi, New Delhi.

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Abstract

Federated learning (FL) has emerged as a key enabler of distributed model training across ubiquitous wireless edge devices while preserving data privacy in next-generation wireless systems. One communication-efficient approach to realize this is leveraging Over-the-Air Federated Learning (OTA-FL), which exploits the superposition property of wireless multiple access channels (MAC) to perform low-latency model aggregation. However, practical OTA-FL deployments are significantly affected by the joint effects of channel noise at the server, fading, and both data and system heterogeneity across participating edge devices, which can degrade the model performance and thereby convergence. In this work, we propose the novel Robust and Convergent Federated Learning (RoCo-FL), a framework that jointly handles these challenges in federated wireless networks. RoCo-FL formulates local updates through inexact optimization, capturing the effects of wireless noise, partial participation, and heterogeneous system capabilities via structured inexactness conditions. These conditions naturally manifest as a proximal constraint at the edge devices that stabilizes local updates and mitigates the impact of channel impairments, data heterogeneity, and stragglers. We establish convergence guarantees for non-convex objectives under the proposed zeroth- and first-order inexactness models, providing theoretical insight into the interplay between channel impairments, data, and system heterogeneity. Experimentally, we validate RoCo-FL on real-world datasets, including CIFAR10, CIFAR100, and FEMNIST, demonstrating its robustness in noisy and heterogeneous environments. Compared to state-of-the-art baselines, RoCo-FL achieves significantly more stable convergence and higher accuracy, particularly in the presence of stragglers.

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Fig. 1: Left: Practical OTA-FL under data and system heterogeneity with wireless channel impairments. Right: Bar plots showing (i) the impact of system heterogeneity (stragglers) on COTAF [ 25 ] and (ii) the impact of noise on FedProx [ 13 ] , both on CIFAR-10. COTAF degrades in the presence of stragglers, while FedProx fails at low SNR, motivating a method that jointly addresses system heterogeneity and noisy wireless environments.
Fig. 2: Comparison of RoCo-FL with the baselines for FEMNIST and CIFAR10 (π=0.1,λ=0.4)(\pi=0.1,\lambda=0.4) and CIFAR100 (π=0.5,λ=0.01)(\pi=0.5,\lambda=0.01) for SNR( τ\tau ) = 00 dB.
Fig. 3: Performance of RoCo-FL and baselines for varying data heterogeneity for SNR = 00 dB.
Fig. 4: Performance of RoCo-FL and COTAF under heterogeneous system settings on CIFAR100 dataset: (a) 0%0\% stragglers, (b) 50%50\% stragglers, and (c) 75%75\% stragglers.
Fig. 5: Performance of RoCo-FL and COTAF under heterogeneous system settings on CIFAR10 and FEMNIST datasets: (a),(d) 0%0\% stragglers, (b),(e) 50%50\% stragglers, and (c),(f) 75%75\% stragglers.
Fig. 6: Performance of RoCo-FL, NoisyProx, and COTAF for varying SNR on CIFAR10 (π=0.1)(\pi=0.1) and CIFAR100 (π=0.5)(\pi=0.5) datasets.
Fig. 7: (a) Contour plot for SNR Vs λ\lambda on CIFAR10 dataset (π=0.5)(\pi=0.5) . (b) Performance of RoCo-FL and COTAF under fading channels at an SNR of 00 dB, where r^\hat{r} is selected such that the minimum number of participating clients is 1010 . (c) Performance of RoCo-FL and COTAF under fading channels at an SNR of −5-5 dB, where r^\hat{r} is selected such that the minimum number of participating clients is 2020 .
Fig. 8: Performance of RoCo-FL and COTAF under the effect of fading and stragglers with the SNR of 00 dB. r^\hat{r} is chosen such that the minimum number of participating clients is 2020 .
MethodWirelessStraggler(B,H)(B,H)ConvergenceConvexity
 AwareHandlingAssump.RateSetting
FedAvg [ 18 ]✗✗(0,H)(0,H)O(1/T)\mathcal{O}(1/T)Convex
FedProx(A) [ 13 ]✗✓(B,0)(B,0)O(1/T)\mathcal{O}(1/T)Non-Convex
FedProx(B) [ 31 ]✗✓✗O(1/T)\mathcal{O}(1/\sqrt{T})Non-Convex
SCAFFOLD [ 10 ]✗✗✗O(1/T)\mathcal{O}(1/T)Non-Convex
FedLin [ 19 ]✗✗✗O(1/T)\mathcal{O}(1/T)Non-Convex
TABLE I: Comparison of assumptions and convergence guarantees of RoCo-FL with existing federated learning methods. Here, TT denotes the total number of communication rounds.
NotationDescription
x\mathbf{x}Boldface small letters denote vectors
X\mathbf{X}Boldface capital letters denote matrices
IM\mathbf{I}_{M}M×MM\times M identity matrix
∣∣x∣∣||\bm{x}||ℓ2\ell_{2} -norm of vector x\bm{x}
P\mathcal{P}A set
∣P∣|\mathcal{P}|Size of the set P\mathcal{P}
TABLE II: List of notations used in the paper
Fig. 9: Performance of RoCo-FL under varying clients.
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