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

Zubair Shaban; Nazreen Shah; Ranjitha Prasad

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.

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.

Figures & tables

Panel of Figure 1 — 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 $(\pi=0.1,\lambda=0.4)$ and CIFAR100 $(\pi=0.5,\lambda=0.01)$ for SNR( $\tau$ ) = $0$ dB.

Fig. 3: Performance of RoCo-FL and baselines for varying data heterogeneity for SNR = $0$ dB.

Fig. 4: Performance of RoCo-FL and COTAF under heterogeneous system settings on CIFAR100 dataset: (a) $0\%$ stragglers, (b) $50\%$ stragglers, and (c) $75\%$ stragglers.

Fig. 5: Performance of RoCo-FL and COTAF under heterogeneous system settings on CIFAR10 and FEMNIST datasets: (a),(d) $0\%$ stragglers, (b),(e) $50\%$ stragglers, and (c),(f) $75\%$ stragglers.

Fig. 6: Performance of RoCo-FL, NoisyProx, and COTAF for varying SNR on CIFAR10 $(\pi=0.1)$ and CIFAR100 $(\pi=0.5)$ datasets.

Fig. 7: (a) Contour plot for SNR Vs $\lambda$ on CIFAR10 dataset $(\pi=0.5)$ . (b) Performance of RoCo-FL and COTAF under fading channels at an SNR of $0$ dB, where $\hat{r}$ is selected such that the minimum number of participating clients is $10$ . (c) Performance of RoCo-FL and COTAF under fading channels at an SNR of $-5$ dB, where $\hat{r}$ is selected such that the minimum number of participating clients is $20$ .

Fig. 8: Performance of RoCo-FL and COTAF under the effect of fading and stragglers with the SNR of $0$ dB. $\hat{r}$ is chosen such that the minimum number of participating clients is $20$ .

Method	Wireless	Straggler	$(B,H)$	Convergence	Convexity
	Aware	Handling	Assump.	Rate	Setting
FedAvg [ 18 ]	✗	✗	$(0,H)$	$\mathcal{O}(1/T)$	Convex
FedProx(A) [ 13 ]	✗	✓	$(B,0)$	$\mathcal{O}(1/T)$	Non-Convex
FedProx(B) [ 31 ]	✗	✓	✗	$\mathcal{O}(1/\sqrt{T})$	Non-Convex
SCAFFOLD [ 10 ]	✗	✗	✗	$\mathcal{O}(1/T)$	Non-Convex
FedLin [ 19 ]	✗	✗	✗	$\mathcal{O}(1/T)$	Non-Convex

TABLE I: Comparison of assumptions and convergence guarantees of RoCo-FL with existing federated learning methods. Here,

T

denotes the total number of communication rounds.

Notation	Description
$\mathbf{x}$	Boldface small letters denote vectors
$\mathbf{X}$	Boldface capital letters denote matrices
$\mathbf{I}_{M}$	$M\times M$ identity matrix
$\|\|\bm{x}\|\|$	$\ell_{2}$ -norm of vector $\bm{x}$
$\mathcal{P}$	A set
$\|\mathcal{P}\|$	Size of the set $\mathcal{P}$

TABLE II: List of notations used in the paper

Fig. 9: Performance of RoCo-FL under varying clients.

Federated Learning

Federated learning trains shared models across data holders without requiring them to pool their raw data.

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Channel-Adaptive Robust Aggregation for Over-the-Air Federated Learning in Heterogeneous Networks

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Federated Learning Aggregation Over-the-Air Federated Learning Wireless Resource Allocation Federated Learning Heterogeneous Federated Learning

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The growing demand for privacy-preserving, data-intensive applications such as IoT, augmented reality, and autonomous systems positions Federated Learning (FL) as a key enabler in 6G networks. Over-the-Air FL (OTA-FL) leverages the superposition property of the wireless multiple access channel for efficient aggregation via simultaneous transmissions. Existing methods rely on fixed aggregation schedules and do not jointly address noise, fading, and client heterogeneity. We propose CHARGE-FL (CHannel-Adaptive Robust agGrEgation), a framework that adaptively schedules aggregation based on channel dynamics and application readiness. By combining a tailored optimization strategy with a dual-purpose precoding mechanism, CHARGE-FL mitigates channel distortion and bias from partial updates, achieving superior accuracy, stability, and convergence under realistic wireless conditions. Empirical results under realistic wireless conditions show that CHARGE-FL significantly improves accuracy, stability, and convergence over state-of-the-art OTA-FL methods, particularly in straggler-prone and noisy scenarios.

Abstract

Federated Learning

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