Over-the-Air Federated Learning in Heterogeneous Mobile Wireless Networks

Ming Xiang; Nicolò Michelusi; Yonina C. Eldar; Lili Su

cs.LGSep 26, 2026

Over-the-Air Federated Learning in Heterogeneous Mobile Wireless Networks

Authors: Ming Xiang, Nicolò Michelusi, Yonina C. Eldar, Lili Su

Organizations: Northeastern University, Boston, MA, USA · Arizona State University, Tempe, AZ, USA · Weizmann Institute of Science, Rehovot, Israel

Abstract

Over-the-air computation has emerged as a scalable and efficient solution for deploying federated learning algorithms in wireless networks by exploiting waveform superposition for simultaneous model aggregation. Most existing work struggles with heterogeneous fading channels. These approaches either enforce unbiased updates from all devices or allow partial device contributions, requiring careful tuning of the convergence bound to mitigate bias under specific fading models. However, the former significantly amplifies receiver noise due to the weakest channel, whereas the latter is sensitive to fading model mismatch and converges only to a biased objective. To tackle these challenges, we propose FedOAG, which employs algorithmic components to automatically satisfy energy constraints via gradient normalization and evenly mix devices' updates through implicit gossiping. Importantly, FedOAG does not require transmission from all devices, nor does it rely on a specific fading model or knowledge of time-varying statistical channel distributions. We show that FedOAG converges to a stationary point of an unbiased non-convex objective at the best possible rate $O(1/\sqrt{T})$ for any stochastic first-order method. We corroborate our analysis with numerical experiments over dynamic wireless conditions on real-world datasets.

Figures & tables

Figure 1. Mobile devices lead to time-varying statistical CDIs, which determine the uplink activation probabilities

p_{i}^{t}

for heterogeneous devices.

Algorithms	Small-scale CDIs $h_{i}^{t}$		Statistical CDIs $\Lambda_{i}^{t}$		Fading Model
Algorithms	The PS	The Devices	The PS	The Devices	Fading Model
Ours ( FedOAG )	$\times$	$\checkmark$	$\bm{\times}$	$\bm{\times}$	Arbitrary
SCA ( Abrar and Michelusi, 2026 ; Abrar and Michelusi, 2025 )	$\times$	$\checkmark$	$\checkmark$	$\times$	Rayleigh
Vanilla OTA ( Yang et al., 2020 )	$\checkmark$	$\checkmark$	$\times$	$\times$	Arbitrary
BB methods ( Zhu et al., 2019 )	$\times$	$\checkmark$	$\checkmark$	$\checkmark$	Rayleigh
OPC/LCPC methods ( Cao et al., 2020 )	$\checkmark$	$\checkmark$	$\checkmark$	$\times$	Rayleigh

Table 1. The knowledge of channel distribution information from key references.

Panel of Figure 2 — Figure 2. Comparisons of different OTA federated learning algorithms on the MNIST dataset with $m=30$ devices. The results are obtained over five repetitions with solid curves depicting mean test accuracy, and the shaded area denotes standard deviation.

Figure 3. Comparison of FedOAG under different

\gamma

on MNIST with

m=30

devices in the stationary regime, averaged over five repetitions. The blue curve (left axis) shows test accuracy over the final

50

rounds; yellow bars (right axis) show the average number of active devices per round. Smaller

\gamma

lowers the truncation threshold, yielding more active uplinks but greater receiver noise amplification, and vice versa.

\gamma

values on the

x

-axis are uniformly spaced for readability.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4. An example of data heterogeneity using

\mathsf{Dirichlet}(\alpha=0.1)

distribution with

20

clients.

x

-axis denotes the categories of images, while

y

-axis denotes the client index. The size of a circle refers to the proportion of pictures in a given class. The color of a circle distinguishes images with different categories.

Dataset	MNIST
Neural network	MLP
Model architecture ∗	L (784,1024) – R – L (10)
Loss function	Cross-entropy loss
Number of local steps $s$	10
Number of global rounds $T$	800
Batch size	32

Appendix

Table 2. Neural network architecture, loss function, training steps, and batch size specifications

Figure 5. Comparisons of the proposed FedOAG under different

\gamma

’s on the MNIST dataset with

m=30

devices in the stationary regime. The results are obtained over five repetitions. Smaller

\gamma

relates to lower truncation threshold and therefore leads to more active uplinks, but at the expense of higher receiver noise amplification, and vice versa.

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