Over-the-Air Federated Learning with Phase Noise: Analysis and Countermeasures
Martin Dahl, Erik G. Larsson
TL;DR
This work tackles over-the-air federated learning under carrier-frequency-offset–induced phase noise by proposing gradient permutations (Flip, Roll, Sort) to reorder transmissions so more influential gradients are sent earlier when phase drift is strongest. It derives the gradient-estimator statistics, showing that an appropriate scaling $a_d$ can render the estimate unbiased, but the variance grows exponentially with the number of symbols in a coherence block, highlighting a key trade-off between ordering and accuracy. Through MNIST/CNN simulations, Roll generally achieves the best learning performance under higher phase noise, while all permutations improve convergence in low phase-noise regimes; genie-aided Sort provides an upper-bound baseline. The results suggest gradient permutation as a practical countermeasure to phase noise in wireless FL and point to future work on more frequent sorting and finer-grained permutation strategies to further stabilize learning in noisy OAC environments.
Abstract
Wirelessly connected devices can collaborately train a machine learning model using federated learning, where the aggregation of model updates occurs using over-the-air computation. Carrier frequency offset caused by imprecise clocks in devices will cause the phase of the over-the-air channel to drift randomly, such that late symbols in a coherence block are transmitted with lower quality than early symbols. To mitigate the effect of degrading symbol quality, we propose a scheme where one of the permutations Roll, Flip and Sort are applied on gradients before transmission. Through simulations we show that the permutations can both improve and degrade learning performance. Furthermore, we derive the expectation and variance of the gradient estimate, which is shown to grow exponentially with the number of symbols in a coherence block.