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.

翻译：无线连接设备可利用联邦学习协作训练机器学习模型，其中模型更新的聚合通过空中计算实现。设备时钟不精确导致的载波频率偏移会使空中信道相位随机漂移，使得相干块中后期符号的传输质量低于前期符号。为缓解符号质量下降的影响，我们提出一种方案：在传输前对梯度施加轮转、翻转与排序中的一种排列操作。仿真结果表明，这些排列既能提升也能降低学习性能。此外，我们推导了梯度估计的期望与方差，该方差随相干块中符号数量呈指数增长。