One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning

To mitigate the multi-access latency in federated edge learning, an efficient broadband analog transmission scheme has been recently proposed, featuring the aggregation of analog modulated gradients via the waveform-superposition property of the wireless medium. However. the assumed linear analog modulation makes it difficult to deploy this technique in modern wireless systems that exclusively use digital modulation. To address this issue, we propose in this work a novel digital version of broadband over-the-air aggregation, called one-bit broadband digital aggregation. The new scheme features one-bit gradient quantization followed by digital modulation at the edge devices and a simple threshold-based decoding at the edge server. We develop a comprehensive analysis framework for quantifying the effects of wireless channel hostilities (channel noise and fading) on the convergence rate. The analysis shows that the hostilities slow down the convergence of the learning process by introducing a scaling factor and a bias term into the gradient norm. However, all the negative effects vanish as the number of devices grows, but at a different rate for each type of channel hostility.