  Federated edge learning (FEEL) is a popular framework for model training at
an edge server using data distributed at edge devices (e.g., smart-phones and
sensors) without compromising their privacy. In the FEEL framework, edge
devices periodically transmit high-dimensional stochastic gradients to the edge
server, where these gradients are aggregated and used to update a global model.
When the edge devices share the same communication medium, the multiple access
channel (MAC) from the devices to the edge server induces a communication
bottleneck. To overcome this bottleneck, an efficient broadband analog
transmission scheme has been recently proposed, featuring the aggregation of
analog modulated gradients (or local models) 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 (OBDA). The new scheme features one-bit
gradient quantization followed by digital quadrature amplitude modulation (QAM)
at edge devices and over-the-air majority-voting based decoding at edge server.
We provide a comprehensive analysis of the effects of wireless channel
hostilities (channel noise, fading, and channel estimation errors) on the
convergence rate of the proposed FEEL scheme. 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, we show that
all the negative effects vanish as the number of participating devices grows,
but at a different rate for each type of channel hostility.
