  Over-the-air (OTA) computation has recently emerged as a
communication-efficient Federated Learning (FL) paradigm to train machine
learning models over wireless networks. However, its performance is limited by
the device with the worst SNR, resulting in fast yet noisy updates. On the
other hand, allocating orthogonal resource blocks (RB) to individual devices
via digital channels mitigates the noise problem, at the cost of increased
communication latency. In this paper, we address this discrepancy and present
ADFL, a novel Analog-Digital FL scheme: in each round, the parameter server
(PS) schedules each device to either upload its gradient via the analog OTA
scheme or transmit its quantized gradient over an orthogonal RB using the
``digital" scheme. Focusing on a single FL round, we cast the optimal
scheduling problem as the minimization of the mean squared error (MSE) on the
estimated global gradient at the PS, subject to a delay constraint, yielding
the optimal device scheduling configuration and quantization bits for the
digital devices. Our simulation results show that ADFL, by scheduling most of
the devices in the OTA scheme while also occasionally employing the digital
scheme for a few devices, consistently outperforms OTA-only and digital-only
schemes, in both i.i.d. and non-i.i.d. settings.
