  We study collaborative machine learning systems where a massive dataset is
distributed across independent workers which compute their local gradient
estimates based on their own datasets. Workers send their estimates through a
multipath fading multiple access channel with orthogonal frequency division
multiplexing to mitigate the frequency selectivity of the channel. We assume
that there is no channel state information (CSI) at the workers, and the
parameter server (PS) employs multiple antennas to align the received signals.
To reduce the power consumption and the hardware costs, we employ
complex-valued low-resolution digital-to-analog converters (DACs) and
analog-to-digital converters (ADCs), at the transmitter and the receiver sides,
respectively, and study the effects of practical low-cost DACs and ADCs on the
learning performance. Our theoretical analysis shows that the impairments
caused by low-resolution DACs and ADCs, including those of one-bit DACs and
ADCs, do not prevent the convergence of the federated learning algorithm, and
the multipath channel effects vanish when a sufficient number of antennas are
used at the PS. We also validate our theoretical results via simulations, and
demonstrate that using low-resolution, even one-bit, DACs and ADCs causes only
a slight decrease in the learning accuracy.
