  We study wireless collaborative machine learning (ML), where mobile edge
devices, each with its own dataset, carry out distributed stochastic gradient
descent (DSGD) over-the-air with the help of a wireless access point acting as
the parameter server (PS). At each iteration of the DSGD algorithm wireless
devices compute gradient estimates with their local datasets, and send them to
the PS over a wireless fading multiple access channel (MAC). Motivated by the
additive nature of the wireless MAC, we propose an analog DSGD scheme, in which
the devices transmit scaled versions of their gradient estimates in an uncoded
fashion. We assume that the channel state information (CSI) is available only
at the PS. We instead allow the PS to employ multiple antennas to alleviate the
destructive fading effect, which cannot be cancelled by the transmitters due to
the lack of CSI. Theoretical analysis indicates that, with the proposed DSGD
scheme, increasing the number of PS antennas mitigates the fading effect, and,
in the limit, the effects of fading and noise disappear, and the PS receives
aligned signals used to update the model parameter. The theoretical results are
then corroborated with the experimental ones.
