  We study federated edge learning (FEEL), where wireless edge devices, each
with its own dataset, learn a global model collaboratively with the help of a
wireless access point acting as the parameter server (PS). At each iteration,
wireless devices perform local updates using their local data and the most
recent global model received from the PS, and send their local updates to the
PS over a wireless fading multiple access channel (MAC). The PS then updates
the global model according to the signal received over the wireless MAC, and
shares it with the devices. Motivated by the additive nature of the wireless
MAC, we propose an analog `over-the-air' aggregation scheme, in which the
devices transmit their local updates in an uncoded fashion. Unlike recent
literature on over-the-air edge learning, here we assume that the devices do
not have channel state information (CSI), while the PS has imperfect CSI.
Instead, the PS is equipped multiple antennas to alleviate the destructive
effect of the channel, exacerbated due to the lack of perfect CSI. We design a
receive beamforming scheme at the PS, and show that it can compensate for the
lack of perfect CSI when the PS has a sufficient number of antennas. We also
derive the convergence rate of the proposed algorithm highlighting the impact
of the lack of perfect CSI, as well as the number of PS antennas. Both the
experimental results and the convergence analysis illustrate the performance
improvement of the proposed algorithm with the number of PS antennas, where the
wireless fading MAC becomes deterministic despite the lack of perfect CSI when
the PS has a sufficiently large number of antennas.
