  The deployment of federated learning in a wireless network, called federated
edge learning (FEEL), exploits low-latency access to distributed mobile data to
efficiently train an AI model while preserving data privacy. In this work, we
study the spatial (i.e., spatially averaged) learning performance of FEEL
deployed in a large-scale cellular network with spatially random distributed
devices. Both the schemes of digital and analog transmission are considered,
providing support of error-free uploading and over-the-air aggregation of local
model updates by devices. The derived spatial convergence rate for digital
transmission is found to be constrained by a limited number of active devices
regardless of device density and converges to the ground-true rate
exponentially fast as the number grows. The population of active devices
depends on network parameters such as processing gain and
signal-to-interference threshold for decoding. On the other hand, the limit
does not exist for uncoded analog transmission. In this case, the spatial
convergence rate is slowed down due to the direct exposure of signals to the
perturbation of inter-cell interference. Nevertheless, the effect diminishes
when devices are dense as interference is averaged out by aggressive
over-the-air aggregation. In terms of learning latency (in second), analog
transmission is preferred to the digital scheme as the former dramatically
reduces multi-access latency by enabling simultaneous access.
