  To enable wireless federated learning (FL) in communication
resource-constrained networks, two communication schemes, i.e., digital and
analog ones, are effective solutions. In this paper, we quantitatively compare
these two techniques, highlighting their essential differences as well as
respectively suitable scenarios. We first examine both digital and analog
transmission schemes, together with a unified and fair comparison framework
under imbalanced device sampling, strict latency targets, and transmit power
constraints. A universal convergence analysis under various imperfections is
established for evaluating the performance of FL over wireless networks. These
analytical results reveal that the fundamental difference between the digital
and analog communications lies in whether communication and computation are
jointly designed or not. The digital scheme decouples the communication design
from FL computing tasks, making it difficult to support uplink transmission
from massive devices with limited bandwidth and hence the performance is mainly
communication-limited. In contrast, the analog communication allows
over-the-air computation (AirComp) and achieves better spectrum utilization.
However, the computation-oriented analog transmission reduces power efficiency,
and its performance is sensitive to computation errors from imperfect channel
state information (CSI). Furthermore, device sampling for both schemes are
optimized and differences in sampling optimization are analyzed. Numerical
results verify the theoretical analysis and affirm the superior performance of
the sampling optimization.
