  In this paper, we propose a framework where over-the-air computation (OAC)
occurs in both uplink (UL) and downlink (DL), sequentially, in a multi-cell
environment to address the latency and the scalability issues of federated edge
learning (FEEL). To eliminate the channel state information (CSI) at the edge
devices (EDs) and edge servers (ESs) and relax the time-synchronization
requirement for the OAC, we use a non-coherent computation scheme, i.e.,
frequency-shift keying (FSK)-based majority vote (MV) (FSK-MV). With the
proposed framework, multiple ESs function as the aggregation nodes in the UL
and each ES determines the MVs independently. After the ESs broadcast the
detected MVs, the EDs determine the sign of the gradient through another OAC in
the DL. Hence, inter-cell interference is exploited for the OAC. In this study,
we prove the convergence of the non-convex optimization problem for the FEEL
with the proposed OAC framework. We also numerically evaluate the efficacy of
the proposed method by comparing the test accuracy in both multi-cell and
single-cell scenarios for both homogeneous and heterogeneous data
distributions.
