  Federated learning (FL) over resource-constrained wireless networks has
recently attracted much attention. However, most existing studies consider one
FL task in single-cell wireless networks and ignore the impact of
downlink/uplink inter-cell interference on the learning performance. In this
paper, we investigate FL over a multi-cell wireless network, where each cell
performs a different FL task and over-the-air computation (AirComp) is adopted
to enable fast uplink gradient aggregation. We conduct convergence analysis of
AirComp-assisted FL systems, taking into account the inter-cell interference in
both the downlink and uplink model/gradient transmissions, which reveals that
the distorted model/gradient exchanges induce a gap to hinder the convergence
of FL. We characterize the Pareto boundary of the error-induced gap region to
quantify the learning performance trade-off among different FL tasks, based on
which we formulate an optimization problem to minimize the sum of error-induced
gaps in all cells. To tackle the coupling between the downlink and uplink
transmissions as well as the coupling among multiple cells, we propose a
cooperative multi-cell FL optimization framework to achieve efficient
interference management for downlink and uplink transmission design. Results
demonstrate that our proposed algorithm achieves much better average learning
performance over multiple cells than non-cooperative baseline schemes.
