  Federated learning (FL) has recently emerged as a promising technology to
enable artificial intelligence (AI) at the network edge, where distributed
mobile devices collaboratively train a shared AI model under the coordination
of an edge server. To significantly improve the communication efficiency of FL,
over-the-air computation allows a large number of mobile devices to
concurrently upload their local models by exploiting the superposition property
of wireless multi-access channels. Due to wireless channel fading, the model
aggregation error at the edge server is dominated by the weakest channel among
all devices, causing severe straggler issues. In this paper, we propose a
relay-assisted cooperative FL scheme to effectively address the straggler
issue. In particular, we deploy multiple half-duplex relays to cooperatively
assist the devices in uploading the local model updates to the edge server. The
nature of the over-the-air computation poses system objectives and constraints
that are distinct from those in traditional relay communication systems.
Moreover, the strong coupling between the design variables renders the
optimization of such a system challenging. To tackle the issue, we propose an
alternating-optimization-based algorithm to optimize the transceiver and relay
operation with low complexity. Then, we analyze the model aggregation error in
a single-relay case and show that our relay-assisted scheme achieves a smaller
error than the one without relays provided that the relay transmit power and
the relay channel gains are sufficiently large. The analysis provides critical
insights on relay deployment in the implementation of cooperative FL. Extensive
numerical results show that our design achieves faster convergence compared
with state-of-the-art schemes.
