Random Aggregate Beamforming for Over-the-Air Federated Learning in Large-Scale Networks

At present, there is a trend to deploy ubiquitous artificial intelligence (AI) applications at the edge of the network. As a promising framework that enables secure edge intelligence, federated learning (FL) has received widespread attention, and over-the-air computing (AirComp) has been integrated to further improve the communication efficiency. In this paper, we consider a joint device selection and aggregate beamforming design with the objectives of minimizing the aggregate error and maximizing the number of selected devices. This yields a combinatorial problem, which is difficult to solve especially in large-scale networks. To tackle the problems in a cost-effective manner, we propose a random aggregate beamforming-based scheme, which generates the aggregator beamforming vector via random sampling rather than optimization. The implementation of the proposed scheme does not require the channel estimation. We additionally use asymptotic analysis to study the obtained aggregate error and the number of the selected devices when the number of devices becomes large. Furthermore, a refined method that runs with multiple randomizations is also proposed for performance improvement. Extensive simulation results are presented to demonstrate the effectiveness of the proposed random aggregate beamforming-based scheme as well as the refined method.