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

Currently, there is a growing trend in deploying ubiquitous artificial intelligence (AI) applications at the network edge. As a promising framework that enables secure edge intelligence, federated learning (FL) has been paid attention, where the over-the-air computing technique has been adopted to enhance the communication efficiency. In this study, we focus on over-the-air FL over a large-scale network with numerous edge devices. Joint device selection and aggregate beamforming design is investigated under two different objectives, i.e., minimizing the aggregate error and maximizing the number of selected devices. Two combinatorial problems are formulated, which are demanding to solve especially in the large-scale network. To reduce the computational complexity, a random aggregate beamforming scheme is proposed, which employs random sampling instead of optimization to determine the aggregator beamforming vector. Notably, the implementation of the proposed scheme does not necessitate the full channel estimation. Asymptotic analysis reveals that the aggregate error asymptotically follows a Gaussian distribution, and the number of selected devices approximates a symmetrical distribution. The distribution parameters are explicitly expressed by the transmit power, the numbers of devices and selected devices. Simulation results confirm the theoretical analysis and demonstrate the effectiveness of the proposed random aggregate beamforming scheme.