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.

在本文中，我们考虑了一种联合设备选择和聚合波束成形设计的问题，目标是最小化聚合误差和最大化选择的设备数量，提出了一种基于随机采样的聚合波束成形方案，并使用渐近分析研究了当设备数量增多时，聚合误差和选择的设备数量。通过大量的模拟结果证明了提出的随机聚合波束成形方案和改进方法的有效性。

大规模网络中的随机汇总波束赋形超空接联邦学习