Facing the upcoming era of Internet-of-Things and connected intelligence, efficient information processing, computation, and communication design becomes a key challenge in large-scale intelligent systems. Recently, Over-the-Air (OtA) computation has been proposed for data aggregation and distributed computation of functions over a large set of network nodes. Theoretical foundations for this concept exist for a long time, but it was mainly investigated within the context of wireless sensor networks. There are still many open questions when applying OtA computation in different types of distributed systems where modern wireless communication technology is applied. In this article, we provide a comprehensive overview of the OtA computation principle and its applications in distributed learning, control, and inference systems, for both server-coordinated and fully decentralized architectures. Particularly, we highlight the importance of the statistical heterogeneity of data and wireless channels, the temporal evolution of model updates, and the choice of performance metrics, for the communication design in OtA federated learning (FL) systems. Several key challenges in privacy, security, and robustness aspects of OtA FL are also identified for further investigation.

翻译：面对即将到来的物联网与连接智能时代，高效的信息处理、计算与通信设计成为大规模智能系统中的关键挑战。近年来，空中计算（Over-the-Air, OtA）被提出用于大规模网络节点间的数据聚合与分布式函数计算。该概念的理论基础虽早已存在，但此前主要是在无线传感器网络背景下进行研究。在应用现代无线通信技术的各类分布式系统中应用OtA计算时，仍存在许多待解决问题。本文全面概述了OtA计算原理及其在分布式学习、控制和推理系统中的应用，涵盖服务器协调与完全去中心化两种架构。我们特别强调了数据与无线信道的统计异质性、模型更新的时间演化以及性能指标的选择，对OtA联邦学习（FL）系统通信设计的重要性。此外，本文还识别了OtA FL在隐私、安全与鲁棒性方面的若干关键挑战，以供进一步研究。