Over-the-Air Computation for Distributed Systems: Something Old and Something New

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.