The development of applications based on artificial intelligence and implemented over wireless networks is increasingly rapidly and is expected to grow dramatically in the future. The resulting demand for the aggregation of large amounts of data has caused serious communication bottlenecks in wireless networks and particularly at the network edge. Over-the-air federated learning (OTA-FL), leveraging the superposition feature of multi-access channels (MACs), enables users at the network edge to share spectrum resources and achieves efficient and low-latency global model aggregation. This paper provides a holistic review of progress in OTA-FL and points to potential future research directions. Specifically, we classify OTA-FL from the perspective of system settings, including single-antenna OTA-FL, multi-antenna OTA-FL, and OTA-FL with the aid of the emerging reconfigurable intelligent surface (RIS) technology, and the contributions of existing works in these areas are summarized. Moreover, we discuss the trust, security and privacy aspects of OTA-FL, and highlight concerns arising from security and privacy. Finally, challenges and potential research directions are discussed to promote the future development of OTA-FL in terms of improving system performance, reliability, and trustworthiness. Specifical challenges to be addressed include model distortion under channel fading, the ineffective OTA aggregation of local models trained on substantially unbalanced data, and the limited accessibility and verifiability of individual local models.

翻译：基于人工智能并部署于无线网络的应用正快速发展，预计未来将呈现爆发式增长。由此产生的大量数据聚合需求，在无线网络（尤其是网络边缘）中引发了严重的通信瓶颈。空中联邦学习（OTA-FL）利用多址信道（MAC）的叠加特性，使网络边缘用户共享频谱资源，实现高效低延迟的全局模型聚合。本文对OTA-FL的进展进行了全面综述，并指出了潜在的未来研究方向。具体而言，我们从系统设置的角度对OTA-FL进行分类，包括单天线OTA-FL、多天线OTA-FL以及借助新兴可重构智能表面（RIS）技术的OTA-FL，并总结了现有工作在这些领域的贡献。此外，我们讨论了OTA-FL的信任、安全与隐私方面的问题，并强调了安全与隐私引发的担忧。最后，探讨了挑战与潜在研究方向，以促进OTA-FL在未来系统性能、可靠性和可信度方面的提升。需要解决的具体挑战包括：信道衰落下的模型失真、对基于严重不均衡数据训练的本地模型进行空中聚合的低效性，以及单个本地模型的可访问性与可验证性受限问题。