Communication and computation are often viewed as separate tasks. This approach is very effective from the perspective of engineering as isolated optimizations can be performed. On the other hand, there are many cases where the main interest is a function of the local information at the devices instead of the local information itself. For such scenarios, information theoretical results show that harnessing the interference in a multiple-access channel for computation, i.e., over-the-air computation (OAC), can provide a significantly higher achievable computation rate than the one with the separation of communication and computation tasks. Besides, the gap between OAC and separation in terms of computation rate increases with more participating nodes. Given this motivation, in this study, we provide a comprehensive survey on practical OAC methods. After outlining fundamentals related to OAC, we discuss the available OAC schemes with their pros and cons. We provide an overview of the enabling mechanisms for achieving reliable computation in the wireless channel. Finally, we summarize the potential applications of OAC and point out some future directions.

翻译：通信与计算常被视为独立的任务。从工程角度来看，这种分离优化的方法非常有效。然而，在许多场景下，核心需求是获取设备本地信息的函数值而非原始信息本身。针对此类场景，信息论结果表明，利用多址信道中的干扰进行计算（即空中计算，OAC）能够实现显著高于通信计算分离方案的可达计算速率。此外，随着参与节点数量的增加，OAC与分离方案在计算速率上的差距将进一步扩大。基于这一动机，本文对实用化空中计算方法进行了全面综述。在阐述OAC基础原理后，我们讨论了现有OAC方案的优缺点，概述了在无线信道中实现可靠计算的关键机制，最后总结了OAC的潜在应用并指出了未来研究方向。