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. However, for many computation-oriented applications, the main interest is a function of the local information at the devices, rather than the local information itself. In 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 separating communication and computation tasks. Moreover, 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：通信与计算通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，对于许多面向计算的应用而言，核心关注点是设备本地信息的函数结果，而非本地信息本身。在此类场景中，信息论结果表明，利用多址接入信道中的干扰进行计算（即空中计算）能够实现远高于分离通信与计算任务的可达计算速率。此外，随着参与节点数量的增加，空中计算与分离方法在计算速率上的差距会进一步扩大。基于这一动机，本文对实际空中计算方法进行了全面综述。在阐述空中计算相关基础理论后，我们讨论了现有空中计算方案及其优缺点，并概述了在无线信道中实现可靠计算的使能机制。最后，我们总结了空中计算的潜在应用场景，并指出了未来研究方向。