This paper addresses the problem of Over-The-Air (OTA) computation in wireless networks which has the potential to realize huge efficiency gains for instance in training of distributed ML models. We provide non-asymptotic, theoretical guarantees for OTA computation in fast-fading wireless channels where the fading and noise may be correlated. The distributions of fading and noise are not restricted to Gaussian distributions, but instead are assumed to follow a distribution in the more general sub-gaussian class. Furthermore, our result does not make any assumptions on the distribution of the sources and therefore, it can, e.g., be applied to arbitrarily correlated sources. We illustrate our analysis with numerical evaluations for OTA computation of two example functions in large wireless networks: the arithmetic mean and the Euclidean norm.

翻译：本文讨论了无线网络超空计算问题,这种计算有可能实现巨大的效率收益,例如,在培训分布式ML模型方面。我们为在快速发泡的无线频道进行OTA计算提供了非简易的理论保障,因为这种无线频道的消逝和噪音可能与此相关。消逝和噪音的分布并不限于Gaussian的分布,而是假定在较普通的Gaussian类下进行分配。此外,我们的结果并没有对来源的分布作出任何假设,因此,例如,它可以任意地应用于相关来源。我们用对OTA计算大型无线网络的两个实例功能的数字评价来说明我们的分析:算术平均数和Euclidean规范。