Over-The-Air Computation in Correlated Channels

TL;DR

This paper provides theoretical guarantees for Over-The-Air computation in fast-fading, correlated wireless channels with sub-gaussian noise, applicable to arbitrary source correlations, enhancing efficiency in distributed machine learning.

Contribution

It offers non-asymptotic, general theoretical analysis of OTA computation in correlated, fast-fading channels without assuming Gaussian distributions or source independence.

Findings

Theoretical guarantees for OTA in correlated channels.

Applicability to non-Gaussian, sub-gaussian noise.

Numerical evaluation of mean and norm computations.

Abstract

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.