ChannelComp: A General Method for Computation by Communications

TL;DR

ChannelComp introduces a novel digital over-the-air computation method that overcomes traditional limitations, enabling accurate function computation using digital modulations with significant performance improvements.

Contribution

The paper proposes a new digital channel computing method called ChannelComp, allowing digital modulations to perform over-the-air computation effectively.

Findings

Over 10 dB reduction in computation error compared to AirComp

Effective computation of product functions over wireless channels

Compatibility with existing digital modulation schemes

Abstract

Over-the-air computation (AirComp) is a well-known technique by which several wireless devices transmit by analog amplitude modulation to achieve a sum of their transmit signals at a common receiver. The underlying physical principle is the superposition property of the radio waves. Since such superposition is analog and in amplitude, it is natural that AirComp uses analog amplitude modulations. Unfortunately, this is impractical because most wireless devices today use digital modulations. It would be highly desirable to use digital communications because of their numerous benefits, such as error correction, synchronization, acquisition of channel state information, and widespread use. However, when we use digital modulations for AirComp, a general belief is that the superposition property of the radio waves returns a meaningless overlapping of the digital signals. In this paper, we break through such beliefs and propose an entirely new digital channel computing method named ChannelComp, which can use digital as well as analog modulations. We propose a feasibility optimization problem that ascertains the optimal modulation for computing arbitrary functions over-the-air. Additionally, we propose pre-coders to adapt existing digital modulation schemes for computing the function over the multiple access channel. The simulation results verify the superior performance of ChannelComp compared to AirComp, particularly for the product functions, with more than 10 dB improvement of the computation error.