Waveform Design for Over-the-Air Computing

TL;DR

This paper develops a theoretical and neural network-based approach to waveform design for over-the-air computing, addressing practical issues like sync errors and ISI, and demonstrating improved performance over traditional waveforms.

Contribution

It introduces a novel DNN-based waveform design method for OTA computing that accounts for synchronization errors and interference, with theoretical analysis and optimal power policies.

Findings

The DNN-designed waveforms outperform RC and BTRC in simulations.

Theoretical analysis of MSE under sync errors and ISI is validated by simulations.

Optimal power policies are derived for devices and base station.

Abstract

In response to the increasing number of devices expected in next-generation networks, a shift to over-the-air (OTA) computing has been proposed. By leveraging the superposition of multiple access channels, OTA computing enables efficient resource management by supporting simultaneous uncoded transmission in the time and frequency domains. To advance the integration of OTA computing, our study presents a theoretical analysis that addresses practical issues encountered in current digital communication transceivers, such as transmitter synchronization (sync) errors and intersymbol interference (ISI). To this end, we investigate the theoretical mean squared error (MSE) for OTA transmission under sync errors and ISI, while also exploring methods for minimizing the MSE in OTA transmission. Using alternating optimization, we also derive optimal power policies for both the devices and the base station. In addition, we propose a novel deep neural network (DNN)-based approach to design waveforms that improve OTA transmission performance under sync errors and ISI. To ensure a fair comparison with existing waveforms such as raised cosine (RC) and better-than-raised-cosine (BTRC), we incorporate a custom loss function that integrates energy and bandwidth constraints along with practical design considerations such as waveform symmetry. Simulation results validate our theoretical analysis and demonstrate performance gains of the designed pulse over RC and BTRC waveforms. To facilitate testing of our results without the need to rebuild the DNN structure, we also provide curve-fitting parameters for the selected DNN-based waveforms.