Waveform Design for Over-the-Air Computing

Abstract: In response to the increasing number of devices anticipated in next-generation networks, a shift toward over-the-air (OTA) computing has been proposed. Leveraging the superposition of multiple access channels, OTA computing enables efficient resource management by supporting simultaneous uncoded transmission in the time and the frequency domain. Thus, to advance the integration of OTA computing, our study presents a theoretical analysis addressing practical issues encountered in current digital communication transceivers, such as time sampling error and intersymbol interference (ISI). To this end, we examine the theoretical mean squared error (MSE) for OTA transmission under time sampling error and ISI, while also exploring methods for minimizing the MSE in the OTA transmission. Utilizing alternating optimization, we also derive optimal power policies for both the devices and the base station. Additionally, we propose a novel deep neural network (DNN)-based approach to design waveforms enhancing OTA transmission performance under time sampling error and ISI. To ensure fair comparison with existing waveforms like the raised cosine (RC) and the better-than-raised-cosine (BRTC), we incorporate a custom loss function integrating 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 necessitating the DNN structure recreation, we provide curve fitting parameters for select DNN-based waveforms as well.