Waveform Design for Over-the-Air Computing

TL;DR

The paper addresses the challenge of computing functions over wireless MACs in OTA computing under practical impairments, notably transmitter sync errors and ISI. It develops a theoretical MSE framework for RC and BTRC waveforms, derives optimal power allocation policies, and introduces a novel DNN-based waveform design that enforces energy and bandwidth constraints while mitigating synchronization and ISI effects. Simulation results show the DNN-generated waveforms achieve meaningful MSE gains over traditional waveforms, especially in mid-range roll-off regimes and under ISI, with robustness to imperfect CSI. The work advances OTA computing by integrating waveform design with power optimization and providing curve-fitting parameters to facilitate testing without retraining the DNN, highlighting practical pathways for deploying OTA-based computations in modern networks.

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.

Figures (10)

• Figure 1: OTA computing model with sync errors.
• Figure 2: Signal amplitude of the target signal \ref{['eq:RecIdeal']} and received signal \ref{['eq:RecISI']} with sync errors with $\sigma_{\epsilon} = 0.1$ for RC waveform of $\alpha = 0.3$ in the absence of noise. The samples for each case are depicted as bullet points. For the rest of the selected parameters, see Section \ref{['sec:Results']}.
• Figure 3: DNN-generated waveforms for OTA computing and various roll-off factors.
• Figure 4: Comparison of bandwidth utilization through DFT.
• Figure 5: Waveform MSE performance for varying roll-off factor and sync errors variance $\sigma_{\epsilon}=0.1$ without the presence of ISI when there are $K=20$ devices.

Theorems & Definitions (4)

• Proposition 1
• Proposition 2
• Proposition 3
• Remark 1