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.

本文提出了关于 OTA 计算的理论分析，探讨了在当前数字通信收发器中遇到的实际问题，如时间采样误差和符号间干扰（ISI），同时研究了减小 OTA 传输中的均方误差的方法。此外，我们还提出了一种基于深度神经网络的波形设计方法，以提升在时间采样误差和 ISI 条件下的 OTA 传输性能。通过仿真结果验证了理论分析并证明了设计脉冲相对于 RC 和 BTRC 波形的性能提升。为了便于测试结果而无需重新创建 DNN 结构，我们还提供了一些基于 DNN 的波形的曲线拟合参数。