  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.
