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.

翻译：为应对下一代网络中预期设备数量的增长，学界已提出向空中计算（OTA）的转变。OTA计算利用多址信道的叠加特性，通过支持时域和频域中的同时无编码传输，实现了高效的资源管理。因此，为推进OTA计算的集成，本研究针对当前数字通信收发机中遇到的实际问题（如时间采样误差和码间干扰）进行了理论分析。为此，我们研究了存在时间采样误差和码间干扰时OTA传输的理论均方误差，并探索了在OTA传输中最小化均方误差的方法。利用交替优化，我们还推导了设备和基站的最优功率策略。此外，我们提出了一种基于深度神经网络的新型方法来设计波形，以在时间采样误差和码间干扰下提升OTA传输性能。为确保与升余弦、超升余弦等现有波形进行公平比较，我们引入了一个结合能量与带宽约束的自定义损失函数，并考虑了波形对称性等实际设计因素。仿真结果验证了我们的理论分析，并证明了所设计脉冲波形相对于升余弦和超升余弦波形的性能增益。为便于在不重建深度神经网络结构的情况下测试我们的结果，我们还提供了部分基于深度神经网络的波形的曲线拟合参数。