Waveform Design for Over-the-Air Computing under Sampling Error

To accommodate the large number of devices expected to operate in next-generation networks, a paradigm shift toward over-the-air (OTA) computing has been proposed, which takes advantage of the superposition principle of multiple access channels aiming to achieve better resource management as it supports simultaneous transmission in time and frequency. However, related studies have focused on analog transmission schemes without considering the components of modern transceivers. Therefore, to facilitate the use of OTA computing in modern systems, we investigate the impact of different waveforms transmission in OTA computing by taking into account the sampling errors that occur at the receiver side due to synchronization problems. To this end, the average minimum square error (MSE), under time sampling error for any utilized waveform, is investigated. Then, the MSE minimization problem is formulated and solved using alternating optimization to extract an efficient power allocation scheme. Simulation results for the raised cosine (RC) and the better-than-raised-cosine (BTRC) waveforms validate the theoretical part of our work and illustrate the efficiency of the extracted power allocation scheme while also providing a fair comparison between the RC and the BTRC waveforms.