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Optimal Receive Filter Design for Misaligned Over-the-Air Computation

H Hellström, S Razavikia, V Fodor… - arXiv preprint arXiv …, 2023 - arxiv.org
arXiv preprint arXiv:2309.16033, 2023arxiv.org
267 天前 - Over-the-air computation (OAC) is a promising wireless communication method for
aggregating data from many devices in dense wireless networks. The fundamental idea of
OAC is to exploit signal superposition to compute functions of multiple simultaneously
transmitted signals. However, the time-and phase-alignment of these superimposed signals
have a significant effect on the quality of function computation. In this study, we analyze the
OAC problem for a system with unknown random time delays and phase shifts. We show …
Over-the-air computation (OAC) is a promising wireless communication method for aggregating data from many devices in dense wireless networks. The fundamental idea of OAC is to exploit signal superposition to compute functions of multiple simultaneously transmitted signals. However, the time- and phase-alignment of these superimposed signals have a significant effect on the quality of function computation. In this study, we analyze the OAC problem for a system with unknown random time delays and phase shifts. We show that the classical matched filter does not produce optimal results, and generates bias in the function estimates. To counteract this, we propose a new filter design and show that, under a bound on the maximum time delay, it is possible to achieve unbiased function computation. Additionally, we propose a Tikhonov regularization problem that produces an optimal filter given a tradeoff between the bias and noise-induced variance of the function estimates. When the time delays are long compared to the length of the transmitted pulses, our filter vastly outperforms the matched filter both in terms of bias and mean-squared error (MSE). For shorter time delays, our proposal yields similar MSE as the matched filter, while reducing the bias.
arxiv.org
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