Over-the-Air Computation over Balanced Numerals

Alphan Sahin; Rui Yang

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arXiv · 2209.11004

Over-the-Air Computation over Balanced Numerals

Alphan Sahin·Rui Yang

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Abstract

In this study, a digital over-the-air computation (OAC) scheme for achieving continuous-valued gradient aggregation is proposed. It is shown that the average of a set of real-valued parameters can be calculated approximately by using the average of the corresponding numerals, where the numerals are obtained based on a balanced number system. By using this property, the proposed scheme encodes the local gradients into a set of numerals. It then determines the positions of the activated orthogonal frequency division multiplexing (OFDM) subcarriers by using the values of the numerals. To eliminate the need for a precise sample-level time synchronization, channel estimation overhead, and power instabilities due to the channel inversion, the proposed scheme also uses a non-coherent receiver at the edge server (ES) and does not utilize a pre-equalization at the edge devices (EDs). Finally, the theoretical mean squared error (MSE) performance of the proposed scheme is derived and its performance for federated edge learning (FEEL) is demonstrated.

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Alphan Sahin, Rui Yang. 2022-09-22. Over-the-Air Computation over Balanced Numerals. https://arxiv.org/abs/2209.11004

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