Over-the-Air Computation over Balanced Numerals

TL;DR

This paper introduces a novel over-the-air computation scheme using balanced numerals for efficient gradient aggregation in federated learning, reducing synchronization and channel estimation overhead.

Contribution

It proposes a new digital OAC scheme based on balanced numerals that simplifies synchronization and channel estimation in federated edge learning.

Findings

Achieves approximate gradient averaging with balanced numerals

Reduces synchronization and channel estimation overhead

Demonstrates effective FEEL performance with theoretical MSE analysis

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.