Abstract

Federated edge learning (FEEL) has been introduced for training machine learning models on distributed datasets for applications such as human monitoring. However, some challenges exist concerning the number of communication rounds and communication energy consumption involved in transmiting gradients during the training process. Moreover, over-the-air computation (AirComp) technology has gained attention recently, benefiting from superposition characteristic of wireless channels to compute functions over the air. While primarily designed for analog systems, there is potential for applying this technology in digital systems with embedded modulation schemes. This paper addresses these challenges by proposing a digital AirComp system for federated learning aggregation. The system employs a multi-bit quantization scheme to modulate gradients, adhering to a maximum transmission power constraint. An adaptive quantization scheme is also introduced, which considers the impact of quantization error and the error induced by additive white Gaussian noise. We derive closed-form expressions for pre-processing coefficients at devices and post-processing scaler at the access point (AP) to minimize the mean-squared error between high-precision and quantized qradients under the maximum transmission power constraint. Finally, the performance of the proposed scheme is evaluated in terms of achieved test accuracy, mean-squared error (MSE), and energy consumption, demonstrating its potential effectiveness compared to the benchmark schemes.