Expanding Over-the-Air Computation with Frequency Modulations

TL;DR

This paper introduces Log-FSK, a novel frequency modulation technique for over-the-air computation that enables efficient, multi-function computation in wireless sensor networks by leveraging non-linear signal processing and frequency domain analysis.

Contribution

The paper presents Log-FSK, a new modulation scheme that allows computing multiple functions simultaneously over-the-air, extending beyond simple summation, with demonstrated advantages in noise robustness and power efficiency.

Findings

Log-FSK outperforms linear analog modulations in MSE.

Log-FSK reduces power consumption compared to existing methods.

Log-FSK enables multi-function computation in a single transmission.

Abstract

In this study we introduce Logarithmic Frequency Shift Keying (Log-FSK), a novel frequency modulation for over-the-air computation (AirComp). Log-FSK leverages non-linear signal processing to produce AirComp in the frequency domain, this is, the maximum frequency of the received signal corresponds to the sum of the individual transmitted frequencies. The demodulation procedure relies on the inverse Discrete Cosine Transform (DCT) and the extraction of the maximum frequency component. Log-FSK enables the computation of functions beyond the sum by incorporating nomographic function representation. Furthermore, unlike existing AirComp modulations, Log-FSK allows to compute several functions in a single transmission. We evaluate the capabilities of the scheme in an additive white Gaussian noise (AWGN) and flat-fading channels. To demonstrate its practicality, we present specific applications and experimental results showcasing the effectiveness of Log-FSK AirComp within linear Wireless Sensor Networks (WSN). Our numerical results show that Log-FSK outperform linear analog modulations in terms of MSE and power consumption.