Log-FSK: A Frequency Modulation for Over-the-Air Computation

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. We provide the theoretical performance in terms of error probability and mean squared error. 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 experiments show that Log-FSK outperforms linear AirComp, implemented with double sideband (DSB), when working above the threshold SNR.