Over-the-Air Computation via Broadband Channels

TL;DR

This paper proposes a multi-frequency over-the-air computation system to enhance wireless sensor data fusion performance, demonstrating significant improvements over single-channel approaches through optimal transmission and processing strategies.

Contribution

It introduces an M-frequency AirComp system with joint design algorithms, enabling better performance in large-scale sensor networks compared to traditional single-channel methods.

Findings

Adding one frequency channel triples performance compared to single-channel.

Optimal transmission and processing strategies improve AirComp accuracy.

Multi-channel diversity significantly enhances large-scale sensor data fusion.

Abstract

Over-the-air computation (AirComp) has been recognized as a low-latency solution for wireless sensor data fusion, where multiple sensors send their measurement signals to a receiver simultaneously for computation. Most existing work only considered performing AirComp over a single frequency channel. However, for a sensor network with a massive number of nodes, a single frequency channel may not be sufficient to accommodate the large number of sensors, and the AirComp performance will be very limited. So it is highly desirable to have more frequency channels for large-scale AirComp systems to benefit from multi-channel diversity. In this letter, we propose an $M$-frequency AirComp system, where each sensor selects a subset of the $M$ frequencies and broadcasts its signal over these channels under a certain power constraint. We derive the optimal sensors' transmission and receiver's signal processing methods separately, and develop an algorithm for joint design to achieve the best AirComp performance. Numerical results show that increasing one frequency channel can improve the AirComp performance by threefold compared to the single-frequency case.