Over-the-Air Computation with Multiple Receivers: A Space-Time Approach

TL;DR

This paper extends Over-the-Air computation to multiple receivers by proposing a space-time joint precoding and decoding scheme, optimizing resource efficiency and accuracy in data aggregation across wireless networks.

Contribution

It introduces a novel multi-slot communication design for OtA with multiple receivers, optimizing joint precoding and decoding to improve efficiency and accuracy.

Findings

Reduces communication time slots compared to baseline methods.

Achieves lower mean squared error in computations.

Effective in resource-constrained wireless networks.

Abstract

The emerging concept of Over-the-Air (OtA) computation has shown great potential for achieving resource-efficient data aggregation across large wireless networks. However, current research in this area has been limited to the standard many-to-one topology, where multiple nodes transmit data to a single receiver. In this study, we address the problem of applying OtA computation to scenarios with multiple receivers, and propose a novel communication design that exploits joint precoding and decoding over multiple time slots. To determine the optimal precoding and decoding vectors, we formulate an optimization problem that aims to minimize the mean squared error of the desired computations while satisfying the unbiasedness condition and power constraints. Our proposed multi-slot design is shown to be effective in saving communication resources (e.g., time slots) and achieving smaller estimation errors compared to the baseline approach of separating different receivers over time.