Optimal Receive Beamforming for Over-the-Air Computation

TL;DR

This paper develops a globally optimal receive beamforming algorithm for over-the-air computation in IoT networks, significantly improving data aggregation accuracy by minimizing estimation error.

Contribution

It introduces a branch and bound algorithm for optimal beamforming, outperforming existing sub-optimal methods and providing a benchmark for future research.

Findings

Proposed BnB algorithm achieves lower MSE than existing methods.

Closed-form solutions for transmit scalars and denoising factor.

Simulation results confirm the algorithm's superior performance.

Abstract

In this paper, we consider fast wireless data aggregation via over-the-air computation (AirComp) in Internet of Things (IoT) networks, where an access point (AP) with multiple antennas aim to recover the arithmetic mean of sensory data from multiple IoT devices. To minimize the estimation distortion, we formulate a mean-squared-error (MSE) minimization problem that involves the joint optimization of the transmit scalars at the IoT devices as well as the denoising factor and the receive beamforming vector at the AP. To this end, we derive the transmit scalars and the denoising factor in closed-form, resulting in a non-convex quadratic constrained quadratic programming (QCQP) problem concerning the receive beamforming vector.Different from the existing studies that only obtain sub-optimal beamformers, we propose a branch and bound (BnB) algorithm to design the globally optimal receive beamformer.Extensive simulations demonstrate the superior performance of the proposed algorithm in terms of MSE. Moreover, the proposed BnB algorithm can serve as a benchmark to evaluate the performance of the existing sub-optimal algorithms.