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.

翻译：在本文中,我们考虑在Things(IoT)网络的互联网上通过超天计算(AirComp)快速无线数据汇总(AirComp),在该网络中,一个拥有多个天线的接入点(AP)旨在从多个IoT设备中恢复感官数据的算术平均值。为尽量减少估计扭曲,我们制定了一个平均半半成色色(MSE)最小化问题,涉及在IoT设备中联合优化传输星标以及分红系数和AP的接收波形矢量。为此,我们从封闭式中得出传输星标和调色系数,从而导致在接收矢量成形时出现非对等梯度受限的二次方程式(QCQP)问题。此外,拟议的BnB演算法从仅获得亚最佳光度光谱的现有研究中得出一个分支和约束(BnB)算法,以设计全球最佳的接收光谱。广泛的模拟展示了拟议算法的优劣性表现。此外,拟议的BnB演算法可以作为MSE的现有基准。