Over-the-air computation (AirComp) has been recognized as a promising technique in Internet-of-Things (IoT) networks for fast data aggregation from a large number of wireless devices. However, the computation accuracy of AirComp highly depends on the devices with the worst channels condition, which degrades severely when the number of devices becomes large. To address this issue, we exploit the massive multiple-input multiple-output (MIMO) with hybrid beamforming, in order to enhance the computational accuracy of AirComp in a cost-effective manner. In particular, we consider the scenario with a large number of multi-antenna devices simultaneously sending data to an access point (AP) equipped with massive antennas for functional computation over the air. Under this setup, we jointly optimize the transmit digital beamforming at the wireless devices and the receive hybrid beamforming at the AP, with the objective of minimizing the computational mean-squared error (MSE) subject to the individual transmit power constraints at the wireless devices. To solve the non-convex hybrid beamforming design optimization problem, we propose an alternating-optimization-based approach, in which the transmit digital beamforming and the receive analog and digital beamforming are optimized in an alternating manner. In particular, we propose two computationally efficient algorithms to handle the challenging receive analog beamforming problem, by exploiting the techniques of successive convex approximation (SCA) and coordinate descent (CD), respectively. It is shown that for the special case with a fully-digital receiver at the AP, the achieved MSE of the massive MIMO AirComp system is inversely proportional to the number of receive antennas. Furthermore, numerical results show that the proposed hybrid beamforming design substantially enhances the computation MSE performance as compared to other benchmark schemes, while the SCA-based algorithm performs closely to the performance upper bound achieved by the fully-digital beamforming.

中文翻译：

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用于大规模MIMO无线计算的混合波束成形

空中计算（AirComp）已被公认为是物联网（IoT）网络中用于从大量无线设备进行快速数据聚合的有前途的技术。但是，AirComp的计算精度很大程度上取决于通道条件最差的设备，当设备数量变大时，AirComp的计算精度会严重下降。为了解决这个问题，我们利用混合波束成形技术开发了大规模的多输入多输出（MIMO），以便以经济高效的方式提高AirComp的计算精度。特别是，我们考虑具有大量多天线设备的情况，这些设备同时将数据发送到配备有大型天线的接入点（AP），以进行空中功能计算。在这种设置下，我们共同优化无线设备上的发射数字波束成形和AP处的接收混合波束成形，目的是将受无线设备上各个发射功率约束的计算均方误差（MSE）最小化。为了解决非凸混合波束成形设计优化问题，我们提出了一种基于交替优化的方法，其中以交替方式优化了发射数字波束成形以及接收模拟和数字波束成形。特别是，我们提出了两种计算有效的算法，分别通过利用连续凸逼近（SCA）和坐标下降（CD）技术来处理具有挑战性的接收模拟波束成形问题。结果表明，对于在AP处具有全数字接收器的特殊情况，大规模MIMO AirComp系统实现的MSE与接收天线的数量成反比。此外，数值结果表明，与其他基准方案相比，所提出的混合波束成形设计显着提高了计算MSE性能，而基于SCA的算法的性能接近于全数字波束成形所实现的性能上限。