This correspondence studies the wireless powered over-the-air computation (AirComp) for achieving sustainable wireless data aggregation (WDA) by integrating AirComp and wireless power transfer (WPT) into a joint design. In particular, we consider that a multi-antenna hybrid access point (HAP) employs the transmit energy beamforming to charge multiple single-antenna low-power wireless devices (WDs) in the downlink, and the WDs use the harvested energy to simultaneously send their messages to the HAP for AirComp in the uplink. Under this setup, we minimize the computation mean square error (MSE), by jointly optimizing the transmit energy beamforming and the receive AirComp beamforming at the HAP, as well as the transmit power at the WDs, subject to the maximum transmit power constraint at the HAP and the wireless energy harvesting constraints at individual WDs. To tackle the non-convex computation MSE minimization problem, we present an efficient algorithm to find a converged high-quality solution by using the alternating optimization technique. Numerical results show that the proposed joint WPT-AirComp approach significantly reduces the computation MSE, as compared to other benchmark schemes.

翻译：本文研究无线供能空中计算（AirComp），通过将空中计算与无线能量传输（WPT）联合设计，实现可持续的无线数据聚合（WDA）。具体而言，我们考虑一个多天线混合接入点（HAP）在下行链路中采用发射能量波束成形为多个单天线低功耗无线设备（WDs）充电，而无线设备利用采集的能量在上行链路中同时向混合接入点发送消息以进行空中计算。在此框架下，我们在混合接入点最大发射功率约束及各无线设备无线能量采集约束下，通过联合优化混合接入点的发射能量波束成形、接收空中计算波束成形以及无线设备的发射功率，最小化计算均方误差（MSE）。针对非凸的计算均方误差最小化问题，我们提出一种利用交替优化技术的高效算法，以获得收敛的高质量解。数值结果表明，与其他基准方案相比，所提出的联合无线能量传输-空中计算方法显著降低了计算均方误差。