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.

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