Optimized Joint Beamforming for Wireless Powered Over-the-Air Computation

This paper studies the integration of over-the-air computation (AirComp) and wireless power transfer (WPT) for achieving sustainable wireless data aggregation (WDA). In such wireless powered AirComp system, 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 utilize their harvested energy to simultaneously send messages to the HAP for AirComp in the uplink. Under this setup, our objective is to minimize the computation mean square error (MSE) by jointly optimizing the transmit en-ergy beamforming and the receive AirComp beamforming at the HAP, as well as the transmit power control at the WDs, subject to 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, in which the transmit energy beamforming (together with WDs' power control) and the receive beamforming are alternately optimized. Simulation results show that the proposed joint WPT-AirComp scheme significantly decreases the system's MSE, as compared to conventional designs without such joint optimization.