An Optimized Transceiver Design for Wireless Powered Over-the-air Computation Systems

A wireless powered over-the-air computation (AirComp) system is studied, where one separately-located energy transmitter (ET) is deployed to charge multiple low-power sensors simultaneously via energy beamforming, and these sensors rely on the harvested energy for sequential data sensing and functional computation along with the access point (AP) . A harvest-then-sense-and-transmit protocol is considered. Under this system setup, an energy-efficient AirComp design is pursued to minimize the transmit energy of the ET, subject to the sensor energy harvesting constraints and the computational mean squared error (MSE) constraints. The energy beamforming vectors of the ET, the receive beamforming vectors of the AP, and the transmit coefficients at the sensors are jointly optimized. Due to the complicated variable coupling, the resultant energy minimization problem is non-convex. As such, an alternating optimization method is presented to obtain a near-optimal design solution in an iteration manner. Numerical results are provided to show the fast convergence performance and the merit of the proposed design solution.