Wirelessly Powered Data Aggregation for IoT via Over-the-Air Function Computation: Beamforming and Power Control

As a revolution in networking, the Internet of Things (IoT) aims at automating the operations of our societies by connecting and leveraging an enormous number of distributed devices (e.g., sensors and actuators). One design challenge is efficient wireless data aggregation (WDA) over the dense IoT devices. This can enable a series of the IoT applications ranging from latency-sensitive high-mobility sensing to data-intensive distributed machine learning. Over-the-air (function) computation (AirComp) has emerged to be a promising solution that merges computing and communication by exploiting analog-wave addition in the air. Another IoT design challenge is battery recharging for dense sensors which can be tackled by wireless power transfer (WPT). The coexisting of AirComp and WPT in the IoT system calls for their integration to enhance the performance and efficiency of WDA. This motivates the current work on developing the wirelessly powered AirComp (WP-AirComp) framework by jointly optimizing wireless power control, energy and (data) aggregation beamforming to minimize the AirComp error. To derive a practical solution, we recast the non-convex joint optimization problem into the equivalent outer and inner sub-problems for (inner) wireless power control and energy beamforming, and (outer) the efficient aggregation beamforming, respectively. The former is solved in closed form while the latter is efficiently solved using the semidefinite relaxation technique. The results reveal that the optimal energy beams point to the dominant Eigen-directions of the WPT channels, and the optimal power allocation tends to equalize the close-loop (downlink WPT and up-link AirComp) effective channels of different sensors. The simulation demonstrates that the controlling WPT provides additional design dimensions for substantially reducing the AirComp error.