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 (down-link 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.

I. Introduction

In the near future, tens of billions of Internet-of-things (IoT) devices (e.g., sensors and actuators) are expected to be deployed to automate the operations of our societies and make the ambient environment smart. Among others, there exist two design challenges for IoT. The first is fast wireless data aggregation (WDA), namely fast collection and processing of data distributed at dense IoT devices by wireless transmission. WDA is an enabling operation for a series of IoT applications such as fusion of sensing values in environmental monitoring [1], aggregation of mobile updates in federated machine learning [2], and distributed consensus in fleet driving [3]. Fast WDA is needed to regulate latency in cases with ultra-dense devices and/or high mobility (e.g., for sensors carried by drones or vehicles). A promising solution is over-the-air (function) computation (AirComp), which realizes fast WDA by simultaneous transmissions and exploiting analog-wave addition in a multi-access channel [22]. The other challenge for IoT is powering dense energy-constrained sensors for WDA and other operations. One attractive solution is wireless power transfer (WPT) using microwaves, whose feasibility has been proved in practical sensor networks [4].