Wirelessly Powered Over-the-Air Computation for High-Mobility Sensing

Abstract

For a dense sensor network in a smart city, efficient data aggregation can be realized by deploying readers mounted on unmanned aerial vehicles (UAVs), At high mobility and given dense sensors, the requirement of ultra-low latency cannot be met using a traditional multi-access scheme such as time-division or orthogonal-frequency-division multiple access. A technique called over-the-air computation (AirComp) has emerged to be a promising solution for high-mobility sensing, which integrates functional computation (e.g., averaging and geometric mean) and multi-access by exploiting analog waveform addition. Targeting high-mobility sensing, the technique supports ultra-fast simultaneous access and function computation. In this paper, building on multi-antenna AirComp, we present a new frame-work of wirelessly powered (WP) AirComp to enable UAVs for simultaneous data aggregation and wirelessly powering sensors, where wireless power solves a key design challenge of battery recharging for many sensors. The key feature of WP-AirComp is the leverage of down-link wireless power transfer (WPT) as an additional design dimension for reducing the sum computation error in up-link AirComp. Designing the framework involves the joint optimization of power control, energy beamforming and AirComp equalization. To derive a practical solution, we recast the non-convex problem into equivalent outer and inner problems for (inner) wireless power control and energy beamforming and (outer) AirComp equalization, respectively. The former is solved in closed form while the latter via semi-definite relaxation, which is shown to reach the global optimum with high probability. The solution reveals that the optimal power beams point to the WPT channels, and the optimal power allocation tends to equalize the round-trip attenuation over sensors.