Adaptively Directional Wireless Power Transfer for Large-scale Sensor Networks

Wireless power transfer (WPT) prolongs the lifetime of wireless sensor network by providing sustainable power supply to the distributed sensor nodes (SNs) via electromagnetic waves. To improve the energy transfer efficiency in a large WPT system, this paper proposes an adaptively directional WPT (AD-WPT) scheme, where the power beacons (PBs) adapt the energy beamforming strategy to SNs' locations by concentrating the transmit power on the nearby SNs within the efficient charging radius. With the aid of stochastic geometry, we derive the closed-form expressions of the distribution metrics of the aggregate received power at a typical SN and further approximate the complementary cumulative distribution function using Gamma distribution with second-order moment matching. To design the charging radius for the optimal AD-WPT operation, we exploit the tradeoff between the power intensity of the energy beams and the number of SNs to be charged. Depending on different SN task requirements, the optimal AD-WPT can maximize the average received power or the active probability of the SNs, respectively. It is shown that both the maximized average received power and the maximized sensor active probability increase with the increased deployment density and transmit power of the PBs, and decrease with the increased density of the SNs and the energy beamwidth. Finally, we show that the optimal AD-WPT can significantly improve the energy transfer efficiency compared with the traditional omnidirectional WPT.