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