Statistical Models for Battery Recharge Time from RF Energy Scavengers in Generalized Wireless Fading Channels

Radio frequency energy harvesting is a promising energy replenishment method for the next generation wireless networks. A key performance metric of energy harvesters is the recharge time, which is often omitted in the literature. On the receiver side, the battery parameters and the conversion efficiency are very critical to obtain a realistic evaluation of the recharge time. On the wireless propagation side, practical channel models that accurately characterize the wireless path of the propagating signal needs to be taken into account. To fill this important research gap, in this paper we present a novel and unified statistical modeling of the recharge time for a capacity-limited battery in the generalized η-μ and κ-μ wireless fading channel. Specifically, new unified and exact closed-form expressions are derived for the probability density function, cumulative distribution function, mean, variance and nth order moments. Due to the strong physical background and practicality of the η-μ and κ-μ generalized fading model, our results include important fading models, such as the Rayleigh, Rician, Hoyt, and Nakagami-m models, as special cases. The paper also provides a comprehensive study of the effect of the battery/fading parameters and the conversion efficiency on the harvested energy and the recharge time, which is supported and verified using numerical results.