Modeling recharge time of radio frequency energy harvesters in alpha-eta-μ and alpha-kappa-μ Fading Channels

Radio frequency energy harvesting (RFEH) is emerging as a highly promising energy replenishment approach for contemporary and futuristic wireless applications such as wireless sensor networks and the Internet-of-Things. An important performance metric of the harvested energy, which has often been omitted in the literature, is the battery recharge time and its dependency on the harvester's conversion efficiency, battery parameters, and most crucially, wireless propagation environment. Against this background, in this work we perform novel statistical analysis for the battery recharge time over highly generalized wireless fading channels. To this end, we consider α-κ-μ and α-η-μ fading models which accurately characterize the line-of-sight (LOS) and non-line- of-sight (NLOS) propagation scenarios, respectively. Notably, the two models are also suitable for signal shadowing effect. With the novel analysis, we derive new closed-form expressions for the probability density function, cumulative distribution function, and the nth moment of the recharge time. Based on the nth moment, we derive the mean, variance, skewness, and kurtosis of the recharge time. The newly derived expressions are analytically tractable and include important fading models such as Rayleigh, Rice, Hoyt, and Nakagami-m as special cases. Theoretical results are verified via numerical evaluation. Finally, we explicitly examine the impact of harvester's conversion efficiency as well as the fading and battery parameters on the statistics of the recharge time.