Characterisation of the Time-to-Recharge of Battery-Free RF Energy Harvesting Devices in Wireless Powered Communication Networks

In this article, we consider battery-free RF energy harvesting devices (BF-EHDs) and characterise the time required to charge them to a pre-decided level (time-to-recharge) by transmitting power through RF signals. We propose a model encompassing nonlinear energy harvesting and constant power charging R-C circuit to find the time-to-recharge for different channel models and the number of antennas at the transmitter. We classify a wireless channel as slow- or fast-fading based on the frequency of its variations relative to the average time-to-recharge. Subsequently, we derive expressions for the distributions of time-to-recharge for both types of fading and validate them through numerical simulations. The analysis and numerical simulation reveal that, unlike wireless communication scenarios, fast-fading channels are more beneficial to networks comprising BF-EHDs than slow-fading ones as the variance of the time-to-recharge for the former is significantly smaller than that of the latter.