Statistical Model for Battery Recharging Time in RIS-assisted WPT Systems

In this paper, we propose an analytical framework to statistically analyze the battery recharging time (BRT) in reconfigurable intelligent surfaces (RISs)-assisted wireless power transfer (WPT) systems. Specifically, we derive novel expressions for the probability density function (PDF), and cumulative distribution function (CDF) of the BRT of the radio frequency energy harvesting (RFEH) wireless nodes. Considering both the direct link and the links provided by the RIS, the received power at the RFEH nodes is modeled as a gamma mixture model (GMM), where the parameters of GMM are calculated using the expectation-maximization algorithm. Utilizing the derived expressions, we provide a comprehensive analysis for the statistical characterization of the BRT and investigate how the system and battery parameters affect the charging time performance. Finally, simulation results are provided to verify the theoretical results.