Martingale Theory Based Definition and Analysis of Energy Self-Sustainability in Batteryless Internet of Things

Radio-frequency (RF) based Wireless Energy Transfer (WET) enables devices to avoid wired power-supply and battery replacements. The ubiquitous availability of RF energy elevates 'energy self-sustainability' as a pivotal goal for wireless sensor networks. However, for RF energy harvesting networks, the term 'energy self-sustainability"lacks a precise mathematical characterization. This paper presents a robust mathematical definition for energy self-sustainability within integrated data and energy networks. By utilizing Martingale theory, we develop a mathematical framework that determines the energy self-sustainability, by acquiring the stochastic properties of energy harvesting and consumption processes. The fundamental paradigm of utilizing this framework to derive energy self-sustainability is demonstrated. In-depth explorations have been conducted on the diverse stochastic characteristics of energy harvesting and consuming processes. Additionally, this study delves into the anticipated uninterrupted operating duration and associated energy expectation. Monte-Carlo simulations confirm the precision of our theoretical evaluations. By analyzing the correlation between harvested and consumed energy in the context of varied energy self-sustainability requirements, this paper provides design guidance for energy transmitters and batteryless wireless devices.