On the Convex Properties of Wireless Power Transfer with Nonlinear Energy Harvesting

TL;DR

This paper characterizes the convexity of nonlinear wireless power transfer, demonstrating that harvested DC power is convex in the reciprocal of input power, which aids in optimizing WPT network design.

Contribution

It proves the convex property of nonlinear WPT models and illustrates its application in improving network design strategies.

Findings

Harvested DC power is convex in the reciprocal of input power.

Convexity property can be used to optimize WPT network performance.

Nonlinear energy harvesting models exhibit specific convex characteristics.

Abstract

The convex property of a nonlinear wireless power transfer (WPT) is characterized in this work. Following a nonlinear energy harvesting model, we express the relationship between the harvested direct current (DC) power and the power of the received radio-frequency signal via an implicit function, based on which the convex property is further proved. In particular, for a predefined rectifier's input signal distribution, we show that the harvested DC power of the nonlinear model is convex in the reciprocal of the rectifier's input signal power. Finally, we provide an example to show the advantages of applying the convex property in WPT network designs.