Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 7849175, 9 pages

http://dx.doi.org/10.1155/2016/7849175

## Characterization of Energy Availability in RF Energy Harvesting Networks

^{1}Instituto de Telecomunicações (IT), Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal^{2}Dep. de Eng. Electrotécnica, Faculdade de Ciências e Tecnologia (FCT), Universidade Nova de Lisboa, 2829-516 Costa da Caparica, Portugal

Received 12 June 2016; Accepted 8 September 2016

Academic Editor: Babak Shotorban

Copyright © 2016 Daniela Oliveira and Rodolfo Oliveira. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The multiple nodes forming a Radio Frequency (RF) Energy Harvesting Network (RF-EHN) have the capability of converting received electromagnetic RF signals in energy that can be used to power a network device (the energy harvester). Traditionally the RF signals are provided by high power transmitters (e.g., base stations) operating in the neighborhood of the harvesters. Admitting that the transmitters are spatially distributed according to a spatial Poisson process, we start by characterizing the distribution of the RF power received by an energy harvester node. Considering Gamma shadowing and Rayleigh fading, we show that the received RF power can be approximated by the sum of multiple Gamma distributions with different scale and shape parameters. Using the distribution of the received RF power, we derive the probability of a node having enough energy to transmit a packet after a given amount of charging time. The RF power distribution and the probability of a harvester having enough energy to transmit a packet are validated through simulation. The numerical results obtained with the proposed analysis are close to the ones obtained through simulation, which confirms the accuracy of the proposed analysis.

#### 1. Introduction

The nodes forming a Radio Frequency (RF) Energy Harvesting Network (RF-EHN) have the capability of converting received electromagnetic RF signals in energy. The RF energy is converted by an energy harvester device, which is composed of an RF antenna, a band pass filter parametrized to the RF signals, and a rectifying circuit able to convert RF to DC power [1]. In this way the converted RF signals are used to charge a battery (usually a supercapacitor) with finite capacity [2]. The harvested energy accumulated in the battery can then be used to transmit a packet. However, the transmission is only possible if the level of accumulated energy is higher than a given threshold representing the minimum level of energy required to complete a packet transmission.

Recently, RF energy harvesting has attracted much attention and many efforts are being dedicated to develop innovative RF energy harvesting technologies as well as to investigate the performance of the networks formed by the harvesting devices. The RF energy harvesting literature dedicated to the efficient design of RF harvesting devices (see [3–7] for a few examples) is mainly focused on the minimization of the loss effects due to the RF-to-DC conversion and battery charging process. A different focus is also found in the literature, where the main goal is the study and characterization of RF-EHNs. Adopting a generic model for the RF energy harvesting devices, the goals are usually related with the scheduling of the harvesting devices in order to maximize the utilization of the RF energy and the frequency band constrained by specific throughput fairness policies [8]; the optimization of the harvester communication task to deal with the multiple tradeoffs associated with the physical and MAC layers [9, 10]; the characterization of the RF-EHN performance (throughput) and stability when RF energy harvesting is adopted [11]. Reference [12] investigates the performance (throughput) of a slotted Aloha random access wireless network consisting of two types of nodes: with unlimited energy supply and solely powered by an RF energy harvesting circuit. To illustrate the design considerations of RF-based harvesting networks, [13] points out the primary challenges of implementing and operating such networks, including nondeterministic energy arrival patterns, energy harvesting mode selection, and energy-aware cooperation among base stations. Reference [14] adopts a stochastic geometry framework based on the Ginibre model to analyze the performance of self-sustainable communications over cellular networks with general fading channels. The expectation of the RF energy harvesting rate, the energy outage probability, and the transmission outage probability are evaluated over Nakagami-m fading channels.

RF-EHNs may also act as cognitive radio networks (CRNs), that is, using the spectrum in an opportunistic way without being licensed. Several works have explored these kinds of networks. Reference [15] provides an overview of the RF-EHNs including system architecture, RF energy harvesting techniques, and existing applications. The authors also explore various key design issues in the development of RF-EHNs, including cognitive radio networks. The work in [16] provides a comprehensive overview of recent development and challenges regarding the operation of cognitive radio networks powered by RF energy. Spectrum efficiency and energy efficiency are two critical issues in designing cognitive radio RF-EHNs. Reference [17] provides an overview of the RF-powered CRNs and discusses the challenges that arise for dynamic spectrum access in these networks. Focusing on the trade-off among spectrum sensing, data transmission, and RF energy harvesting, the authors discuss the dynamic channel selection problem in a multichannel RF-powered CRN. Reference [18] proposes a novel method for wireless networks coexisting where low-power mobiles in a secondary network, harvest ambient RF energy from transmissions by nearby active transmitters, while opportunistically accessing the spectrum licensed to the primary network. The authors analyze the transmission probability of harvesting terminals and the resulting spatial throughput. The optimal transmission power and terminals’ density are also derived for maximizing the throughput. The work in [19] considers an RF-powered green cognitive radio network, where a central node harvests energy from ambient sources and wirelessly delivers random harvested energy to cognitive users. The work evaluates the performance of such a network, showing the feasibility of the behavior if the energy transmission rate is below a certain threshold. Reference [20] considers a network where the unlicensed users can perform channel access to transmit a packet or to harvest RF energy when the selected channel is idle or occupied by the primary user, respectively. The work is mainly focused on finding the channel access policy that maximizes the throughput of the secondary user. Reference [21] analyzes an energy harvesting-based cognitive radio system to find the optimal spectrum sensing time, which maximizes the harvested energy. The work in [22] analyzes a cognitive and energy harvesting-based device-to-device (D2D) communication in cellular networks. The authors employ tools from stochastic geometry to evaluate the performance of the proposed communication system model with general path-loss exponent in terms of outage probability for D2D and cellular users. One of the work conclusions is that energy harvesting can be a reliable alternative to power cognitive D2D transmitters, while achieving acceptable performance.

In this work we are particularly focused on the characterization of the RF power received by each harvester and its impact in terms of the probability of accumulating enough energy to transmit a packet. A generalized radio propagation environment is considered. Assuming that the sources of high power RF signals (e.g., base stations) are distributed according to a spatial Poisson process, we characterize the distribution of the received RF power from the multiple transmitters. Path loss, shadowing, and fading effects are considered. The distribution of the RF power is then used to derive the probability of a harvester node having enough energy to transmit a packet after a given period of time. A soft computational model (Gaussian approach) and a more complex model (non-Gaussian approach) are presented to compute the probability of a harvester node having enough energy to transmit. These are the main contributions of the paper. Considering multiple spatial and propagation scenarios, we validate the distribution of the RF power and the probability of a harvester have enough energy to transmit a packet. The numerical results obtained with the proposed analysis are close to the ones obtained through simulation, which confirms the accuracy of the proposed analysis. In this way, we provide a characterization of the battery charging time considering innovative assumptions, including the spatial distribution of the RF transmitters, the propagation effects, and the losses associated with the RF-to-DC conversion and battery charging process. The proposed model can thus be adopted to determine the probability of a harvester accumulating enough energy after a given period of time, which is a determinant condition to compute the throughput of RF-EHNs. As far as we known, this is the first work to derive such a probability when the multiple RF signals received by the harvesters are differently affected by multiple propagation effects.

The rest of the paper is organized as follows. The system description is presented in Section 2. The characterization of the received RF power is characterized in Section 3. Section 4 derives the probability of accumulating enough energy to transmit a packet through the Gaussian and non-Gaussian approaches. Finally, validation results are presented in Section 5 and conclusions are drawn in Section 6.

#### 2. System Description

This work considers a RF energy harvesting network, where each node accumulates energy from the base stations and other RF transmitters located in the neighborhood. A harvester node is able to initiate a packet transmission whenever the level of accumulated energy is above a transmission threshold.

##### 2.1. Spatial Distribution of the RF Transmitters

We consider the scenario illustrated in Figure 1, where the node (the harvester node) accumulates energy from the transmitters that might be located in the area . The area can be obtained via calculus by dividing the annulus up into an infinite number of annuli of infinitesimal width and area and then integrating from to ; that is; . Using the Riemann sum, can be approximated by the sum of the area of a finite number () of annuli of width ,where denotes the area of the annulus . and represent the radius of the larger and smaller circles of the annulus , respectively.