The charger positioning problem in clustered RF-power harvesting wireless sensor networks
Introduction
Wireless sensor networks are capable of periodically monitoring their vicinity and reporting important information about the integrity and security of their environment. The sensor nodes are powered by batteries and depending on how often they take measurements, communicate or interfere with other devices, their energy may be depleted fast. The node battery replacement may be a difficult task since sensors networks are often deployed in inaccessible places or the cost of the replacement may be high.
A technology that has been recently developed takes advantage of the transmitted neighboring RF signals to harvest a small portion of energy. More specifically, an RF-power harvesting antenna is used which can convert part of the received signal power to electricity. Depending on the transmitted power and the distance between the transmitting source and the receiver, a node can harvest power from some uW to some mW [1]. However, this technology presents some major limitations mainly due to the strong signal attenuation and the low efficiency of the conversion unit [2]. The harvested power rapidly decreases when the receiver is moving more than a few meters away from the source; the conversion efficiency is substantial only for a short range, and there is a minimum received signal power corresponding to a maximum distance below which no conversion is possible. These weaknesses substantially limit the effective range around the transmitting source, making this solution advantageous only for a few neighboring nodes. On the other hand, a possible use of multiple chargers to cover big parts of the network could considerably increase the expenditure and operating costs [3].
In this paper, we consider networks consisting of nodes which can acquire energy from energy transmitters (chargers). We assume that a charger periodically and omni-directionally transmits data to the network.1 Due to the restrictions described before, we organize the network in clusters so that the majority of the nodes use short communication links and the most of the communication burden falls onto the shoulders of the cluster heads. By using chargers close to these nodes, we alleviate their communication cost and, thus, extend the network lifetime. An example of the proposed model is depicted in Fig. 1.
The RF-power harvesting paradigm using dedicated chargers can meet several industrial applications such as the use of wire-free or battery-free sensors. Moreover, modern Internet of Things protocols, like Zigbee, are designed to operate at 2.4 GHz whereas some known RF-power harvesting manufacturers propose equipment that uses the sub-gigahertz spectrum. This permits collision-free communications between the nodes and the chargers, and facilitates the nodes deployment.
However, the question that arises is where to place a charger so that the network lifetime is prolonged as much as possible. In this paper we choose a charger placement strategy that (a) does not allow the cluster head to run out of energy throughout the whole monitoring process and (b) it provides the rest of the nodes (especially the most distant ones) with as much energy as possible. We explain that the placement problem is a special case of the Weber problem and we propose a local search algorithm that finds a solution very close to the optimal. The algorithm can operate in both centralized or distributed manner since it uses localized information and a number of successive steps to gradually move the charger towards more efficient positions. We, also, present an exhaustive search algorithm that examines a very large range of possible solutions exhibiting, however, higher computation costs.
The contribution of this paper is threefold; (a) we model a network that takes advantage of the very short efficient harvesting range and we organize the nodes in clusters so that by placing a charger close to the cluster head, it will have enough energy to forward the data of the rest of the nodes. (b) We analyze whether clustering is energy efficient and we compute the maximum possible cluster size. (c) We introduce the optimal charger positioning problem and we propose efficient algorithms to find solutions very close to the optimal. Finally, (d) we simulate our approach using realistic harvesting values and we compare to other approaches.
The present paper extends our previous work [4] by (a) presenting the theoretical background behind clustering in RF-power harvesting networks, (b) distinguishing two flavors of the optimal charger placement problem based on two network lifetime definitions, and (c) extending the theoretical and simulation results with comparison with other approaches in the literature.
The rest of the work is organized as follows. In Section 2, we make a discussion about previous works related to RF-power harvesting, routing, and placement problems. In Section 3 we describe the considered consumption, harvesting, communication, and network lifetime models. Section 4 presents a theoretical analysis on energy efficient clustering with RF-power harvesting nodes and Section 5 introduces the optimal charger positioning problem. Section 6 describes the proposed solutions and Section 7 presents the theoretical and simulation results. Finally, Section 8 concludes the paper and presents ideas for future work.
Section snippets
Related work
RF-energy harvesting networks have been extensively studied from different research aspects. Lu et al. [2] gives a general review of RF-power harvesting networks including a system architecture, RF energy harvesting techniques, and existing applications. Then, it surveys the state-of-the-art circuitry implementations, and reviews the communication protocols specially designed for this type of networks. Soyata et al. [5] focus on design tradeoffs to represent the diversity in the applications
Energy consumption
We consider wireless sensor nodes powered by rechargeable batteries. Each node spends its energy by taking measurements and by communicating with other nodes. A small amount of energy is, also, spent for the rest of the sensor functions (storage, processing etc.).
We assume that each node has m power transmission levels and each level corresponds to a distance range. There is, also, a maximum achievable transmission range using the maximum power transmission level. The energy spent per bit is
Maximum cluster size
During the entire network operation the CH should be supplied with enough energy to forward the data of multiple nodes and operate at least until one node is depleted. Since the charger can transfer a limited amount of energy per round, the number of nodes a CH can support is also limited.
Assuming that the optimal charger position has been found, we set where I is the node with the maximum energy consumption in the network (excluding the CH). Solving for n and considering that k′ has
The optimal charger positioning problem
The optimal charger position is apparently affected by the definition of the network lifetime. Given the first network lifetime definition we gave in Section 3.3, the network lifetime is upper bounded by the node with the highest energy consumption in the network. In this case, the charger must be placed somewhere such as the CH gets enough energy to operate (at least) until one node dies, and at the same time, the most consuming node lasts as long as possible. On the other hand, if we assume
Local search algorithm
In this section, we present a local search algorithm (LS) which computes a charger position not far from the optimal. We first present the solution for the Simple-OCP and then we extend it for the Extended-OCP.
First of all, before the charger deployment, the nodes need to select a member that will be the CH. The CH is chosen based on two criteria; (a) to be accessible by all the nodes of the group and (b) to be connected with the sink. Every node that satisfies these two criteria can become CH.
Setup
In this section we present numerical as well as simulation results regarding the concept of clustering and the optimal charger positioning problem. We assume a scenario with a fixed size square terrain of 25 m side and a variable number of nodes randomly and uniformly scattered on the terrain. We create 10 instances for each scenario. We measure the maximum energy consumption of the nodes (displayed as “Consumption”) for one round and the execution time of the algorithms. For the Extended-OCP
Conclusion & future work
In this paper we examined the feasibility of organizing RF-power harvesting nodes in clusters and of extending the network lifetime by positioning a charger close to the cluster head. We introduced the problem of the optimal charger placement and we proposed both localized and centralized algorithms that perform close to the optimal. Numerical results showed that the harvesting with clustering is energy efficient for a wide range of deployments. This range can be slightly expanded by
Acknowledgments
This work was carried out within the action “Strengthening Post Doctoral Research” of the “Human Resources Development Program, Education and Lifelong Learning”, 2014–2020, which is being implemented from IKY and is co-financed by the European Social Fund – ESF and the Greek government.
Dimitrios Zorbas received his Ph.D. in 2011 from the University of Piraeus in Greece. During 2011 and 2014 he was member of the FUN team at Inria Lille - Nord Europe in France as a post doctoral researcher. He also spent one year as researcher at University of La Rochelle. He is currently research fellow of IKY (national scholarship institute) in Greece and researcher at University of Pireaus. He has also worked on several EU projects in Greece and in France.
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Dimitrios Zorbas received his Ph.D. in 2011 from the University of Piraeus in Greece. During 2011 and 2014 he was member of the FUN team at Inria Lille - Nord Europe in France as a post doctoral researcher. He also spent one year as researcher at University of La Rochelle. He is currently research fellow of IKY (national scholarship institute) in Greece and researcher at University of Pireaus. He has also worked on several EU projects in Greece and in France.
Patrice Raveneau received his Ph.D. from Research Institute of Informatics in Toulouse in 2014. He worked as post doctoral researcher at Inria and at University of Lyon. He is currently associate professor at University of La Rochelle in France.
Yacine Ghamri-Doudane is currently professor at University of La Rochelle in France. He received an engineering degree in computer science from the National Institute of Computer Science (INI), Algiers, Algeria, in 1998, an M.S. degree in signal, image and speech processing from the National Institute of Applied Sciences (INSA), Lyon, France, and a Ph.D. degree in computer networks from the Pierre & Marie Curie University, Paris 6, France, in 1999 and 2003, respectively. His current research interests include Mobility Management in 4G Mobile Networks, Ad hoc and Sensor Networks, Vehicular Communications, TCP and Multimedia over Wireless, QoS in WLAN/WMAN, and Management of Wireless/Mobile Networks. He is also acting as ICC Selected Area in Communications Symposium Co-Chair in 2009 and 2010. Since December 2007, he is the Secretary of the IEEE ComSoc Technical Committee on Information Infrastructure (TCII). He is founding co-editor of the IEEE ComSoc Ad Hoc and Sensor Network Technical Committee (AHSN TC) Newsletter. He is a Member of IEEE and the Communications Society.
Christos Douligeris received the Diploma in Electrical Engineering from the National Technical University of Athens in 1984 and the M.S., M.Phil. and Ph.D. degrees from Columbia University in 1985, 1987, 1990, respectively. He is currently a professor in the Department of Informatics, University of Piraeus, Greece. He has held positions with the Department of Electrical and Computer Engineering at the University of Miami. He has served in technical program committees of several conferences. His main interests lie in the areas of performance evaluation of high speed net works, neurocomputing in networking, resource allocation in wireless networks and information management, risk assessment and evaluation for emergency response operations. He is an editor of the IEEE Communications Letters, a technical editor of IEEE Network, and a technical editor of Computer Networks (Elsevier).