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Energy Cooperation in Energy Harvesting Communications
, 2013
"... In energy harvesting communications, users transmit messages using energy harvested from nature during the course of communication. With an optimum transmit policy, the performance of the system depends only on the energy arrival profiles. In this paper, we introduce the concept of energy cooperatio ..."
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In energy harvesting communications, users transmit messages using energy harvested from nature during the course of communication. With an optimum transmit policy, the performance of the system depends only on the energy arrival profiles. In this paper, we introduce the concept of energy cooperation, where a user wirelessly transmits a portion of its energy to another energy harvesting user. This enables shaping and optimization of the energy arrivals at the energyreceiving node, and improves the overall system performance, despite the loss incurred in energy transfer. We consider several basic multiuser network structures with energy harvesting and wireless energy transfer capabilities: relay channel, twoway channel and multiple access channel. We determine energy management policies that maximize the system throughput within a given duration using a Lagrangian formulation and the resulting KKT optimality conditions. We develop a twodimensional directional waterfilling algorithm which optimally controls the flow of harvested energy in two dimensions: in time (from past to future) and among users (from energytransferring to energyreceiving) and show that a generalized version of this algorithm achieves the boundary of the capacity region of the twoway channel.
Energy Cooperation in Energy Harvesting TwoWay Communications
"... Abstract—In this paper, we investigate a twoway communication channel where users can harvest energy from nature and energy can be transferred in oneway from one of the users to the other. Energy required for data transmission is randomly harvested by the users throughout the communication duratio ..."
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Cited by 7 (5 self)
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Abstract—In this paper, we investigate a twoway communication channel where users can harvest energy from nature and energy can be transferred in oneway from one of the users to the other. Energy required for data transmission is randomly harvested by the users throughout the communication duration and users have unlimited batteries to store energy for future use. In addition, there is a separate wireless energy transfer unit that facilitates energy transfer only in oneway and with efficiency α. We study the energy cooperation made possible by wireless energy transfer in the twoway channel. Assuming that both users know the energy arrivals in advance, we find jointly optimal offline energy management policies that maximize the sum throughput of the users. We show that this problem is a convex optimization problem, and find the solution by a generalized twodimensional directional waterfilling algorithm which transfers energy from one user to another while maintaining that the energy is allocated in the time dimension optimally. Optimal solution equalizes the energy levels as much as possible both among users and among slots, permitted by causality constraints of the energy arrivals and oneway energy transfer. I.
Iterative dynamic waterfilling for fading multipleaccess channels with energy harvesting,” available at arXiv 1401.2376
, 2013
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Optimum policies for an energy harvesting transmitter under energy storage losses
 IEEE J. Sel. Areas Commun
, 2015
"... AbstractWe consider an energy harvesting network where the transmitter harvests energy from nature, and the harvested energy can be saved in an imperfect battery which suffers from charging/discharging inefficiency. In particular, when E units of energy is to be stored in the battery, only ηE unit ..."
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AbstractWe consider an energy harvesting network where the transmitter harvests energy from nature, and the harvested energy can be saved in an imperfect battery which suffers from charging/discharging inefficiency. In particular, when E units of energy is to be stored in the battery, only ηE units is saved and (1 − η)E is lost due to charging/discharging inefficiency, where 0 ≤ η ≤ 1 represents the storing efficiency. We determine the optimum offline transmit power schedule for such a system for singleuser and broadcast channel models, for static and fading channels, with and without a finite battery size. We show that the optimum policy is a doublethreshold policy: specifically, we store energy in the battery only when the harvested energy is above an upper threshold, and retrieve energy from the battery only when the harvested energy is below a lower threshold; when the harvested energy is in between these two thresholds, we use it in its entirety in the current slot. We show that the two thresholds remain constant unless the battery is depleted or full. We provide an algorithm to determine the sequence of optimum thresholds. For the case with fading, we develop a directional waterfilling algorithm which has a doublethreshold structure. Finally, we formulate the online problem using dynamic programming, and numerically observe that the online policy exhibits a doublethreshold structure as well. Index TermsEnergy harvesting communications, optimal packet scheduling, nodes with rechargeable batteries, inefficient energy storage. I. INTRODUCTION We consider an energy harvesting network where the transmitter harvests energy from nature to sustain its operation. In particular, the transmitter uses the energy harvested from nature to transmit its data packets. Such energy harvesting capabilities bring new constraints into the communication problem in the physical layer in the form of energy causality and noenergyoverflow conditions. The first constraint imposes that the energy that has not yet been harvested cannot be used for communication, and the second constraint imposes that no harvested energy should be allowed to overflow due to a finite battery size. Therefore, in such energy harvesting systems, packet scheduling and the corresponding energy management
Energy Harvesting Diamond Channel with Energy Cooperation
"... Abstract—We consider the energy harvesting diamond channel, where the source and two relays harvest energy from nature, the relays help deliver the source’s messages via signal cooperation, and the source has the option of wirelessly transferring some of its energy to the relays via energy cooperati ..."
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Abstract—We consider the energy harvesting diamond channel, where the source and two relays harvest energy from nature, the relays help deliver the source’s messages via signal cooperation, and the source has the option of wirelessly transferring some of its energy to the relays via energy cooperation. We find the optimal offline transmit power allocations and energy transfer policies that maximize the endtoend throughput. For the case of no energy cooperation, we decompose the problem into inner and outer maximization problems, and solve the overall problem iterating between the two. We show that the class of procrastinating policies, where energy is transferred only when it will be immediately used, is optimal. We then show that the problem with energy cooperation is equivalent to a problem without energy cooperation with suitably modified rate expressions. We show that, in this system, if the source sends more energy to a relay, then it sends less data, showing us how data and energy should flow together optimally in this network. I.
On the Precoder Design of a Wireless Energy Harvesting Node in Linear Vector Gaussian Channels with Arbitrary Input Distribution
"... in linear vector Gaussian channels with arbitrarily distributed input symbols is considered in this paper. The precoding strategy that maximizes the mutual information along N independent channel accesses is studied under noncausal knowledge of the channel state and harvested energy (commonly known ..."
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in linear vector Gaussian channels with arbitrarily distributed input symbols is considered in this paper. The precoding strategy that maximizes the mutual information along N independent channel accesses is studied under noncausal knowledge of the channel state and harvested energy (commonly known as offline approach). It is shown that, at each channel use, the left singular vectors of the precoder are equal to the eigenvectors of the Gram channel matrix. Additionally, an expression that relates the optimal singular values of the precoder with the energy harvesting profile through the Minimum MeanSquare Error (MMSE) matrix is obtained. Then, the specific situation in which the right singular vectors of the precoder are set to the identity matrix is considered. In this scenario, the optimal offline power allocation, named Mercury WaterFlowing, is derived and an intuitive graphical representation is presented. Two optimal offline algorithms to compute the Mercury WaterFlowing solution are proposed and an exhaustive study of their computational complexity is performed. Moreover, an online algorithm is designed, which only uses causal knowledge of the harvested energy and channel state. Finally, the achieved mutual information is evaluated through simulation. Index Terms—Energy harvesting, mutual information, arbitrary input distribution, precoder optimization, power allocation, linear vector Gaussian channels, MMSE. I.
Energy Harvesting Wireless Communications: A Review of Recent Advances
"... Abstract—This paper summarizes recent contributions in the broad area of energy harvesting wireless communications. In particular, we provide the current state of the art for wireless networks composed of energy harvesting nodes, starting from the informationtheoretic performance limits to transmis ..."
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Abstract—This paper summarizes recent contributions in the broad area of energy harvesting wireless communications. In particular, we provide the current state of the art for wireless networks composed of energy harvesting nodes, starting from the informationtheoretic performance limits to transmission scheduling policies and resource allocation, medium access, and networking issues. The emerging related area of energy transfer for selfsustaining energy harvesting wireless networks is considered in detail covering both energy cooperation aspects and simultaneous energy and information transfer. Various potential models with energy harvesting nodes at different network scales are reviewed, as well as models for energy consumption at the nodes. Index Terms—Energy harvesting communications, energy cooperation, simultaneous wireless information and energy transfer. I.
Optimal Scheduling for Energy Harvesting Transmitters with Hybrid Energy Storage
"... Abstract—We consider data transmission with an energy harvesting transmitter which has a hybrid energy storage unit composed of a perfectly efficient supercapacitor (SC) and an inefficient battery. The SC has finite space for energy storage while the battery has unlimited space. The transmitter can ..."
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Abstract—We consider data transmission with an energy harvesting transmitter which has a hybrid energy storage unit composed of a perfectly efficient supercapacitor (SC) and an inefficient battery. The SC has finite space for energy storage while the battery has unlimited space. The transmitter can choose to store the harvested energy in the SC or in the battery. The energy is drained from the SC and the battery simultaneously. In this setting, we consider the offline throughput maximization problem by a deadline over a pointtopoint channel. In contrast to previous works, the hybrid energy storage model with finite and unlimited storage capacities imposes a generalized set of constraints on the transmission policy. As such, we show that the solution generalizes that for a single battery and is obtained by applying directional waterfilling algorithm multiple times. I.
Twoway and multipleaccess energy harvesting systems with energy cooperation
 in 46th Asilomar Conf. Signals, Syst. and Comp
, 2012
"... Abstract—We study the capacity regions of twoway and multipleaccess energy harvesting communication systems with oneway wireless energy transfer. In these systems, energy required for data transmission is harvested by the users from nature throughout the communication duration, and there is a sep ..."
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Cited by 3 (1 self)
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Abstract—We study the capacity regions of twoway and multipleaccess energy harvesting communication systems with oneway wireless energy transfer. In these systems, energy required for data transmission is harvested by the users from nature throughout the communication duration, and there is a separate unit that enables energy transfer from the first user to the second user with an efficiency of α. Energy harvests are known by the transmitters a priori. We first investigate the capacity region of the energy harvesting Gaussian twoway channel (TWC) with oneway energy transfer. We show that the boundary of the capacity region is achieved by a generalized twodimensional directional waterfilling algorithm. Then, we study the capacity region of the energy harvesting Gaussian multiple access channel (MAC) with oneway energy transfer. We show that if the priority of the first user is higher, then energy transfer is not needed. In addition, if the priority of the second user is sufficiently high, then the first user must transfer all of its energy to the second user. I.
Energy Harvesting TwoWay HalfDuplex Relay Channel with DecodeandForward Relaying: Optimum Power Policies
"... Abstract—In this paper, a halfduplex twoway relay channel with energy harvesting nodes is considered. In particular, shortterm throughput maximization problems are solved using a decodeandforward relay. Necessary properties of the optimal transmission policy are derived to gain insights into the ..."
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Abstract—In this paper, a halfduplex twoway relay channel with energy harvesting nodes is considered. In particular, shortterm throughput maximization problems are solved using a decodeandforward relay. Necessary properties of the optimal transmission policy are derived to gain insights into the optimal solution. Then, a subgradient descent algorithm is used to find the optimal policy. It is observed through simulations that energydeficient nodes act as bottlenecks on the achieved throughput. The achieved average throughput is observed to be close to the upper bound when nodes have no energy intermittency, and significantly higher than the throughput achieved by naïve policies. I.