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Optimal power policy for energy harvesting transmitters with inefficient energy storage
 in Proc. Annual Conference on Information Sciences and Systems (CISS
, 2012
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Optimal packet scheduling on an energy harvesting broadcast link
 IEEE J. Sel. Areas Commun
, 2011
"... The minimization of transmission completion time for a given number of bits per user in an energy harvesting communication system, where energy harvesting instants are known in an offline manner is considered. An achievable rate region with structural properties satisfied by the 2user AWGN Broadcas ..."
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Cited by 53 (1 self)
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The minimization of transmission completion time for a given number of bits per user in an energy harvesting communication system, where energy harvesting instants are known in an offline manner is considered. An achievable rate region with structural properties satisfied by the 2user AWGN Broadcast Channel capacity region is assumed. It is shown that even though all data are available at the beginning, a nonnegative amount of energy from each energy harvest is deferred for later use such that the transmit power starts at its lowest value and rises as time progresses. The optimal scheduler ends the transmission to both users at the same time. Exploiting the special structure in the problem, the iterative offline algorithm, FlowRight, from earlier literature, is adapted and proved to solve this problem. The solution has polynomial complexity in the number of harvests used, and is observed to converge quickly on numerical examples. Index Terms Packet scheduling, energy harvesting, AWGN broadcast channel, flowright, energyefficient scheduling.
Optimal broadcast scheduling for an energy harvesting rechargeable transmitter with a finite capacity battery
 IEEE Trans. Wireless Commun
"... Abstract—We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in an Muser AWGN broadcast channel where the transmitter is able to harvest energy from the nature, using a finite storage capacity rechargeable battery. The harvested ener ..."
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Cited by 40 (19 self)
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Abstract—We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in an Muser AWGN broadcast channel where the transmitter is able to harvest energy from the nature, using a finite storage capacity rechargeable battery. The harvested energy is modeled to arrive (be harvested) at the transmitter during the course of transmissions at arbitrary time instants. The transmitter has fixed number of packets for each receiver. Due to the finite battery capacity, energy may overflow without being utilized for data transmission. We derive the optimal offline transmission policy that minimizes the time by which all of the data packets are delivered to their respective destinations. We analyze the structural properties of the optimal transmission policy using a dual problem. We find the optimal total transmit power sequence by a directional waterfilling algorithm. We prove that there exist M − 1 cutoff power levels such that user i is allocated the power between the i−1st and the ith cutoff power levels subject to the availability of the allocated total power level. Based on these properties, we propose an algorithm that gives the globally optimal offline policy. The proposed algorithm uses directional waterfilling repetitively. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings. Index Terms—Energy harvesting, rechargeable wireless networks, broadcast channels, finitecapacity battery, transmission completion time minimization, throughput maximization. I.
Achieving AWGN capacity under stochastic energy harvesting
 IEEE Trans. on Inform. Theory
"... Abstract—In energy harvesting communication systems, an exogenous recharge process supplies energy necessary for data transmission and the arriving energy can be buffered in a battery before consumption. We determine the informationtheoretic capacity of the classical additive white Gaussian noise ( ..."
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Cited by 37 (17 self)
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Abstract—In energy harvesting communication systems, an exogenous recharge process supplies energy necessary for data transmission and the arriving energy can be buffered in a battery before consumption. We determine the informationtheoretic capacity of the classical additive white Gaussian noise (AWGN) channelwithanenergyharvestingtransmitterwithanunlimited sized battery. As the energy arrives randomly and can be saved in the battery, codewords must obey cumulative stochastic energy constraints. We show that the capacity of the AWGN channel with such stochastic channel input constraints is equal to the capacity with an average power constraint equal to the average recharge rate. We provide two capacity achieving schemes: saveandtransmit and bestefforttransmit. In the saveandtransmit scheme, the transmitter collects energy in a saving phase of proper duration that guarantees that there will be no energy shortages during the transmission of code symbols. In the bestefforttransmit scheme, the transmission starts right away without an initial saving period, and the transmitter sends a code symbol if there is sufficient energy in the battery, and a zero symbol otherwise. Finally, we consider a system in which the average recharge rate is time varying in a larger time scale and derive the optimal offline power policy that maximizes the average throughput, by using majorization theory. Index Terms—Additive white Gaussian noise (AWGN) channel, energy harvesting, offline power management, Shannon capacity. I.
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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Cited by 21 (8 self)
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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.
Communicating with Energy Harvesting Transmitters and Receivers
"... Abstract—This paper provides a general framework for utility maximization of a wireless network with energy harvesting nodes. The focus is on applying this framework to the singlelink problem with an energy harvesting transmitter and an energy harvesting receiver. For the general utility maximizati ..."
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Cited by 14 (5 self)
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Abstract—This paper provides a general framework for utility maximization of a wireless network with energy harvesting nodes. The focus is on applying this framework to the singlelink problem with an energy harvesting transmitter and an energy harvesting receiver. For the general utility maximization problem, it is shown that if the utility of a network can be expressed instantaneously as a function of the powers of the nodes, then the maximum utility achieving power policy for each node can be found using a waterfilling approach for each user. This is achieved by expressing the general utility maximization problem as a pair of nested problems focusing on energy efficiency and adapting to energy harvests separately. The framework extends the previous results on offline optimization of energy harvesting transmitters to networks with all energy harvesting nodes including receivers and relays as well as any network utility, provided that the achieved utility is instantaneous and additive in time. The implications of the energy efficiency problem on the energy harvesting problem are demonstrated over an energy harvesting transmitterreceiver pair, and simulation results are presented to exhibit the performance of the optimal policy along with some alternatives for a range of storage capacities. Index Terms—Energy harvesting, utility maximization, wireless networks, optimal scheduling, battery limited nodes. I.
Broadcasting with a Battery Limited Energy Harvesting Rechargeable Transmitter
 9th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
"... Abstract—We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in a twouser AWGN broadcast channel. The transmitter has fixed number of packets for each receiver and energy is modeled to arrive (be harvested) at the transmitter at rand ..."
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Cited by 13 (4 self)
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Abstract—We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in a twouser AWGN broadcast channel. The transmitter has fixed number of packets for each receiver and energy is modeled to arrive (be harvested) at the transmitter at random instants. The battery at the transmitter has a finite storage capacity, hence energy may overflow without being utilized for data transmission. We derive the optimal offline transmission policy that minimizes the time by which all of the data packets are delivered to their respective destinations. We analyze the structural properties of the optimal transmission policy using a dual problem. We find the optimal total transmit power sequence by a directional waterfilling algorithm. We prove that there exists a cutoff power level such that if the allocated power is lower than this level, then only the stronger user is served in that epoch; otherwise, the power above this level is allocated to the weaker user. Based on these properties, we propose an algorithm that gives the globally optimal offline policy. The proposed algorithm uses directional waterfilling repetitively. I.
Fundamentals of heterogeneous cellular networks with energy harvesting,” submitted to
 IEEE Tran. Wireless Communications
, 2013
"... Abstract—We develop a new tractable model for Ktier heterogeneous cellular networks (HetNets), where each base station (BS) is powered solely by a selfcontained energy harvesting module. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power an ..."
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Cited by 11 (2 self)
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Abstract—We develop a new tractable model for Ktier heterogeneous cellular networks (HetNets), where each base station (BS) is powered solely by a selfcontained energy harvesting module. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power and deployment density. Since a BS may not always have enough energy, it may need to be kept OFF and allowed to recharge while nearby users are served by neighboring BSs that are ON. We show that the fraction of time a kth tier BS can be kept ON, termed availability ρk, is a fundamental metric of interest. Using tools from random walk theory, fixed point analysis and stochastic geometry, we characterize the set of Ktuples (ρ1, ρ2,... ρK), termed the availability region, that is achievable by general uncoordinated operational strategies, where the decision to toggle the current ON/OFF state of a BS is taken independently of the other BSs. If the availability vector corresponding to the optimal system performance, e.g., in terms of rate, lies in this availability region, there is no performance loss due to the presence of unreliable energy sources. As a part of our analysis, we model the temporal dynamics of the energy level at each BS as a birthdeath process, derive the energy utilization rate, and use hitting/stopping time analysis to prove that there exists a fundamental limit on ρk that cannot be surpassed by any uncoordinated strategy. Index Terms—Heterogeneous cellular networks, energy harvesting, availability region, stochastic geometry, random walk theory, fixed point analysis, Poisson point process. I.
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.
Cooperative Energy Harvesting Communications with Relaying and Energy Sharing
"... Abstract—This paper considers twohop communication networks where the transmitters harvest their energy in an intermittent fashion. In this network, communication is carried out by signal cooperation, i.e., relaying. Additionally, the transmitters have the option of transferring energy to one anoth ..."
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Cited by 7 (3 self)
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Abstract—This paper considers twohop communication networks where the transmitters harvest their energy in an intermittent fashion. In this network, communication is carried out by signal cooperation, i.e., relaying. Additionally, the transmitters have the option of transferring energy to one another, i.e., energy cooperation. Energy is partially lost during transfer, exposing a tradeoff between energy cooperation and use of harvested energy for transmission. A multiaccess relay model is considered and transmit power allocation and energy transfer policies that jointly maximize the sumrate are found. It is shown that a class of power policies achieves the optimal sumrate, allowing a separation of optimal energy transfer and optimal power allocation problems. The optimal energy transfer policy is shown to be an ordered node selection, where nodes with better energy transfer efficiency and worse channels transfer all their energy to the relay or other source nodes via the relay. For the special case of single source, the optimal policy requires the direction of energy transfer to remain unchanged unless either node depletes all of its energy. Overall, the findings provide the insight that cooperation of the source nodes by sharing energy with the relay node leads to them indirectly cooperating with each other, and that such cooperation can be carried out in a lastminute fashion. I.