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Optimum transmission policies for battery limited energy harvesting nodes,” Submitted to IEEE Transactions on Wireless Communications, available at: http://arxiv.org/PS_cache/arxiv/pdf/1010/1010.6280v1.pdf. This full text paper was peer reviewed at the di
 in the IEEE ICC 2011 proceedings
"... Abstract—Wireless networks with energy harvesting battery equipped nodes are quickly emerging as a viable option for future wireless networks with extended lifetime. Equally important to their counterpart in the design of energy harvesting radios are the design principles that this new networking pa ..."
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Cited by 122 (23 self)
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Abstract—Wireless networks with energy harvesting battery equipped nodes are quickly emerging as a viable option for future wireless networks with extended lifetime. Equally important to their counterpart in the design of energy harvesting radios are the design principles that this new networking paradigm calls for. In particular, unlike wireless networks considered to date, the energy replenishment process and the storage constraints of the rechargeable batteries need to be taken into account in designing efficient transmission strategies. In this work, such transmission policies for rechargeable nodes are considered, and optimum solutions for two related problems are identified. Specifically, the transmission policy that maximizes the short term throughput, i.e., the amount of data transmitted in a finite time horizon is found. In addition, the relation of this optimization problem to another, namely, the minimization of the transmission completion time for a given amount of data is demonstrated, which leads to the solution of the latter as well. The optimum transmission policies are identified under the constraints on energy causality, i.e., energy replenishment process, as well as the energy storage, i.e., battery capacity. For battery replenishment, a model with discrete packets of energy arrivals is considered. The necessary conditions that the throughputoptimal allocation satisfies are derived, and then the algorithm that finds the optimal transmission policy with respect to the shortterm throughput and the minimum transmission completion time is given. Numerical results are presented to confirm the analytical findings. Index Terms—Energy harvesting, optimal scheduling, wireless networks, battery limited nodes. I.
Broadcasting with an energy harvesting rechargeable transmitter
 IEEE Trans. Wireless Comm
, 2010
"... Abstract—In this paper, we investigate the transmission completion time minimization problem in an additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature, using a rechargeable battery. The harvested energy is modeled to arrive at the t ..."
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Cited by 76 (22 self)
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Abstract—In this paper, we investigate the transmission completion time minimization problem in an additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature, using a rechargeable battery. The harvested energy is modeled to arrive at the transmitter during the course of transmissions. The transmitter has a fixed number of packets to be delivered to each receiver. The objective is to minimize the time by which all of the packets are delivered to their respective destinations. To this end, we optimize the transmit powers and transmission rates in a deterministic setting. We first analyze the structural properties of the optimal transmission policy in a twouser broadcast channel via the dual problem of maximizing the departure region by a fixed time
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 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.
Stability analysis and power optimization for energy harvesting cooperative networks
 IEEE Signal Process. Lett
, 2012
"... Abstract—In this letter, we investigate the effects of networklayer cooperation in a wireless threenode network with energyharvesting nodes and bursty data traffic. By modelling energy harvesting in each node as a queue (buffer) that stores the received energy, we study the interaction between d ..."
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Cited by 23 (5 self)
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Abstract—In this letter, we investigate the effects of networklayer cooperation in a wireless threenode network with energyharvesting nodes and bursty data traffic. By modelling energy harvesting in each node as a queue (buffer) that stores the received energy, we study the interaction between data and energy queues when only knowledge of the arrival rates is available. The maximum stable throughput (in packets/slot) of the source as well as the required transmitted power for both a noncooperative and an orthogonal decodeandforward cooperative schemes are derived in closedform. We prove that cooperation achieves a higher maximum stable throughout than direct link for scenarios with poor energy arrival rates. Index Terms—Cooperative networks, energy harvesting, power optimization, stable throughput. 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.
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.