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Transmission with energy harvesting nodes in fading wireless channels: Optimal policies
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2011
"... Wireless systems comprised of rechargeable nodes have a significantly prolonged lifetime and are sustainable. A distinct characteristic of these systems is the fact that the nodes can harvest energy throughout the duration in which communication takes place. As such, transmission policies of the nod ..."
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Cited by 168 (43 self)
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Wireless systems comprised of rechargeable nodes have a significantly prolonged lifetime and are sustainable. A distinct characteristic of these systems is the fact that the nodes can harvest energy throughout the duration in which communication takes place. As such, transmission policies of the nodes need to adapt to these harvested energy arrivals. In this paper, we consider optimization of pointtopoint data transmission with an energy harvesting transmitter which has a limited battery capacity, communicating in a wireless fading channel. We consider two objectives: maximizing the throughput by a deadline, and minimizing the transmission completion time of the communication session. We optimize these objectives by controlling the time sequence of transmit powers subject to energy storage capacity and causality constraints. We, first, study optimal offline policies. We introduce a directional waterfilling algorithm which provides a simple and concise interpretation of the necessary optimality conditions. We show the optimality of an adaptive directional waterfilling algorithm for the throughput maximization problem. We solve the transmission completion time minimization problem by utilizing its equivalence to its throughput maximization counterpart. Next, we consider online policies. We use stochastic dynamic programming to solve for the optimal online policy that maximizes the average number of bits delivered by a deadline under stochastic fading and energy arrival processes with causal channel state feedback. We also propose nearoptimal policies with reduced complexity, and numerically study their performances along with the performances of the offline and online optimal policies under various different configurations.
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 packet scheduling in a multiple access channel with rechargeable nodes
 in Proc. IEEE ICC
, 2011
"... Abstract: In this paper, we investigate the optimal packet scheduling problem in a twouser multiple access communication system, where the transmitters are able to harvest energy from the nature. Under a deterministic system setting, we assume that the energy harvesting times and harvested energy a ..."
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Cited by 61 (16 self)
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Abstract: In this paper, we investigate the optimal packet scheduling problem in a twouser multiple access communication system, where the transmitters are able to harvest energy from the nature. Under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. For the packet arrivals, we assume that packets have already arrived and are ready to be transmitted at the transmitter before the transmission starts. Our goal is to minimize the time by which all packets from both users are delivered to the destination through controlling the transmission powers and transmission rates of both users. We first develop a generalized iterative backward waterfilling algorithm to characterize the maximum departure region of the transmitters for any given deadline T. Then, based on the sequence of maximum departure regions at energy arrival instants, we decompose the transmission completion time minimization problem into convex optimization problems and solve the overall problem efficiently. Index Terms: Energyharvesting communications, iterative backward waterfilling, multiaccess channel, throughput maximization.
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.
Optimal transmission policies for energy harvesting twohop networks
 in Proc. 2012 Conf. Inform. Sciences and Systems
, 2012
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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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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.
Throughput maximization for an energy harvesting communication system with processing cost
 Proc. IEEE Information Theory Workshop (ITW
, 2012
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Optimal power allocation for energy harvesting and power grid coexisting wireless communication systems
 IEEE Transactions on Communications
, 2013
"... Abstract—This paper considers the power allocation of a singlelink wireless communication with joint energy harvesting and grid power supply. We formulate the problem as minimizing the grid power consumption with random energy and data arrival in fading channel, and analyze the structure of the opt ..."
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Cited by 15 (10 self)
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Abstract—This paper considers the power allocation of a singlelink wireless communication with joint energy harvesting and grid power supply. We formulate the problem as minimizing the grid power consumption with random energy and data arrival in fading channel, and analyze the structure of the optimal power allocation policy in some special cases. For the case that all the packets are arrived before transmission, it is a dual problem of throughput maximization, and the optimal solution is found by the twostage water filling (WF) policy, which allocates the harvested energy in the first stage, and then allocates the power grid energy in the second stage. For the random data arrival case, we first assume grid energy or harvested energy supply only, and then combine the results to obtain the optimal structure of the coexisting system. Specifically, the reverse multistage WF policy is proposed to achieve the optimal power allocation when the battery capacity is infinite. Finally, some heuristic online schemes are proposed, of which the performance is evaluated by numerical simulations. Index Terms—Energy harvesting and power grid coexisting, convex optimization, twostage water filling, reverse multistage water filling. I.