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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.
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.
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.
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.
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.
1 Optimal Strategies for Communication and Remote Estimation with an Energy Harvesting Sensor
"... We consider a remote estimation problem with an energy harvesting sensor and a remote estimator. The sensor observes the state of a discretetime source which may be a finite state Markov chain or a multidimensional linear Gaussian system. It harvests energy from its environment (say, for example, ..."
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Cited by 12 (0 self)
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We consider a remote estimation problem with an energy harvesting sensor and a remote estimator. The sensor observes the state of a discretetime source which may be a finite state Markov chain or a multidimensional linear Gaussian system. It harvests energy from its environment (say, for example, through a solar cell) and uses this energy for the purpose of communicating with the estimator. Due to the randomness of energy available for communication, the sensor may not be able to communicate all the time. The sensor may also want to save its energy for future communications. The estimator relies on messages communicated by the sensor to produce realtime estimates of the source state. We consider the problem of finding a communication scheduling strategy for the sensor and an estimation strategy for the estimator that jointly minimize an expected sum of communication and distortion costs over a finite time horizon. Our goal of joint optimization leads to a decentralized decisionmaking problem. By viewing the problem from the estimator’s perspective, we obtain a dynamic programming characterization for the decentralized decisionmaking problem that involves optimization over functions. Under some symmetry assumptions on the source statistics and the distortion metric, we show that an optimal communication strategy is described by easily computable thresholds and that the optimal estimate is a simple function of the most recently received sensor observation. I.