This paper studies online transmission policies for an energy harvesting transmitter. Unlike the existing online policies which more or less require the knowledge on the future behavior of the energy and data arrival processes, we consider a practical but significantly more challenging scenario where the energy and data arrival processes are assumed to be totally unknown. Our design is formulated as a robust-optimal control problem which aims to optimize the worst-case performance. The transmission policy is designed only based on the current battery energy level and the data queue length directly monitored by the transmitter itself. Specifically, we apply an event-trigger approach in which the transmitter continuously monitors the battery energy and data queue length, and triggers an event when a significant change occurs in either of them. Once an event is triggered, the transmission policy is updated by the solution to the robust-optimal control problem. We consider both the transmission time and throughput as the performance metrics and formulated two optimization problems. The solutions are given in either a simple analytical form or an easy-to-implement algorithm.
The development of energy harvesting devices has attracted significant attention in recent years with many potential applications in communication networks for green and self-sustainable communications @cite_3 . In order to make efficient use of harvested energy, both offline and online solutions have been investigated for designing the optimal transmission policy. Offline solutions are possible in highly predictable environments where the energy and data arrivals in a sufficiently distant future (for communication purpose) can be accurately estimated @cite_23 @cite_10 @cite_4 @cite_0 @cite_18 @cite_9 . On the other hand, online solutions typically reduce the dependence on the future knowledge of the energy and data arrival processes, and hence are more applicable in practice. The online algorithms can be roughly categorized into two frameworks as follows:
@cite_18 @cite_4 @cite_9 @cite_3 @cite_0 @cite_23 @cite_10
2081751842 2145834571 2111844221 2614312052 2952044966 2075914509 1990808825 2088506000 2342830374 2206189632 2490752264 1988876637 2035229442 2042738017 2963531496 2153679452 2015786472 2141058243 2584574674 1979096885
We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in an M-user 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 water-filling algorithm. We prove that there exist M-1 cut-off power levels such that user i is allocated the power between the i-1st and the ith cut-off 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 water-filling repetitively. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings. 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 point-to-point 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 water-filling algorithm which provides a simple and concise interpretation of the necessary optimality conditions. We show the optimality of an adaptive directional water-filling 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 near-optimal policies with reduced complexity, and numerically study their performances along with the performances of the offline and online optimal policies under various different configurations. Energy harvesting is a promising solution to prolong the operation of energy-constrained wireless networks. In particular, scavenging energy from ambient radio signals, namely wireless energy harvesting (WEH), has recently drawn significant attention. In this paper, we consider a point-to-point wireless link over the narrowband flat-fading channel subject to time-varying co-channel interference. It is assumed that the receiver has no fixed power supplies and thus needs to replenish energy opportunistically via WEH from the unintended interference and or the intended signal sent by the transmitter. We further assume a single-antenna receiver that can only decode information or harvest energy at any time due to the practical circuit limitation. Therefore, it is important to investigate when the receiver should switch between the two modes of information decoding (ID) and energy harvesting (EH), based on the instantaneous channel and interference condition. In this paper, we derive the optimal mode switching rule at the receiver to achieve various trade-offs between wireless information transfer and energy harvesting. Specifically, we determine the minimum transmission outage probability for delay-limited information transfer and the maximum ergodic capacity for no-delay-limited information transfer versus the maximum average energy harvested at the receiver, which are characterized by the boundary of so-called "outage-energy" region and "rate-energy" region, respectively. Moreover, for the case when the channel state information (CSI) is known at the transmitter, we investigate the joint optimization of transmit power control, information and energy transfer scheduling, and the receiver's mode switching. The effects of circuit energy consumption at the receiver on the achievable rate-energy trade-offs are also characterized. Our results provide useful guidelines for the efficient design of emerging wireless communication systems powered by opportunistic WEH. Energy harvesting (EH) two-hop communications are considered. The transmitter and the relay harvest energy from the environment and use it exclusively for transmitting data. A data arrival process is assumed at the transmitter. At the relay, a finite data buffer is used to store the received data. We consider a realistic scenario in which the EH nodes have only local causal knowledge, i.e., at any time instant, each EH node only knows the current value of its EH process, channel state, and data arrival process. Our goal is to find a power allocation policy to maximize the throughput at the receiver. We show that because the EH nodes have local causal knowledge, the two-hop communication problem can be separated into two point-to-point problems. Consequently, independent power allocation problems are solved at each EH node. To find the power allocation policy, reinforcement learning with linear function approximation is applied. Moreover, to perform function approximation two feature functions which consider the data arrival process are introduced. Numerical results show that the proposed approach has only a small degradation as compared to the offline optimum case. Furthermore, we show that with the use of the proposed feature functions a better performance is achieved compared to standard approximation techniques. We consider the optimal online packet scheduling problem in a single-user energy harvesting wireless communication system, where energy is harvested from natural renewable sources, making future energy arrivals instants and amounts random in nature. The most general case of arbitrary energy arrivals is considered where neither the future energy arrival instants or amount, nor their distribution is known. The problem considered is to adaptively change the transmission rate according to the causal energy arrival information, such that the time by which all packets are delivered is minimized. We assume that all bits have arrived and are ready at the source before the transmission begins. For a minimization problem, the utility of an online algorithm is tested by finding its competitive ratio or competitiveness that is defined to be the maximum of the ratio of the gain of the online algorithm with the optimal offline algorithm over all input sequences. We derive a lower and upper bound on the competitive ratio of any online algorithm to minimize the total transmission time in an energy harvesting system. The upper bound is obtained using a lazy' transmission policy that chooses its transmission power to minimize the transmission time assuming that no further energy arrivals are going to occur in future. The lazy transmission policy is shown to be strictly two-competitive. We also derive an adversarial lower bound that shows that competitive ratio of any online algorithm is at least 1.325. This paper considers a two-user Gaussian interference channel with energy harvesting transmitters. Different than conventional battery powered wireless nodes, energy harvesting transmitters have to adapt transmission to availability of energy at a particular instant. In this setting, the optimal power allocation problem to maximize the sum throughput with a given deadline is formulated. The convergence of the proposed iterative coordinate descent method for the problem is proved and the short-term throughput maximizing offline power allocation policy is found. Examples for interference regions with known sum capacities are given with directional waterfilling interpretations. Next, stochastic data arrivals are addressed. Finally, online and or distributed near-optimal policies are proposed. Performance of the proposed algorithms are demonstrated through simulations. Communication over a broadband fading channel powered by an energy harvesting transmitter is studied. Assuming non-causal knowledge of energy data arrivals and channel gains, optimal transmission schemes are identified by taking into account the energy cost of the processing circuitry as well as the transmission energy. A constant processing cost for each active sub-channel is assumed. Three different system objectives are considered: i) throughput maximization, in which the total amount of transmitted data by a deadline is maximized for a backlogged transmitter with a finite capacity battery; ii) energy maximization, in which the remaining energy in an infinite capacity battery by a deadline is maximized such that all the arriving data packets are delivered; iii) transmission completion time minimization, in which the delivery time of all the arriving data packets is minimized assuming infinite size battery. For each objective, a convex optimization problem is formulated, the properties of the optimal transmission policies are identified, and an algorithm which computes an optimal transmission policy is proposed. Finally, based on the insights gained from the offline optimizations, low-complexity online algorithms performing close to the optimal dynamic programming solution for the throughput and energy maximization problems are developed under the assumption that the energy data arrivals and channel states are known causally at the transmitter. 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 information-theoretic capacity of the classical additive white Gaussian noise (AWGN) channel with an energy harvesting transmitter with an unlimited 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: save-and-transmit and best-effort-transmit. In the save-and-transmit 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 best-effort-transmit 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. Recent emphasis on green communications has generated great interest in the investigations of energy harvesting communications and networking. Energy harvesting from ambient energy sources can potentially reduce the dependence on the supply of grid or battery energy, providing many attractive benefits to the environment and deployment. However, unlike the conventional stable energy, the intermittent and random nature of the renewable energy makes it challenging in the realization of energy harvesting transmission schemes. Extensive research studies have been carried out in recent years to address this inherent challenge from several aspects: energy sources and models, energy harvesting and usage protocols, energy scheduling and optimization, implementation of energy harvesting in cooperative, cognitive radio, multiuser and cellular networks, etc. However, there has not been a comprehensive survey to lay out the complete picture of recent advances and future directions. To fill such a gap, in this paper, we present an overview of the past and recent developments in these areas and highlight a number of possible future research avenues. This paper studies online transmission policies for an energy harvesting transmitter. Unlike the existing online policies which more or less require the knowledge on the future behavior of the energy and data arrival processes, we consider a practical but significantly more challenging scenario where the energy and data arrival processes are assumed to be totally unknown. Our design is formulated as a robust-optimal control problem which aims to optimize the worst-case performance. The transmission policy is designed only based on the current battery energy level and the data queue length directly monitored by the transmitter itself. Specifically, we apply an event-trigger approach in which the transmitter continuously monitors the battery energy and data queue length, and triggers an event when a significant change occurs in either of them. Once an event is triggered, the transmission policy is updated by the solution to the robust-optimal control problem. We consider both the transmission time and throughput as the performance metrics and formulated two optimization problems. The solutions are given in either a simple analytical form or an easy-to-implement algorithm. Energy harvesting point-to-point communications are considered. The transmitter harvests energy from the environment and stores it in a finite battery. It is assumed that the transmitter has always data to transmit and the harvested energy is used exclusively for data transmission. As in practical scenarios prior knowledge about the energy harvesting process might not be available, we assume that at each time instant only information about the current state of the transmitter is available, i.e., harvested energy, battery level and channel coefficient. We model the scenario as a Markov decision process and we implement reinforcement learning at the transmitter to find a power allocation policy that aims at maximizing the throughput. To overcome the limitations of traditional reinforcement learning algorithms, we apply the concept of function approximation and we propose a set of binary functions to approximate the expected throughput given the state of the transmitter. Numerical results show that the performance of the proposed approach, which requires only causal knowledge of the energy harvesting process and channel coefficients, has only a small degradation compared to the optimum case which requires perfect non-causal knowledge. Additionally, the proposed approach outperforms naive policies that assume only causal knowledge at the transmitter. Energy harvesting (EH) technology has emerged as a promising energy-supplier to unattended wireless systems. In the commonly used harvest-store-use (HSU) scheme, harvested energy is always stored in a battery before its subsequent use. The existence of storage loss in practical battery systems, however, unavoidably reduces the energy efficiency. In this paper, we therefore propose the use of a more efficient harvest-use-store (HUS) architecture for point-to-point data transmission, where the harvested energy is prioritized for use in data transmission while its balance debt is stored in or extracted from the storage device. We derive the optimal energy polices, under the criterion of throughput maximization, for the HUS architecture on static and block fading channels, and investigate the properties of the resulting power allocation pattern. The optimization is done in the Lagrangian framework, uncovering the special structure of the optimal power pattern and obtaining a closed-form solution conditioned on the knowledge of the block locations for zero battery level. A dynamic programming (DP) based algorithm is developed for locating such blocks in the optimal power patterns. Numerical results are presented to demonstrate the properties of the proposed HUS architecture and its superior performance over the existing schemes. 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 throughput-optimal allocation satisfies are derived, and then the algorithm that finds the optimal transmission policy with respect to the short-term throughput and the minimum transmission completion time is given. Numerical results are presented to confirm the analytical findings. Energy harvesting is a promising solution to prolong the operation time of energy-constrained wireless networks. In particular, scavenging energy from ambient radio signals, namely wireless energy harvesting (WEH), has recently drawn significant attention. In this paper, we consider a point-to-point wireless link over the flat-fading channel, where the receiver has no fixed power supplies and thus needs to replenish energy via WEH from the signals sent by the transmitter. We first consider a SISO (single-input single-output) system where the single-antenna receiver cannot decode information and harvest energy independently from the same signal received. Under this practical constraint, we propose a dynamic power splitting (DPS) scheme, where the received signal is split into two streams with adjustable power levels for information decoding and energy harvesting separately based on the instantaneous channel condition that is assumed to be known at the receiver. We derive the optimal power splitting rule at the receiver to achieve various trade-offs between the maximum ergodic capacity for information transfer and the maximum average harvested energy for power transfer, which are characterized by the boundary of a so-called "rate-energy (R-E)" region. Moreover, for the case when the channel state information is also known at the transmitter, we investigate the joint optimization of transmitter power control and receiver power splitting. The achievable R-E region by the proposed DPS scheme is also compared against that by the existing time switching scheme as well as a performance upper bound by ignoring the practical receiver constraint. Finally, we extend the result for optimal DPS to the SIMO (single-input multiple-output) system where the receiver is equipped with multiple antennas. In particular, we investigate a low-complexity power splitting scheme, namely antenna switching, which achieves the near-optimal rate-energy trade-offs as compared to the optimal DPS. This paper studies the resource allocation algorithm design for secure information and renewable green energy transfer to mobile receivers in distributed antenna communication systems. In particular, distributed remote radio heads (RRHs antennas) are connected to a central processor (CP) via capacity-limited backhaul links to facilitate joint transmission. The RRHs and the CP are equipped with renewable energy harvesters and share their energies via a lossy micropower grid for improving the efficiency in conveying information and green energy to mobile receivers via radio frequency signals. The considered resource allocation algorithm design is formulated as a mixed nonconvex and combinatorial optimization problem taking into account the limited backhaul capacity and the quality-of-service requirements for simultaneous wireless information and power transfer (SWIPT). We aim at minimizing the total network transmit power when only imperfect channel state information of the wireless energy harvesting receivers, which have to be powered by the wireless network, is available at the CP. In light of the intractability of the problem, we reformulate it as an optimization problem with binary selection, which facilitates the design of an iterative resource allocation algorithm to solve the problem optimally using the generalized Bender's decomposition (GBD). Furthermore, a suboptimal algorithm is proposed to strike a balance between computational complexity and system performance. Simulation results illustrate that the proposed GBD-based algorithm obtains the global optimal solution and the suboptimal algorithm achieves a close-to-optimal performance. In addition, the distributed antenna network for SWIPT with renewable energy sharing is shown to require a lower transmit power compared with a traditional system with multiple colocated antennas. We consider the transmission completion time minimization problem in a single-user energy harvesting wireless communication system. In this system, both the data packets and the harvested energy are modelled to arrive at the source node randomly. Our goal is to adaptively change the transmission rate according to the traffic load and available energy, such that the transmission completion time is minimized. Under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. For the data traffic arrivals, we consider two different scenarios. In the first scenario, we assume that all bits have arrived and are ready at the transmitter before the transmission starts. In the second scenario we consider, packets arrive during the transmissions with known arriving times and sizes. We develop optimal off-line scheduling policies which minimize the overall transmission completion time under causality constraints on both data and energy arrivals. Energy harvesting (EH) from ambient radio-frequency (RF) electromagnetic waves is an efficient solution for fully autonomous and sustainable communication networks. Most of the related works presented in the literature are based on specific (and small-scale) network structures, which although give useful insights on the potential benefits of the RF-EH technology, cannot characterize the performance of general networks. In this paper, we adopt a large-scale approach of the RF-EH technology and we characterize the performance of a network with random number of transmitter-receiver pairs by using stochastic-geometry tools. Specifically, we analyze the outage probability performance and the average harvested energy, when receivers employ power splitting (PS) technique for "simultaneous" information and energy transfer. A non-cooperative scheme, where information energy are conveyed only via direct links, is firstly considered and the outage performance of the system as well as the average harvested energy are derived in closed form in function of the power splitting. For this protocol, an interesting optimization problem which minimizes the transmitted power under outage probability and harvesting constraints, is formulated and solved in closed form. In addition, we study a cooperative protocol where sources' transmissions are supported by a random number of potential relays that are randomly distributed into the network. In this case, information energy can be received at each destination via two independent and orthogonal paths (in case of relaying). We characterize both performance metrics, when a selection combining scheme is applied at the receivers and a single relay is randomly selected for cooperative diversity. Wireless networks composed of energy harvesting devices will introduce several transformative changes in wireless networking as we know it: energy self-sufficient, energy self-sustaining, perpetual operation; reduced use of conventional energy and accompanying carbon footprint; untethered mobility; and an ability to deploy wireless networks in hard-to-reach places such as remote rural areas, within structures, and within the human body. Energy harvesting brings new dimensions to the wireless communication problem in the form of intermittency and randomness of available energy, which necessitates a fresh look at wireless communication protocols at the physical, medium access, and networking layers. Scheduling and optimization aspects of energy harvesting communications in the medium access and networking layers have been relatively wellunderstood and surveyed in the recent paper [1]. This branch of literature takes a physical layer rate-power relationship that is valid in energy harvesting conditions under large-enough batteries and long-enough durations between energy harvests so that information-theoretic asymptotes are achieved, and optimizes the transmit power over time in order to maximize the throughput. Another branch of recent literature aims to understand the fundamental capacity limits, i.e. information-theoretic capacities, of energy harvesting links under smaller scale dynamics, considering energy harvests at the channel use level. This branch necessitates a deeper look at the coding and transmission schemes in the physical layer, and ultimately aims to develop an information theory of energy harvesting communications, akin to Shannon's development of an information theory for average power constrained communications. In this introductory article, we survey recent results in this branch and point to open problems that could be of interest to a broad set of researchers in the fields of communication theory, information theory, signal processing, and networking. In particular, we review capacities of energy harvesting links with infinite-sized, finitesized, and no batteries at the transmitter. This paper analyzes the performance of information and energy beamforming in multiple-input multiple- output (MIMO) wireless communications systems, where a self-powered multi-antenna hybrid access point (AP) coordinates wireless information and power transfer (WIPT) with an energy-constrained multi-antenna user terminal (UT). The wirelessly powered UT scavenge energy from the hybrid AP radio-frequency (RF) signal in the downlink (DL) using the harvest-then-transmit protocol, then uses the harvested energy to send its information to the hybrid AP in the uplink (UL). To maximize the overall signal-to-noise ratio (SNR) as well as the harvested energy so as to mitigate the severe effects of fading and enable long-distance wireless power transfer, information and energy beamforming is investigated by steering the transmitted information and energy signals along the strongest eigenmode. To this end, exact and lower-bound expressions for the outage probability and ergodic capacity are presented in closed-form, through which the throughput of the delay- constrained and delay-tolerant transmission modes are analyzed, respectively. Numerical results sustained by Monte Carlo simulations show the exactness and tightness of the proposed analytical expressions. The impact of various parameters such as energy harvesting time, hybrid AP transmit power and the number of antennas on the system throughput is also considered. We consider the optimal packet scheduling problem in a single-user energy harvesting wireless communication system. In this system, both the data packets and the harvested energy are modeled to arrive at the source node randomly. Our goal is to adaptively change the transmission rate according to the traffic load and available energy, such that the time by which all packets are delivered is minimized. Under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. For the data traffic arrivals, we consider two different scenarios. In the first scenario, we assume that all bits have arrived and are ready at the transmitter before the transmission starts. In the second scenario, we consider the case where packets arrive during the transmissions, with known arrival times and sizes. We develop optimal off-line scheduling policies which minimize the time by which all packets are delivered to the destination, under causality constraints on both data and energy arrivals.