Transmission with Energy Harvesting Nodes in Fading Wireless Channels: Optimal Policies
TL;DR: In this paper, the authors consider a point-to-point data transmission with an energy harvesting transmitter which has a limited battery capacity, communicating in a wireless fading channel, and they consider two objectives: maximizing the throughput by a deadline, and minimizing the transmission completion time of the communication session.
Abstract: 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.
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TL;DR: In this paper, a low-complexity online algorithm is proposed, namely, the Lyapunov optimization-based dynamic computation offloading algorithm, which jointly decides the offloading decision, the CPU-cycle frequencies for mobile execution, and the transmit power for computing offloading.
Abstract: Mobile-edge computing (MEC) is an emerging paradigm to meet the ever-increasing computation demands from mobile applications. By offloading the computationally intensive workloads to the MEC server, the quality of computation experience, e.g., the execution latency, could be greatly improved. Nevertheless, as the on-device battery capacities are limited, computation would be interrupted when the battery energy runs out. To provide satisfactory computation performance as well as achieving green computing, it is of significant importance to seek renewable energy sources to power mobile devices via energy harvesting (EH) technologies. In this paper, we will investigate a green MEC system with EH devices and develop an effective computation offloading strategy. The execution cost , which addresses both the execution latency and task failure, is adopted as the performance metric. A low-complexity online algorithm is proposed, namely, the Lyapunov optimization-based dynamic computation offloading algorithm, which jointly decides the offloading decision, the CPU-cycle frequencies for mobile execution, and the transmit power for computation offloading. A unique advantage of this algorithm is that the decisions depend only on the current system state without requiring distribution information of the computation task request, wireless channel, and EH processes. The implementation of the algorithm only requires to solve a deterministic problem in each time slot, for which the optimal solution can be obtained either in closed form or by bisection search. Moreover, the proposed algorithm is shown to be asymptotically optimal via rigorous analysis. Sample simulation results shall be presented to corroborate the theoretical analysis as well as validate the effectiveness of the proposed algorithm.
1,385 citations
TL;DR: Numerical results show that by optimizing the trajectory of the relay and power allocations adaptive to its induced channel variation, mobile relaying is able to achieve significant throughput gains over the conventional static relaying.
Abstract: In this paper, we consider a novel mobile relaying technique, where the relay nodes are mounted on unmanned aerial vehicles (UAVs) and hence are capable of moving at high speed. Compared with conventional static relaying, mobile relaying offers a new degree of freedom for performance enhancement via careful relay trajectory design. We study the throughput maximization problem in mobile relaying systems by optimizing the source/relay transmit power along with the relay trajectory, subject to practical mobility constraints (on the UAV’s speed and initial/final relay locations), as well as the information-causality constraint at the relay. It is shown that for the fixed relay trajectory, the throughput-optimal source/relay power allocations over time follow a “staircase” water filling structure, with non-increasing and non-decreasing water levels at the source and relay, respectively. On the other hand, with given power allocations, the throughput can be further improved by optimizing the UAV’s trajectory via successive convex optimization. An iterative algorithm is thus proposed to optimize the power allocations and relay trajectory alternately. Furthermore, for the special case with free initial and final relay locations, the jointly optimal power allocation and relay trajectory are derived. Numerical results show that by optimizing the trajectory of the relay and power allocations adaptive to its induced channel variation, mobile relaying is able to achieve significant throughput gains over the conventional static relaying.
1,079 citations
TL;DR: In this article, the authors consider the optimal packet scheduling problem in a single-user EH wireless communication system, where both the data packets and the harvested energy are modeled to arrive at the source node randomly and the 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.
Abstract: 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.
867 citations
TL;DR: The current state of the art for wireless networks composed of energy harvesting nodes, starting from the information-theoretic performance limits to transmission scheduling policies and resource allocation, medium access, and networking issues are provided.
Abstract: This paper summarizes recent contributions in the broad area of energy harvesting wireless communications. In particular, we provide the current state of the art for wireless networks composed of energy harvesting nodes, starting from the information-theoretic performance limits to transmission scheduling policies and resource allocation, medium access, and networking issues. The emerging related area of energy transfer for self-sustaining energy harvesting wireless networks is considered in detail covering both energy cooperation aspects and simultaneous energy and information transfer. Various potential models with energy harvesting nodes at different network scales are reviewed, as well as models for energy consumption at the nodes.
829 citations
TL;DR: If unlimited energy can be stored in the battery with harvested energy and the full SI is available, it is proved the optimality of a water-filling energy allocation solution where the so-called water levels follow a staircase function.
Abstract: We consider the use of energy harvesters, in place of conventional batteries with fixed energy storage, for point-to-point wireless communications. In addition to the challenge of transmitting in a channel with time selective fading, energy harvesters provide a perpetual but unreliable energy source. In this paper, we consider the problem of energy allocation over a finite horizon, taking into account channel conditions and energy sources that are time varying, so as to maximize the throughput. Two types of side information (SI) on the channel conditions and harvested energy are assumed to be available: causal SI (of the past and present slots) or full SI (of the past, present and future slots). We obtain structural results for the optimal energy allocation, via the use of dynamic programming and convex optimization techniques. In particular, if unlimited energy can be stored in the battery with harvested energy and the full SI is available, we prove the optimality of a water-filling energy allocation solution where the so-called water levels follow a staircase function.
726 citations
References
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TL;DR: The Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone is obtained, analogous to water-pouring in frequency for time-invariant frequency-selective fading channels.
Abstract: We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "water-pouring" in time, analogous to water-pouring in frequency for time-invariant frequency-selective fading channels. Inverting the channel results in a large capacity penalty in severe fading.
2,163 citations
TL;DR: In this article, the authors consider the optimal packet scheduling problem in a single-user EH wireless communication system, where both the data packets and the harvested energy are modeled to arrive at the source node randomly and the 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.
Abstract: 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.
867 citations
TL;DR: This work considers transmission policies for rechargeable nodes with energy harvesting battery equipped nodes, and optimum solutions for two related problems are identified, including the transmission policy that maximizes the short term throughput.
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, ie, 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, ie, energy replenishment process, as well as the energy storage, ie, 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
784 citations
TL;DR: A greedy policy is identified which, in low SNR regime, is throughput optimal and also minimizes mean delay and two energy management policies which minimize the mean delay in the queue are obtained.
Abstract: We study a sensor node with an energy harvesting source. The generated energy can be stored in a buffer. The sensor node periodically senses a random field and generates a packet. These packets are stored in a queue and transmitted using the energy available at that time. We obtain energy management policies that are throughput optimal, i.e., the data queue stays stable for the largest possible data rate. Next we obtain energy management policies which minimize the mean delay in the queue. We also compare performance of several easily implementable sub-optimal energy management policies. A greedy policy is identified which, in low SNR regime, is throughput optimal and also minimizes mean delay.
707 citations