This paper investigates the offline packet-delay-minimization problem for an energy harvesting transmitter. To overcome the non-convexity of the problem, we propose a C2-diffeomorphic transformation and provide the necessary and sufficient condition for the transformed problem to a standard convex optimization problem. Based on this condition, a simple choice of the transformation is determined which allows an analytically tractable solution of the original non-convex problem to be easily obtained once the transformed convex problem is solved. We further study the structure of the optimal transmission policy in a special case and find it to follow a weighted-directional-water-filling structure. In particular, the optimal policy tends to allocate more power in earlier time slots and less power in later time slots. Our analytical insight is verified by simulation results.
Energy harvesting is recognized as a key enabling technology for self-sustainable communication networks. It also brings in significant and necessary changes in the design of the communication protocol when energy harvesting becomes the main or sole source of energy supply for the communication nodes @cite_1 @cite_13 @cite_14 . By focusing on the design of an energy harvesting transmitter, the existing studies can be categorized into offline and online scenarios. For offline scenarios, all future information (such as the energy arrival process, data arrival process and channel fading process) is assumed to be predictable or completely deterministic. Hence, the transmission policy is designed offline by using the available knowledge about the future. For online scenarios, although the exact future behaviors of the energy arrival, data arrival and channel fading processes are not known, the existing literature have considered different levels of statistical knowledge: the statistics of the processes in the future are exactly known (e.g., @cite_16 ), partly known (e.g., @cite_3 ) or completely unknown (e.g., @cite_11 ).
@cite_14 @cite_1 @cite_3 @cite_16 @cite_13 @cite_11
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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. From being a scientific curiosity only a few years ago, energy harvesting (EH) is well on its way to becoming a game-changing technology in the field of autonomous wireless networked systems. The promise of long-term, uninterrupted and self-sustainable operation in a diverse array of applications has captured the interest of academia and industry alike. Yet the road to the ultimate network of perpetual communicating devices is plagued with potholes: ambient energy is intermittent and scarce, energy storage capacity is limited, and devices are constrained in size and complexity. In dealing with these challenges, this article will cover recent developments in the design of intelligent energy management policies for EH wireless devices and discuss pressing research questions in this rapidly growing field. A point-to-point wireless communication system in which the transmitter is equipped with an energy harvesting device and a rechargeable battery, is studied. Both the energy and the data arrivals at the transmitter are modeled as Markov processes. Delay-limited communication is considered assuming that the underlying channel is block fading with memory, and the instantaneous channel state information is available at both the transmitter and the receiver. The expected total transmitted data during the transmitter's activation time is maximized under three different sets of assumptions regarding the information available at the transmitter about the underlying stochastic processes. A learning theoretic approach is introduced, which does not assume any a priori information on the Markov processes governing the communication system. In addition, online and offline optimization problems are studied for the same setting. Full statistical knowledge and causal information on the realizations of the underlying stochastic processes are assumed in the online optimization problem, while the offline optimization problem assumes non-causal knowledge of the realizations in advance. Comparing the optimal solutions in all three frameworks, the performance loss due to the lack of the transmitter's information regarding the behaviors of the underlying Markov processes is quantified. 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. 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. 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.