Age Minimization in Energy Harvesting Communications: Energy-Controlled Delays

We consider an energy harvesting source that is collecting measurements from a physical phenomenon and sending updates to a destination within a communication session time. Updates incur transmission delays that are function of the energy used in their transmission. The more transmission energy used per update, the faster it reaches the destination. The goal is to transmit updates in a timely manner, namely, such that the total age of information is minimized by the end of the communication session, subject to energy causality constraints. We consider two variations of this problem. In the first setting, the source controls the number of measurement updates, their transmission times, and the amounts of energy used in their transmission (which govern their delays, or service times, incurred). In the second setting, measurement updates externally arrive over time, and therefore the number of updates becomes fixed, at the expense of adding data causality constraints to the problem. We characterize age-minimal policies in the two settings, and discuss the relationship of the age of information metric to other metrics used in the energy harvesting literature.Comment: Appeared in Asilomar 201

Energy Management Policies for Energy-Neutral Source-Channel Coding

In cyber-physical systems where sensors measure the temporal evolution of a given phenomenon of interest and radio communication takes place over short distances, the energy spent for source acquisition and compression may be comparable with that used for transmission. Additionally, in order to avoid limited lifetime issues, sensors may be powered via energy harvesting and thus collect all the energy they need from the environment. This work addresses the problem of energy allocation over source acquisition/compression and transmission for energy-harvesting sensors. At first, focusing on a single-sensor, energy management policies are identified that guarantee a maximal average distortion while at the same time ensuring the stability of the queue connecting source and channel encoders. It is shown that the identified class of policies is optimal in the sense that it stabilizes the queue whenever this is feasible by any other technique that satisfies the same average distortion constraint. Moreover, this class of policies performs an independent resource optimization for the source and channel encoders. Analog transmission techniques as well as suboptimal strategies that do not use the energy buffer (battery) or use it only for adapting either source or channel encoder energy allocation are also studied for performance comparison. The problem of optimizing the desired trade-off between average distortion and delay is then formulated and solved via dynamic programming tools. Finally, a system with multiple sensors is considered and time-division scheduling strategies are derived that are able to maintain the stability of all data queues and to meet the average distortion constraints at all sensors whenever it is feasible.Comment: Submitted to IEEE Transactions on Communications in March 2011; last update in July 201

Age-Minimal Transmission in Energy Harvesting Two-hop Networks

We consider an energy harvesting two-hop network where a source is communicating to a destination through a relay. During a given communication session time, the source collects measurement updates from a physical phenomenon and sends them to the relay, which then forwards them to the destination. The objective is to send these updates to the destination as timely as possible; namely, such that the total age of information is minimized by the end of the communication session, subject to energy causality constraints at the source and the relay, and data causality constraints at the relay. Both the source and the relay use fixed, yet possibly different, transmission rates. Hence, each update packet incurs fixed non-zero transmission delays. We first solve the single-hop version of this problem, and then show that the two-hop problem is solved by treating the source and relay nodes as one combined node, with some parameter transformations, and solving a single-hop problem between that combined node and the destination.Comment: Appeared in IEEE Globecom 201

Optimal Energy Management Policies for Energy Harvesting Sensor Nodes

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.Comment: Submitted to the IEEE Transactions on Wireless Communications; 22 pages with 10 figure

Source-Channel Coding under Energy, Delay and Buffer Constraints

Source-channel coding for an energy limited wireless sensor node is investigated. The sensor node observes independent Gaussian source samples with variances changing over time slots and transmits to a destination over a flat fading channel. The fading is constant during each time slot. The compressed samples are stored in a finite size data buffer and need to be delivered in at most $d$ time slots. The objective is to design optimal transmission policies, namely, optimal power and distortion allocation, over the time slots such that the average distortion at destination is minimized. In particular, optimal transmission policies with various energy constraints are studied. First, a battery operated system in which sensor node has a finite amount of energy at the beginning of transmission is investigated. Then, the impact of energy harvesting, energy cost of processing and sampling are considered. For each energy constraint, a convex optimization problem is formulated, and the properties of optimal transmission policies are identified. For the strict delay case, $d=1$, $2D$ waterfilling interpretation is provided. Numerical results are presented to illustrate the structure of the optimal transmission policy, to analyze the effect of delay constraints, data buffer size, energy harvesting, processing and sampling costs.Comment: 30 pages, 15 figures. Submitted to IEEE Transactions on Wireless Communication