Transmission Strategies for Remote Estimation with an Energy Harvesting Sensor

TL;DR

This paper investigates optimal power allocation strategies for remote estimation of correlated signals using energy harvesting sensors, highlighting the importance of signal correlation and proposing practical solutions.

Contribution

It introduces novel power allocation strategies that account for signal correlation in energy harvesting sensor networks, including water-filling solutions and low-complexity policies.

Findings

Balanced power allocation is optimal for static c.w.s.s. signals.

Water-filling type solution is optimal for fading channels.

Low-complexity policies perform close to optimal solutions.

Abstract

We consider the remote estimation of a time-correlated signal using an energy harvesting (EH) sensor. The sensor observes the unknown signal and communicates its observations to a remote fusion center using an amplify-and-forward strategy. We consider the design of optimal power allocation strategies in order to minimize the mean-square error at the fusion center. Contrary to the traditional approaches, the degree of correlation between the signal values constitutes an important aspect of our formulation. We provide the optimal power allocation strategies for a number of illustrative scenarios. We show that the most majorized power allocation strategy, i.e. the power allocation as balanced as possible, is optimal for the cases of circularly wide-sense stationary (c.w.s.s.) signals with a static correlation coefficient, and sampled low-pass c.w.s.s. signals for a static channel. We show that the optimal strategy can be characterized as a water-filling type solution for sampled low-pass c.w.s.s. signals for a fading channel. Motivated by the high-complexity of the numerical solution of the optimization problem, we propose low-complexity policies for the general scenario. Numerical evaluations illustrate the close performance of these low-complexity policies to that of the optimal policies, and demonstrate the effect of the EH constraints and the degree of freedom of the signal.