Optimal Communication Scheduling and Remote Estimation over an Additive Noise Channel

TL;DR

This paper develops optimal sensor scheduling and remote estimation strategies over a noisy additive channel, revealing surprising phase transition phenomena in transmission usage under power constraints.

Contribution

It introduces a framework for optimal encoding, scheduling, and estimation over noisy channels, extending prior noiseless models with new analytical insights.

Findings

Optimal policies derived for noisy channels

Identification of phase transition in transmission opportunities

Numerical analysis demonstrating impact of noise on scheduling

Abstract

This paper considers a sequential sensor scheduling and remote estimation problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process and makes a decision as to whether or not to send this measurement to the estimator. The sensor and the estimator have the common objective of minimizing expected distortion in the estimation of the state of the process, over a finite time horizon. The sensor is either charged a cost for each transmission or constrained on transmission times. As opposed to the prior work where communication between the sensor and the estimator was assumed to be perfect (noiseless), in this work an additive noise channel with fixed power constraint is considered; hence, the sensor has to encode its message before transmission. Under some technical assumptions, we obtain the optimal encoding and estimation policies in conjunction with the optimal transmission schedule. The impact of the presence of a noisy channel is analyzed numerically based on dynamic programming. This analysis yields some rather surprising results such as a phase transition phenomenon in the number of used transmission opportunities, which was not encountered in the noiseless communication setting.