Infinite Horizon Optimal Transmission Power Control for Remote State Estimation over Fading Channels

TL;DR

This paper investigates optimal transmission power control and remote estimation over fading channels, formulating the problem as a belief-state Markov decision process and deriving properties of the optimal policies.

Contribution

It proves the existence of an optimal stationary policy and characterizes the structure of optimal remote estimates and power control for scalar processes.

Findings

Optimal deterministic stationary policy exists.

Remote estimates depend only on the latest received observation.

Optimal power increases monotonically with innovation error.

Abstract

Jointly optimal transmission power control and remote estimation over an infinite horizon is studied. A sensor observes a dynamic process and sends its observations to a remote estimator over a wireless fading channel characterized by a time-homogeneous Markov chain. The successful transmission probability depends on both the channel gains and the transmission power used by the sensor. The transmission power control rule and the remote estimator should be jointly designed, aiming to minimize an infinite-horizon cost consisting of the power usage and the remote estimation error. A first question one may ask is: Does this joint optimization problem have a solution? We formulate the joint optimization problem as an average cost belief-state Markov decision process and answer the question by proving that there exists an optimal deterministic and stationary policy. We then show that when the monitored dynamic process is scalar, the optimal remote estimates depend only on the most recently received sensor observation, and the optimal transmission power is symmetric and monotonically increasing with respect to the innovation error.