On Remote Estimation with Multiple Communication Channels

TL;DR

This paper investigates remote estimation with two different communication channels, proposing a threshold-in-threshold policy and analyzing its optimality and performance through numerical methods.

Contribution

It introduces a new optimal scheduling policy for remote estimation with multiple channels, including a side channel for sign information, extending classical single-channel results.

Findings

Symmetric threshold policies are not always optimal in multi-channel settings.

A threshold-in-threshold policy is shown to be optimal under certain conditions.

Numerical analysis reveals that not all noisy channel opportunities are utilized.

Abstract

This paper considers a sequential sensor scheduling and remote estimation problem with multiple communication channels. Departing from the classical remote estimation paradigm, which involves one communication channel (noiseless or noisy), we consider here the more realistic setting of two channels with different characteristics (one is cheap but noisy, the other one is costly but noiseless). We first show, via a counter-example, that the common folklore of applying symmetric threshold-based policy, which is well known to be optimal (for unimodal state densities) in the classical remote estimation problem, can no longer be optimal in our setting. In view of that, and in order to make the problem tractable, we introduce a side channel which signals to the receiver the sign of the underlying state. We show, under some technical assumptions, that a threshold-in-threshold based communication scheduling is optimal. The impact of the results is analyzed numerically based on dynamic programming. This numerical analysis reveals some rather surprising results inheriting known properties from the single channel settings, such as not exhausting all the opportunities available for the noisy channel.