Remote State Estimation over a Wearing Channel: Information Freshness vs. Channel Aging

We study the remote estimation of a linear Gaussian system over a channel that wears out over time and with every use. The sensor can either transmit a fresh measurement in the current time slot, restore the channel quality at the cost of downtime, or remain silent. Frequent transmissions yield accurate estimates but incur significant wear on the channel. Renewing the channel too often improves channel conditions but results in poor estimation quality. What is the optimal timing to transmit measurements and restore the channel? This problem is formulated as a semi-Markov decision process (SMDP). We establish monotonicity properties of the optimal policy and propose structure-aware solution methods.