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

TL;DR

The paper studies remote state estimation over a wearing channel whose reliability degrades with channel age and usage. It models the problem as an average-cost MDP with two coupled age processes, AoI and AoC, and proves the existence of a deterministic optimal policy; it further shows the optimal policy is AoC-monotone and develops a structured policy-iteration algorithm to compute it efficiently. Numerical results demonstrate monotonicity properties and illustrate how thresholds adapt to system parameters such as process instability and renewal duration, highlighting the trade-off between information freshness and channel wear. The work provides a principled framework for scheduling transmissions and channel renewals in nonstationary networks, with potential impact on networked control, wireless sensing, and quantum/brain-inspired communication contexts.

Abstract

We study the remote estimation of a linear Gaussian system over a nonstationary 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. More 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? We formulate the problem as a Markov decision process (MDP) and show the monotonicity properties of an optimal policy. A structured policy iteration algorithm is proposed to find the optimal policy.

Figures (6)

• Figure 1: The remote estimation system with a wearing channel.
• Figure 2: An illustration of different timelines and the evolution of the age processes, where 'I', 'T', and 'R' stand for idle, transmit, and renewal actions, respectively. The sensor triggers a transmission at the $2$th slot and renews the channel at the $3$th slot. The sensor must remain silent during the renewal period. Consequently, both the AoC and AoI continue to increase. Since data transmission takes one slot, the AoI resets to $1$ at slot $3$.
• Figure 3: State transitions induced by the transmit-always policy $\tilde{\pi}$.
• Figure 4: The threshold structure of the optimal policy $\pi^*(\tau,\delta)$ with fixed $\delta$.
• Figure 5: The structure of the optimal policy under different values of $\beta$ when $\alpha=0.1, \tau_\textrm{D}=6, \delta_\textrm{R}=15$. (a) $\beta=0.9$, the system is always stable; (b) $\beta=1.0$, the system becomes unstable with large AoC; and (c) $\beta=1.1$, the system might be unstable even with moderate AoC.

Theorems & Definitions (19)

• Lemma 1: Leong2017TAC
• Remark 1
• Definition 1: Mean-square stability
• Remark 2
• Remark 3
• Lemma 2
• Lemma 3
• Theorem 1
• proof
• Proposition 1