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Status Updating via Integrated Sensing and Communication: Freshness Optimisation

Touraj Soleymani, Mohamad Assaad, John S. Baras

TL;DR

The paper addresses coordinating sensing and communication in ISAC to maintain timely situational awareness for a remote source, quantified by the Age of Information (AoI). It models the problem as a discounted infinite-horizon MDP with state $S=( abla^s, abla^b)$ and stage cost $g(S_k,u_k)$ that couples AoI with action costs. The key contribution is proving the optimal policy exhibits a monotone threshold structure defined by a nondecreasing switching curve $ au( abla^b)$, derived from submodularity and single-crossing properties, and corroborated by numerical results showing a stable, interpretable decision boundary. These results demonstrate that freshness objectives can be naturally and efficiently integrated into ISAC design, yielding practical scheduling rules for real-time remote navigation systems.

Abstract

This paper studies strategic design in an integrated sensing and communication (ISAC) architecture for status updating of remotely navigating agents. We consider an ISAC-enabled base station that can sense the state of a remote source and communicate this information back to the source. Both sensing and communication succeed with given probabilities and incur distinct costs. The objective is to optimise a long-term cost that captures information freshness, measured by the age of information (AoI), at the source together with sensing and communication overheads. The resulting sequential decision problem is formulated as a discounted infinite-horizon Markov decision process with a two-dimensional AoI state, representing information freshness at the source and at the base station. We prove that the optimal stationary policy admits a monotone threshold structure characterised by a nondecreasing switching curve in the AoI state space. Our numerical analysis illustrates the structures of the value function and the optimal decision map. These results demonstrate that freshness-based objectives can be naturally integrated into ISAC design, while yielding interpretable and implementable strategies.

Status Updating via Integrated Sensing and Communication: Freshness Optimisation

TL;DR

The paper addresses coordinating sensing and communication in ISAC to maintain timely situational awareness for a remote source, quantified by the Age of Information (AoI). It models the problem as a discounted infinite-horizon MDP with state and stage cost that couples AoI with action costs. The key contribution is proving the optimal policy exhibits a monotone threshold structure defined by a nondecreasing switching curve , derived from submodularity and single-crossing properties, and corroborated by numerical results showing a stable, interpretable decision boundary. These results demonstrate that freshness objectives can be naturally and efficiently integrated into ISAC design, yielding practical scheduling rules for real-time remote navigation systems.

Abstract

This paper studies strategic design in an integrated sensing and communication (ISAC) architecture for status updating of remotely navigating agents. We consider an ISAC-enabled base station that can sense the state of a remote source and communicate this information back to the source. Both sensing and communication succeed with given probabilities and incur distinct costs. The objective is to optimise a long-term cost that captures information freshness, measured by the age of information (AoI), at the source together with sensing and communication overheads. The resulting sequential decision problem is formulated as a discounted infinite-horizon Markov decision process with a two-dimensional AoI state, representing information freshness at the source and at the base station. We prove that the optimal stationary policy admits a monotone threshold structure characterised by a nondecreasing switching curve in the AoI state space. Our numerical analysis illustrates the structures of the value function and the optimal decision map. These results demonstrate that freshness-based objectives can be naturally integrated into ISAC design, while yielding interpretable and implementable strategies.
Paper Structure (18 sections, 7 theorems, 23 equations, 3 figures)

This paper contains 18 sections, 7 theorems, 23 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Semantics of Information
  4. Integrated Sensing and Communication
  5. Contributions and Outline
  6. Notation
  7. Problem Formulation
  8. System Model
  9. Freshness Metric
  10. Performance Criterion and Optimisation Problem
  11. Main Results and Derivation
  12. Evolution of the Freshness Metric
  13. Operator-Level Structural Properties
  14. Single-Crossing Property of the Action Difference
  15. Submodularity Preservation
  16. ...and 3 more sections

Key Result

Theorem 1

The problem in (eq:objective) admits an optimal stationary deterministic policy $\pi^\star: S \to \{\mathop{\mathrm{\mathsf{sense}}}\nolimits,\mathop{\mathrm{\mathsf{comm}}}\nolimits\}$ with a monotone switching structure. Specifically, there exists a nondecreasing integer-valued function $\tau: \ma for all $(\alpha^s, \alpha^b) \in S$, where the function $\tau(\alpha_b)$ is nondecreasing in $\alp

Figures (3)

  • Figure 1: Illustration of an unmanned ground vehicle leveraging ISAC support from a base station to enhance situational awareness when onboard sensing is limited.
  • Figure 2: Value function as a function of the source and base-station AoIs. The value function is increasing in both coordinates and exhibits a structured surface induced by the monotone optimal policy.
  • Figure 3: Optimal ISAC switching decision map as a function of the source and base-station AoIs. The boundary separating sensing and communication actions follows a monotone switching curve, consistent with the theoretical results.

Theorems & Definitions (7)

  • Theorem 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Lemma 6