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Age of Information Optimization for Status Updates in Integrated Sensing and Communication Systems

This paper investigates Age of Information (AoI) optimization in Integrated Sensing and Communication (ISAC) systems by formulating the single-source scenario as a Markov decision process with a proven threshold-based optimal policy and the multi-source scenario as a restless multi-armed bandit problem, for which both exact and approximate Whittle index policies are developed to minimize a discounted cost combining AoI and operational expenses.

Original authors: Marco Zanni, Mohamad Assaad, Touraj Soleymani

Published 2026-05-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Marco Zanni, Mohamad Assaad, Touraj Soleymani

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a high-tech control room where a remote operator needs to keep an eye on a busy factory floor or a self-driving car navigating a city. The operator can't see everything directly; they rely on a central "hub" (the Base Station) to gather information and send it back.

The problem this paper tackles is about timing. In the world of real-time data, information gets "stale" the moment it's created. If you receive a report about a robot's position that is five seconds old, it might be useless if the robot has already moved. The paper uses a metric called Age of Information (AoI) to measure this staleness. Think of AoI as a "freshness timer" that ticks up every second until a new update arrives. The goal is to keep this timer as low as possible.

However, the hub has a tricky job. It has three ways to operate, each with a different cost and success rate:

Sensing: The hub looks at the factory/car to get new data. (Like a security guard checking the scene).
Communicating: The hub sends old data it already has to the remote operator. (Like a messenger running a note to the boss).
Joint Action: The hub does both at once—looks at the scene and sends the previous note simultaneously. (Like a guard checking the scene while shouting the previous update to the boss).

The catch? None of these actions are guaranteed to work (signals can drop), and they all cost energy or money. The hub needs a smart strategy to decide which action to take at every moment to keep the operator's information as fresh as possible without wasting resources.

The Single Source Story: The "Traffic Light" Strategy

First, the authors looked at a simple scenario with just one factory and one operator. They modeled this as a game where the hub makes decisions based on two numbers:

How old is the data at the operator's end?
How old is the data at the hub's end?

They discovered that the best strategy isn't random; it follows a very neat, predictable pattern called a "Threshold Structure."

Imagine the state of the system as a map with two axes. The optimal strategy acts like a set of traffic lights on this map:

Zone 1 (Low Freshness at Operator): If the operator's data is very fresh, the hub should just Sense (look for new info) to keep its own records up to date.
Zone 2 (Medium Freshness): If the operator's data is getting a bit old, but the hub still has fresh info, the hub should do the Joint Action (send the old info while grabbing new info).
Zone 3 (High Freshness at Operator): If the operator's data is very stale, the hub should stop looking for new info and just Communicate (rush the best available data to the operator).

The paper proves mathematically that you never jump back and forth between these zones randomly. As the data gets older, you move smoothly from Sensing → Joint → Communicating. They also figured out exactly how much of the "map" you need to calculate to get a perfect answer, saving a lot of computer power.

The Multi-Source Story: The "Traffic Cop" with Many Lanes

Next, they made it harder. Imagine one hub trying to manage many factories or cars at once, but it can only talk to a few of them at any given second. This is like a traffic cop trying to direct cars on a busy highway with only a few hands to wave.

This is a classic "Restless Multi-Armed Bandit" problem (a fancy name for a game where you have to pick the best options from a group of things that keep changing even when you aren't watching them).

To solve this, the authors developed a Whittle Index Policy.

The Analogy: Imagine every factory has a "Priority Score" (an index). This score tells the hub how urgent it is to talk to that specific factory right now.
The Strategy: The hub simply looks at the scores of all factories, picks the top $M$ (the ones it can handle), and talks to them. It ignores the rest for that moment.

The paper does two things here:

The Exact Method: They found a rule to calculate these scores perfectly, but only if the system behaves in a certain predictable way (a condition called "indexability").
The Approximate Method: They realized that sometimes the system is too messy for the perfect rule. So, they created a "smart guess" method. They calculate the scores for a few key "anchor" points and then fill in the gaps using a straight line (linear interpolation).

The Results

The authors ran computer simulations to test their ideas:

For the single source: The simulations confirmed the "traffic light" zones. When the operator is hungry for info, the hub rushes to send data. When the operator is fine, the hub takes a moment to gather fresh data.
For multiple sources: Their "smart guess" (Approximate Whittle Index) worked almost as well as the perfect method when the perfect method was possible. Even more impressively, when the system was too messy for the perfect method to exist, their "smart guess" still performed much better than random guessing or simple greedy rules (like just picking the oldest data).

In Summary

This paper provides a rulebook for a central hub that needs to manage the flow of information between a physical world and a remote monitor. It proves that the best way to do this is to follow clear "thresholds" (switching actions based on how stale the data is) and offers a highly efficient, low-complexity way to manage many sources at once using a priority scoring system that works even when the math gets complicated.

Technical Summary: Age of Information Optimization for Status Updates in Integrated Sensing and Communication Systems

Problem Formulation
This paper addresses the optimization of Age of Information (AoI) in Integrated Sensing and Communication (ISAC) systems designed for real-time remote monitoring. The system architecture consists of a physical process (source), an ISAC-enabled base station, and a remote monitor. The monitor cannot directly observe the physical process and relies entirely on the base station to acquire and transmit status updates.

The core challenge lies in the base station's decision-making process at each discrete time slot. The base station must choose between three operational modes, each with distinct costs and success probabilities:

Sensing: Acquiring fresh information about the physical process from the source.
Communication: Transmitting previously acquired information to the remote monitor.
Joint Sensing and Communication: Simultaneously acquiring fresh information and transmitting previously acquired data.

All operations are subject to unreliable channels (lossy transmission). The objective is to minimize a discounted infinite-horizon cost function that balances the AoI at the remote monitor against the operational costs of the selected actions. The problem is modeled as a Markov Decision Process (MDP) where the state is defined by the pair of AoIs: the AoI at the monitor and the AoI at the base station.

Methodology
The authors approach the problem in two distinct scenarios: single source-monitor pairs and multiple source-monitor pairs.

Single-Source Scenario: The problem is formulated as a two-dimensional MDP. The authors analyze the structural properties of the optimal stationary policy. Unlike standard AoI problems that rely on submodularity, this paper establishes the policy structure through monotonicity and concavity properties of the Bellman operator and bounds on directional increments of the value function. To handle the infinite state space, the authors propose truncating the state space and derive a rigorous, closed-form bound on the approximation error induced by this truncation.
Multi-Source Scenario: The scheduling problem for multiple independent sources sharing a single base station is modeled as a Restless Multi-Armed Bandit (RMAB). The authors employ Lagrangian relaxation to decouple the global problem into independent single-arm problems. They investigate the indexability of the system to derive Whittle index policies.
- Exact Policy: A sufficient condition for indexability is provided, allowing for the computation of exact Whittle indices via a bisection method.
- Approximate Policy: Recognizing that the indexability condition may not hold for all parameters and that exact computation is computationally intensive, the authors develop an approximate Whittle index policy. This heuristic uses linear interpolation of index values computed on anchor states (diagonal and boundary states) to estimate indices for the entire state space.

Key Contributions

Structural Characterization: For the single-source case, the paper proves that the optimal policy admits an ordered switching-threshold structure in the AoI state space. Specifically, for a fixed base station AoI, the optimal action transitions in the order: Sensing $\to$ Joint Sensing/Communication $\to$ Communication, governed by two switching thresholds.
Truncation Error Analysis: The authors provide a theoretical analysis to bound the error resulting from truncating the infinite state space, offering a closed-form criterion for selecting the truncation level to meet a specific error tolerance.
Whittle Index Formulation: For the multi-source case, the paper formulates the scheduling problem as an RMAB and derives a sufficient condition for indexability. It defines the exact Whittle index policy for the indexable regime.
Approximate Index Policy: The paper introduces a computationally efficient approximate Whittle index policy based on linear interpolation. This policy is designed to function effectively even in regimes where the strict indexability condition is not satisfied.
Numerical Validation: Extensive numerical results are presented to illustrate the threshold geometry of the optimal single-source policy and to demonstrate the performance of the proposed policies in multi-source settings.

Results

Single-Source: Numerical results confirm the theoretical threshold structure. The optimal policy prioritizes sensing when the monitor and base station have comparable freshness, switches to joint operations in intermediate regions, and prioritizes communication when the monitor's AoI becomes significantly large.
Multi-Source (Indexable Regime): In scenarios where the indexability condition holds, the proposed Approximate Whittle Index Policy (AWIP) performs comparably to the exact Whittle Index Policy (WIP) and significantly outperforms random and greedy baselines. The AWIP achieves performance nearly identical to the globally optimal policy in small-scale instances while offering substantial reductions in offline computation time (up to 86.7% savings in the tested scenarios).
Multi-Source (Non-Indexable Regime): When the sufficient condition for indexability is violated, the AWIP remains effective, outperforming random and greedy policies, suggesting its utility extends beyond the theoretically guaranteed indexable regime.

Significance and Claims
The paper claims to advance the understanding of scheduling in ISAC systems by shifting focus from physical-layer metrics (e.g., waveform design) to the decision and scheduling layer. It highlights that the introduction of a joint sensing-and-communication action fundamentally alters the problem geometry, rendering standard submodularity approaches inapplicable and necessitating the novel structural analysis provided.

The significance of the work lies in providing a tractable framework for optimizing freshness in ISAC systems where information acquisition and delivery are coupled. The proposed approximate Whittle index policy is presented as a practical solution that balances computational complexity with performance, offering a robust scheduling rule for both indexable and non-indexable parameter regimes. The paper does not claim global optimality for the multi-source case in general but demonstrates that the proposed heuristics are asymptotically optimal in specific settings and empirically effective in others.

The Single Source Story: The "Traffic Light" Strategy

The Multi-Source Story: The "Traffic Cop" with Many Lanes

The Results

In Summary

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