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Network-Wide PAoI Guarantee in CF-mMIMO Networks with S&C Coexistence: A Unified Framework for Spatial Partitioning Toward xURLLC

This paper proposes a unified analytical framework combining stochastic geometry and stochastic network calculus to derive a tractable upper bound on peak age of information violation probability, enabling the optimization of access point partitioning between sensing and communication roles in cell-free massive MIMO networks to guarantee network-wide information freshness for xURLLC applications.

Original authors: Yanxi Zhang, Mingwu Yao, Qinghai Yang, Muyu Mei

Published 2026-04-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yanxi Zhang, Mingwu Yao, Qinghai Yang, Muyu Mei

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 futuristic city where every streetlamp, traffic light, and building sensor is also a super-smart Wi-Fi router. This is the world of 6G, and specifically, a technology called Cell-Free Massive MIMO.

In this paper, the authors tackle a tricky problem: How do you make sure this network is both "seeing" the world perfectly and "talking" to your devices instantly?

Here is the breakdown using simple analogies.

1. The Setting: The "Swiss Army Knife" Network

Imagine a massive team of workers (Access Points or APs) scattered all over a city. In the past, these workers were divided into two separate teams:

The Lookouts (Sensing): They scan the environment to find cars, people, or obstacles.
The Messengers (Communication): They carry data packets (like video calls or emergency alerts) to users.

In this new 6G world, every worker is a Swiss Army Knife. They can do both jobs. But here's the catch: They can't do both at the exact same time with full power. If a worker spends all day looking around, they can't carry many messages. If they spend all day carrying messages, they stop looking.

2. The Problem: The "Freshness" Dilemma

The goal is xURLLC (Ultra-Reliable, Low-Latency Communication). Think of this as a self-driving car that needs to know right now if a pedestrian is stepping off the curb.

Age of Information (AoI): This is a measure of how "stale" the information is. If the car sees a pedestrian 5 seconds ago, that info is "stale." If it sees them 0.1 seconds ago, it's "fresh."
The Peak Age (PAoI): This is the worst-case scenario. How long could it possibly take for the car to get the freshest update?

The authors want to guarantee that this "worst-case" time never gets too long.

3. The Conflict: The "Tug-of-War"

The network has a fixed number of workers. The big question is: How many should be Lookouts, and how many should be Messengers?

More Lookouts: You get updates faster (the pedestrian is spotted sooner). But, you have fewer Messengers to deliver that news, so the message gets stuck in traffic.
More Messengers: You can deliver news incredibly fast. But, you have fewer Lookouts, so you might not spot the pedestrian for a long time.

If you go 100% Lookouts, you see everything but can't tell anyone. If you go 100% Messengers, you have a super-fast delivery service, but you have no news to deliver.

4. The Solution: A "Mathematical Crystal Ball"

The authors created a Unified Framework (a fancy math model) to solve this tug-of-war without having to build the whole network and test it a million times.

They used two main tools:

Stochastic Geometry: Imagine the workers and users are raindrops falling randomly on a floor. This math helps predict how crowded the floor is and how likely a drop is to hit a target, even with random placement.
Stochastic Network Calculus (SNC): This is like a traffic simulator that predicts the worst-case traffic jams, accounting for bad weather (channel noise) and short, urgent messages (short packets).

The Magic Formula:
They combined these tools to create a "Safety Bound." It's a mathematical guarantee that says: "No matter how the workers are scattered or how the weather changes, if we split the team this way, the information will never be older than X seconds."

5. The Discovery: The "Sweet Spot"

By running their math model, they found the Perfect Split (Optimal Partition).

If the deadline is super tight (e.g., a robot surgery happening now): The model says, "Put more workers on Sensing." You need to find the problem immediately, even if it takes a tiny bit longer to deliver the message.
If the deadline is slightly relaxed (e.g., a factory robot moving a box): The model says, "Put more workers on Communication." You can wait a split second to find the object, but you need to move the data super fast once you find it.

They also found that if the "targets" are easier to see (like a shiny car vs. a dark bush), you can afford to have fewer Lookouts and more Messengers.

6. Why This Matters

Before this paper, network planners had to guess or run expensive, slow computer simulations to figure out how to split their resources.

This paper gives them a low-complexity calculator. Instead of guessing, they can plug in their city size, how many users they have, and how fast they need to react, and the formula tells them exactly how many workers should be Lookouts and how many should be Messengers to keep the network "fresh" and safe.

In a nutshell: It's a recipe for balancing the eyes and the voice of a 6G network so that critical information is never too old to be useful.

1. Problem Statement

The paper addresses the challenge of ensuring information freshness in next-generation xURLLC (extreme Ultra-Reliable Low-Latency Communication) applications (e.g., autonomous driving, remote surgery) within Cell-Free Massive MIMO (CF-mMIMO) networks.

Core Conflict: In these networks, Access Points (APs) must serve dual roles: Sensing (detecting targets to generate updates) and Communication (delivering those updates to users).
The Trade-off: Allocating more APs to sensing improves the rate of update generation but reduces the resources available for reliable, low-latency packet delivery. Conversely, allocating more APs to communication improves delivery reliability but slows down the generation of new updates.
The Metric: Traditional metrics like latency are insufficient. The paper focuses on the Peak Age of Information (PAoI), which measures the worst-case data staleness. The goal is to minimize the PAoI Violation Probability (PAVP)—the probability that the PAoI exceeds a strict threshold $\zeta$ .
The Gap: Existing literature lacks a unified analytical framework that accounts for the spatial randomness of APs and users, imperfect Channel State Information (CSI), Finite Blocklength Coding (FBC), and the coupled dynamics of sensing-driven arrivals and communication-limited service in large-scale distributed networks.

2. Methodology

The authors propose a unified analytical framework combining Stochastic Geometry and Stochastic Network Calculus (SNC) to derive a tractable upper bound on the network-wide PAVP.

A. System Model

Network Topology: APs and users are distributed as independent Poisson Point Processes (PPPs).
Spatial Partitioning: A parameter $\beta \in [0, 1]$ determines the fraction of APs dedicated to communication ( $\lambda_c = \beta\lambda$ ), while the rest are dedicated to sensing ( $\lambda_s = (1-\beta)\lambda$ ).
Sensing Subsystem: APs act as monostatic radars. A "sensing event" occurs if at least one AP detects a target within range and beamwidth, triggering a short packet generation.
Communication Subsystem:
- Uses TDD with uplink pilot training (subject to pilot contamination) and downlink data transmission.
- Employs Conjugate Beamforming with LMMSE channel estimation.
- Utilizes Finite Blocklength Coding (FBC) to model short-packet transmission rates and decoding error probabilities (DEP).
- Includes ARQ retransmissions to meet xURLLC reliability requirements.

B. Analytical Framework (SNC)

The system is modeled as a First-Come-First-Served (FCFS) queuing system.

Derivation of MGFs: The authors derive the Moment Generating Functions (MGFs) for:
- Inter-arrival times ( $T_A$ ): Based on the network sensing coverage probability ( $P_{cv}^s$ ) derived via stochastic geometry.
- Service times ( $T_S$ ): Based on the communication coverage probability ( $P_{cv}^c$ ) and the FBC retransmission process.
PAVP Bound: Using SNC, they apply a Chernoff bound to the MGFs of inter-arrival and service times to derive a closed-form upper bound on the PAVP.
Optimization: The derived bound is minimized with respect to the partitioning factor $\beta$ to find the optimal resource allocation ( $\beta^*$ ) that minimizes information staleness.

3. Key Contributions

Unified Framework: Established the first tractable analytical framework for network-wide PAoI in large-scale CF-mMIMO networks with S&C coexistence, integrating stochastic geometry (spatial randomness) and SNC (queuing dynamics).
Tractable Bounds:
- Derived a closed-form expression for network sensing coverage probability considering random AP orientation and bounded path loss.
- Derived a lower bound for communication coverage probability in the presence of pilot contamination and imperfect CSI.
- Combined these to formulate a tractable upper bound on the network-wide PAVP.
Optimization of Spatial Partitioning: Formulated and solved the problem of finding the optimal AP partitioning factor ( $\beta^*$ ). The analysis reveals that neither extreme (100% sensing or 100% communication) is optimal; a balanced trade-off is required.
Validation: Extensive Monte Carlo simulations confirm that the analytical bound accurately tracks performance trends and identifies the optimal partition factor with significantly lower complexity than exhaustive simulation.

4. Key Results & Insights

Optimal Partitioning ( $\beta^*$ ): The optimal allocation of APs is not static; it depends on system parameters:
- Stricter PAoI deadlines: Require a higher $\beta$ (more resources to sensing) to ensure rapid update generation.
- Favorable sensing conditions (e.g., large target RCS): Allow for a lower $\beta$ (more resources to communication) because fewer sensing APs are needed to maintain update rates, shifting the bottleneck to delivery reliability.
- High user density: Requires more communication resources to mitigate interference and pilot contamination.
Sensing Interval Trade-off: There is a non-monotonic relationship between the sensing interval ( $T_s$ $T_{s}$ ) and PAVP.
- Too fast ( $T_s$ small): Overwhelms the communication queue, causing high queuing delay.
- Too slow ( $T_s$ large): Introduces inherent staleness.
- An intermediate value often yields the best performance.
Densification vs. Power: In dense networks, increasing AP density is more effective for sensing performance than increasing transmit power, as the system becomes interference-limited rather than noise-limited.
Pilot Overhead: In dense user scenarios, allocating more coherence resources to uplink training (longer pilot sequences) is critical to maintain communication reliability, even at the cost of reduced data transmission time.

5. Significance

This paper provides a critical theoretical foundation for the design of 6G xURLLC networks.

Design Tool: The derived bound serves as a low-complexity surrogate for network planning. Instead of running computationally expensive simulations for every network configuration, operators can use the analytical formula to quickly determine the optimal split between sensing and communication resources.
Coexistence Strategy: It moves beyond simple waveform integration, addressing the fundamental resource allocation problem in shared infrastructure. It demonstrates that spatial partitioning is a dominant design dimension for ensuring information freshness.
Realism: By incorporating FBC, imperfect CSI, and stochastic spatial distributions, the model offers a realistic assessment of performance limits for future distributed sensing-communication systems.

In summary, the paper bridges the gap between physical-layer constraints (channel fading, blocklength) and application-layer requirements (freshness, reliability), offering a mathematically rigorous method to optimize CF-mMIMO networks for the demanding needs of xURLLC.