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arxiv: 2604.06657 · v1 · submitted 2026-04-08 · 💻 cs.IT · cs.SY· eess.SY· math.IT

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

Yanxi Zhang , Mingwu Yao , Qinghai Yang , Muyu Mei This is my paper

Pith reviewed 2026-05-10 18:05 UTC · model grok-4.3

classification 💻 cs.IT cs.SYeess.SYmath.IT
keywords peak age of informationcell-free massive MIMOsensing-communication coexistencestochastic geometrystochastic network calculusaccess point partitioningfinite blocklength codingultra-reliable low-latency communication
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The pith

A framework combining stochastic geometry and network calculus derives a tractable upper bound on peak age of information violation probability in cell-free massive MIMO networks with sensing-communication coexistence, minimized by optimal

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that access points in large-scale cell-free massive MIMO networks can be spatially partitioned between sensing and communication roles to support both real-time environmental updates and reliable short-packet delivery for next-generation ultra-reliable low-latency applications. It develops a unified analysis by merging stochastic geometry, which models the random locations of access points and users, with stochastic network calculus to track the statistics of packet arrivals and transmissions. This yields moment generating functions for inter-arrival and service times that incorporate imperfect channel estimates and finite blocklength effects, producing a closed-form upper bound on the network-wide probability that peak age of information exceeds a target threshold. The bound is then minimized over the partition factor to identify the allocation that best balances the two functions. A reader would care because the resulting low-complexity design tool directly informs how to configure distributed infrastructure for applications that need both freshness of sensed data and guaranteed delivery.

Core claim

By deriving the moment generating functions of sensory packet inter-arrival and service times under the joint stochastic spatial distribution of access points and users, imperfect CSI, and finite blocklength coding, the paper obtains a tractable upper bound on the peak age of information violation probability that can be minimized to determine the optimal access point partitioning factor between sensing and communication roles.

What carries the argument

The unified analytical framework that merges stochastic geometry for spatial point processes with stochastic network calculus to derive moment generating functions of inter-arrival and service times, thereby producing a minimizable upper bound on network-wide peak age of information violation probability.

If this is right

  • The optimal partition factor can be computed directly from the closed-form bound without exhaustive search.
  • The bound accurately tracks the performance trend observed in simulations for varying densities and reliability targets.
  • Network-wide PAoI guarantees become achievable through a single scalar tuning parameter that balances sensing update rate against communication reliability.
  • The framework supplies a low-complexity design tool that scales to large CF-mMIMO deployments for xURLLC.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same MGF-based bounding technique could be reused to incorporate additional constraints such as energy harvesting or mobility-induced channel aging.
  • Extending the spatial model to clustered user distributions might shift the optimal partition toward more communication APs in dense hotspots.
  • If sensing and communication share the same spectrum, an additional interference term in the service-time MGF would be needed to keep the bound representative.

Load-bearing premise

The moment generating functions of inter-arrival and service times remain valid under the joint stochastic spatial distribution of access points and users, imperfect CSI, and finite blocklength coding.

What would settle it

Compare the analytical minimizing partition factor and the predicted PAVP values against exhaustive Monte Carlo simulations that use measured channels and actual finite-blocklength error rates; large systematic deviation in either the optimal split or the bound tightness would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.06657 by Mingwu Yao, Muyu Mei, Qinghai Yang, Yanxi Zhang.

Figure 1
Figure 1. Figure 1: The CF-mMIMO coexistence networks. eling, a gap remains at their intersection. The literature still lacks a tractable analytical framework for quantifying network￾wide PAoI in large-scale CF-mMIMO coexistence networks, where sensing-driven packet generation and communication￾limited packet delivery are jointly shaped by stochastic topol￾ogy and shared infrastructure constraints. This paper aims to bridge t… view at source ↗
Figure 2
Figure 2. Figure 2: P s cv vs. δ for various σ¯ and Θ. coverage compared to narrower beams. In a network with random AP orientations, a wider beam significantly increases the target illumination probability. This spatial coverage gain outweighs the increased susceptibility to co-channel interfer￾ence, establishing a crucial design principle: for wide-area surveillance with unknown target locations, employing broad￾beam APs im… view at source ↗
Figure 4
Figure 4. Figure 4: P c cv vs. λc for various N and γth. -10 -8 -6 -4 -2 0 2 4 6 8 10 10-4 10-3 10-2 10-1 100 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Υnw vs. ζ for various Ts. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10-2 10-1 100 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

As a key capability of 6G, sensing-communication (S&C) coexistence over distributed infrastructure is expected to support next-generation ultra-reliable and low-latency communication (xURLLC) applications, which demand both robust connectivity and real-time environmental awareness. This paper investigates network-wide information freshness in large-scale cell-free massive multiple-input multiple-output (CF-mMIMO) with S&C coexistence. A challenge arises from the spatial partitioning of access points (APs) into S&C roles: allocating more APs to sensing improves update generation, whereas allocating more APs to communication enhances reliable short-packet delivery. To address this, we develop a unified analytical framework by combining stochastic geometry and stochastic network calculus (SNC) to characterize the peak age of information (PAoI) violation probability (PAVP). Specifically, we derive the moment generating functions (MGFs) of sensory packet inter-arrival and service times, accounting for the joint stochastic spatial distribution of APs and users, imperfect channel state information (CSI), and finite blocklength coding (FBC). This facilitates the derivation of a tractable upper bound on the PAVP, which is minimized to determine the optimal AP partitioning. The derived bound accurately captures the performance trend and yields a minimizing partition factor that closely matches simulations. Therefore, the framework provides an efficient and low-complexity tool for network-wide PAoI guarantee and coexistence-oriented design in CF-mMIMO networks toward xURLLC.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops a unified analytical framework combining stochastic geometry and stochastic network calculus (SNC) for cell-free massive MIMO (CF-mMIMO) networks with sensing-communication (S&C) coexistence. It derives the moment generating functions (MGFs) of sensory packet inter-arrival and service times, incorporating the joint PPP spatial distributions of APs and users, MMSE channel estimation, and finite-blocklength coding (FBC). These enable a tractable upper bound on the network-wide peak age of information violation probability (PAVP), which is minimized over the AP partitioning factor β to obtain an optimal spatial split that provides PAoI guarantees; the bound is stated to capture performance trends and yield a minimizing β that closely matches simulations.

Significance. If the MGF derivations prove rigorous and the SNC upper bound remains sufficiently tight after the spatial averaging and FBC approximations, the framework would offer a valuable low-complexity tool for coexistence-oriented xURLLC design in large-scale CF-mMIMO systems. The integration of SNC for PAoI with stochastic geometry to handle random AP allocation is a technical strength that could reduce reliance on Monte-Carlo optimization while delivering network-wide guarantees.

major comments (2)
  1. [§III-B] §III-B (MGF of service time): the derivation averages the FBC error-probability expression (inverse-Q approximation) over the random effective SINR seen by a typical user when only a random subset of APs is allocated to communication. The joint PPP of sensing and communication APs introduces spatial correlations that are typically handled by moment-matching or independence assumptions; the manuscript does not quantify how these steps affect the tail of the service-time distribution or shift the location of the minimized PAVP bound.
  2. [§IV] §IV (PAVP upper bound and optimization): the tractable SNC-based upper bound on PAVP is minimized w.r.t. β and reported to yield an optimum that closely matches simulations. However, no sensitivity analysis is provided on how the FBC approximation parameters or imperfect-CSI variance propagate into the argmin_β, leaving open whether the reported agreement guarantees a reliable network-wide PAoI bound under realistic variations in blocklength or CSI quality.
minor comments (2)
  1. [Abstract] The abstract introduces the partition factor β without an explicit definition or range; a brief sentence in the system model would improve readability.
  2. [Figures] Figure captions should explicitly state which curves are analytical bounds versus Monte-Carlo simulations to avoid ambiguity when comparing trends.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on our manuscript. We address each major comment below with clarifications and indicate the revisions we will make to improve the paper.

read point-by-point responses

  1. Referee: [§III-B] §III-B (MGF of service time): the derivation averages the FBC error-probability expression (inverse-Q approximation) over the random effective SINR seen by a typical user when only a random subset of APs is allocated to communication. The joint PPP of sensing and communication APs introduces spatial correlations that are typically handled by moment-matching or independence assumptions; the manuscript does not quantify how these steps affect the tail of the service-time distribution or shift the location of the minimized PAVP bound.

    Authors: We appreciate the referee pointing out the need for further quantification in the MGF derivation of §III-B. The effective SINR distribution is obtained via stochastic geometry applied to the joint PPP of sensing and communication APs, and the FBC error probability is averaged over this distribution using standard tools (e.g., Campbell's theorem). Independence approximations are used for tractability in the MGF, as is common in such analyses. While the overall accuracy is supported by Monte Carlo simulations that include full spatial correlations, we acknowledge that explicit quantification of the approximation's effect on the service-time tail and the location of the minimized PAVP is not provided. In the revision, we will add a discussion and supplementary numerical comparisons (e.g., empirical vs. approximated service-time distributions) to assess any resulting shifts. revision: partial

  2. Referee: [§IV] §IV (PAVP upper bound and optimization): the tractable SNC-based upper bound on PAVP is minimized w.r.t. β and reported to yield an optimum that closely matches simulations. However, no sensitivity analysis is provided on how the FBC approximation parameters or imperfect-CSI variance propagate into the argmin_β, leaving open whether the reported agreement guarantees a reliable network-wide PAoI bound under realistic variations in blocklength or CSI quality.

    Authors: We thank the referee for this suggestion regarding robustness. The reported close match between the analytically optimized β and simulation results is intended to indicate that the bound captures key trends reliably. However, we agree that explicit sensitivity analysis on parameters such as blocklength, target error probability, and CSI quality would strengthen the claims about the argmin_β. In the revised manuscript, we will include additional results (e.g., in a new subsection or appendix) showing how variations in these parameters affect the location of the minimizing β and the tightness of the PAVP bound. revision: yes

Circularity Check

0 steps flagged

Analytical derivation of MGFs, SNC bound, and partition minimization is self-contained

full rationale

The paper derives the MGFs of inter-arrival and service times from stochastic geometry applied to the joint PPP of APs/users plus MMSE estimation and FBC error-probability expressions, then applies SNC to obtain a closed-form upper bound on network-wide PAVP, and finally minimizes that bound over the partition factor β. This chain is presented as first-principles and is validated post-derivation by comparing the analytical argmin(β) to Monte-Carlo simulations; no equation reduces the minimized bound or its optimum to a fitted parameter, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The framework therefore remains independent of its own simulation outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only abstract available; framework rests on standard domain assumptions for spatial modeling and queueing analysis with no new entities or explicitly fitted free parameters described.

axioms (2)
  • domain assumption Stochastic geometry accurately models the joint spatial distribution of APs and users for deriving MGFs of packet inter-arrival and service times
    Invoked to characterize PAoI under random AP partitioning, imperfect CSI, and FBC.
  • domain assumption Stochastic network calculus provides valid bounds on PAoI violation probability when combined with the MGFs
    Central to obtaining the tractable upper bound on PAVP.

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