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.

翻译：作为6G的关键能力，分布式基础设施上的感知-通信（S&C）同存有望支撑下一代超可靠低延迟通信（xURLLC）应用，这些应用同时要求稳健的连通性和实时环境感知能力。本文研究了具有感知-通信同存的大规模无小区大规模多输入多输出（CF-mMIMO）中的全网信息新鲜度问题。将接入点（AP）划分为感知与通信角色面临一个挑战：分配更多AP用于感知可改进更新生成，而分配更多AP用于通信则能增强可靠短包传输。为应对此问题，我们通过结合随机几何与随机网络演算（SNC）构建了一个统一的分析框架，用以表征峰值信息年龄（PAoI）违反概率（PAVP）。具体而言，我们推导了感知数据包到达间隔时间与服务时间的矩生成函数（MGF），其中考虑了AP与用户联合随机空间分布、非完美信道状态信息（CSI）以及有限块长编码（FBC）。这有助于推导PAVP的可处理上界，并通过最小化该上界确定最优AP分割。推导出的界限能准确捕捉性能变化趋势，并得到与仿真高度匹配的最优分割因子。因此，该框架为面向xURLLC的CF-mMIMO网络中实现全网PAoI保障及同存导向设计提供了一种高效低复杂度的工具。