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