Integrated sensing and communication (ISAC) is increasingly recognized as a pivotal technology for next-generation cellular networks, offering mutual benefits in both sensing and communication capabilities. This advancement necessitates a re-examination of the fundamental limits within networks where these two functions coexist via shared spectrum and infrastructures. However, traditional stochastic geometry-based performance analyses are confined to either communication or sensing networks separately. This paper bridges this gap by introducing a generalized stochastic geometry framework in ISAC networks. Based on this framework, we define and calculate the coverage and ergodic rate of sensing and communication performance under resource constraints. Then, we shed light on the fundamental limits of ISAC networks by presenting theoretical results for the coverage rate of the unified performance, taking into account the coupling effects of dual functions in coexistence networks. Further, we obtain the analytical formulations for evaluating the ergodic sensing rate constrained by the maximum communication rate, and the ergodic communication rate constrained by the maximum sensing rate. Extensive numerical results validate the accuracy of all theoretical derivations, and also indicate that denser networks significantly enhance ISAC coverage. Specifically, increasing the base station density from $1$ $\text{km}^{-2}$ to $10$ $\text{km}^{-2}$ can boost the ISAC coverage rate from $1.4\%$ to $39.8\%$. Further, results also reveal that with the increase of the constrained sensing rate, the ergodic communication rate improves significantly, but the reverse is not obvious.

翻译：集成感知与通信（ISAC）正被广泛认为是下一代蜂窝网络的关键技术，能在感知与通信能力方面实现互利共赢。这一进步要求重新审视感知与通信功能通过共享频谱与基础设施共存的网络中的基本限制。然而，传统基于随机几何的性能分析仅限于单独讨论通信网络或感知网络。本文通过引入ISAC网络中的广义随机几何框架来填补这一空白。基于该框架，我们定义并计算了资源约束下感知与通信性能的覆盖率和遍历速率。随后，我们通过考虑共存网络中双功能的耦合效应，给出统一性能覆盖率的理论结果，揭示了ISAC网络的基本限制。进一步，我们推导了受最大通信速率约束的遍历感知速率，以及受最大感知速率约束的遍历通信速率的解析表达式。大量数值结果验证了所有理论推导的准确性，并表明更密集的网络能显著提升ISAC覆盖率。具体而言，将基站密度从$1$ $\text{km}^{-2}$增加到$10$ $\text{km}^{-2}$可使ISAC覆盖率从$1.4\%$提升至$39.8\%$。此外，结果还揭示，随着约束感知速率的增加，遍历通信速率显著提升，但反之则不明显。