From an information theoretic perspective, joint communication and sensing (JCAS) represents a natural generalization of communication network functionality. However, it requires the re-evaluation of network performance from a multi-objective perspective. We develop a novel mathematical framework for characterizing the sensing and communication coverage probability and ergodic rate in JCAS networks. We employ a formulation of sensing parameter estimation based on mutual information to extend the notions of coverage probability and ergodic rate to the radar setting. We define sensing coverage probability as the probability that the rate of information extracted about the parameters of interest associated with a typical radar target exceeds some threshold, and sensing ergodic rate as the spatial average of the aforementioned rate of information. Using this framework, we analyze the downlink sensing and communication coverage and rate of a mmWave JCAS network employing a shared waveform, directional beamforming, and monostatic sensing. Leveraging tools from stochastic geometry, we derive upper and lower bounds for these quantities. We also develop several general technical results including: i) a generic method for obtaining closed form upper and lower bounds on the Laplace Transform of a shot noise process, ii) a new analog of H{\"o}lder's Inequality to the setting of harmonic means, and iii) a relation between the Laplace and Mellin Transforms of a non-negative random variable. We use the derived bounds to numerically investigate the performance of JCAS networks under varying base station and blockage density. Among several insights, our numerical analysis indicates that network densification improves sensing SINR performance -- in contrast to communications.

翻译：从信息论角度来看，联合通信与感知（JCAS）是通信网络功能的自然推广，但需要从多目标角度重新评估网络性能。我们提出了一种新颖的数学框架，用于刻画JCAS网络中感知与通信的覆盖概率和遍历速率。我们基于互信息建立感知参数估计的数学表达，将覆盖概率和遍历速率的概念拓展至雷达场景：感知覆盖概率定义为从典型雷达目标相关参数中提取的信息速率超过某阈值的概率，而感知遍历速率则为该信息速率的空间平均值。利用该框架，我们分析了采用共享波形、定向波束赋形与单站感知的毫米波JCAS网络的下行感知与通信覆盖及速率。借助随机几何工具，推导了这些性能指标的上界与下界，并发展了若干通用技术结果：i) 散粒噪声过程拉普拉斯变换闭合上界与下界的通用求解方法；ii) 调和均值场景下赫尔德不等式的新类比形式；iii) 非负随机变量拉普拉斯变换与梅林变换之间的关联。通过推导的界值，我们数值分析了不同基站密度与阻塞密度下JCAS网络的性能。数值分析表明（与通信相反），网络密集化可提升感知信干噪比性能。