This paper aims to analyze the stochastic performance of a multiple input multiple output (MIMO) integrated sensing and communication (ISAC) system in a downlink scenario, where a base station (BS) transmits a dual-functional radar-communication (DFRC) signal matrix, serving the purpose of transmitting communication data to the user while simultaneously sensing the angular location of a target. The channel between the BS and the user is modeled as a random channel with Rayleigh fading distribution, and the azimuth angle of the target is assumed to follow a uniform distribution. Due to the randomness inherent in the network, the challenge is to consider suitable performance metrics for this randomness. To address this issue, for users, we employ the user's rate outage probability (OP) and ergodic rate, while for target, we propose using the OP of the Cram\'er-Rao lower bound (CRLB) for the angle of arrival and the ergodic CRLB. We have obtained the expressions of these metrics for scenarios where the BS employs two different beamforming methods. Our approach to deriving these metrics involves computing the probability density function (PDF) of the signal-to-noise ratio for users and the CRLB for the target. We have demonstrated that the central limit theorem provides a viable approach for deriving these PDFs. In our numerical results, we demonstrate the trade-off between sensing and communication (S \& C) by characterizing the region of S \& C metrics and by obtaining the Pareto optimal boundary points, confirmed with simulations.

翻译：本文旨在分析下行场景中多输入多输出（MIMO）集成感知与通信（ISAC）系统的随机性能。在该场景中，基站（BS）发射双功能雷达通信（DFRC）信号矩阵，既向用户传输通信数据，又同时感知目标的角度位置。基站与用户之间的信道被建模为具有瑞利衰落的随机信道，目标的方位角假设服从均匀分布。由于网络固有的随机性，如何选取合适的性能指标来应对这种随机性成为挑战。为解决此问题，针对用户，我们采用用户的速率中断概率（OP）和遍历速率；针对目标，我们提出采用到达角的克拉美-罗下界（CRLB）的中断概率和遍历CRLB。我们推导了基站采用两种不同波束赋形方法时这些指标的表达式。我们的推导方法涉及计算用户的信噪比概率密度函数（PDF）以及目标的CRLB的PDF。我们证明了中心极限定理为推导这些PDF提供了一种可行方法。数值结果中，我们通过刻画感知与通信（S&C）指标的区域并获取帕累托最优边界点，展示了感知与通信之间的权衡，仿真结果验证了这些结论。