  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. We use a maximum ratio
transmission (MRT) beamformer to share resource between sensing and
communication (S \& C) and observe the trade-off between them. We derive the
approximate probability density function (PDF) of the signal-to-noise ratio
(SNR) for both the user and the target. Subsequently, leveraging the obtained
PDF, we derive the expressions for the user's rate outage probability (OP), as
well as the OP for the Cramer-Rao lower bound (CRLB) of the angle of arrival
(AOA). In our numerical results, we demonstrate the trade-off between S \& C,
confirmed with simulations.
