On Stochastic Fundamental Limits in a Downlink Integrated Sensing and Communication Network

TL;DR

This paper analyzes the stochastic performance limits of a MIMO integrated sensing and communication system in a downlink scenario, focusing on probabilistic metrics for both communication and sensing performance under channel randomness.

Contribution

It introduces a framework for evaluating stochastic performance metrics in ISAC systems, deriving expressions for outage and ergodic rates for communication and sensing, considering different beamforming methods.

Findings

Trade-off between sensing and communication performance characterized.

Derived closed-form expressions for outage and ergodic rates.

Identified Pareto optimal boundary points for S&C performance.

Abstract

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.