Low-Altitude UAV-Assisted Bistatic ISAC: Closed-form 3D CRLB and Coverage Analysis

Abstract

This paper investigates the fundamental performance limits of three-dimensional (3D) localization in unmanned aerial vehicle (UAV)-assisted integrated sensing and communication (ISAC) systems. Specifically, a base station (BS) estimates the 3D position of a sensing target with the aid of a UAV acting as a flexible aerial anchor node. We derive a closed-form expression for the 3D Cramer-Rao lower bound (CRLB), which explicitly quantifies the achievable localization accuracy as a function of both the UAV's location and the target's position. The CRLB is shown to decompose naturally into three distinct components, arising from signal propagation delay, angular measurements, and their coupling effect, respectively. To validate the analytical results, we consider a representative orthogonal frequency-division multiplexing (OFDM)-based ISAC system and demonstrate that the derived CRLB closely predicts the performance of maximum-likelihood estimation across diverse geometric configurations and UAV mobility patterns. Furthermore, we introduce the notion of CRLB-constrained sensing coverage to characterize the spatial region within which a prescribed localization accuracy can be guaranteed. Through local boundary approximations and coverage-size evaluations, we reveal how UAV displacement, altitude, and the CRLB threshold jointly shape the extent and geometry of the reliable sensing region.