Cooperative LEO-Terrestrial Multistatic ISAC: CRLB Analysis, Scaling Laws, and Satellite Selection

Abstract

Low Earth orbit (LEO) satellites provide elevated and spatially diverse viewpoints for enhancing three-dimensional (3-D) sensing in integrated satellite-terrestrial networks (ISTNs). This paper investigates a LEO-assisted terrestrial multistatic integrated sensing and communication (ISAC) network for 3-D target localisation, where multiple LEO satellites act as cooperative sensing illuminators and provide additional bistatic observations to distributed terrestrial radar receivers. We first model cooperative satellites as a homogeneous Poisson point process (PPP) and derive a tractable approximation of the average hybrid Cram\'er-Rao lower bound (CRLB). The resulting scaling laws show that the root-CRLB decreases with the inverse square root of the mean number of cooperative satellites for a fixed cooperation region, while increasing the cooperation radius at fixed satellite density yields logarithmic diminishing returns. We then develop an Earth-curvature-aware Walker model incorporating orbital structure, satellite motion, visibility, and time-varying sensing geometry, and derive a tractable approximation of the corresponding hybrid CRLB. Analytical bounds on the marginal gain and a sufficient condition for ordering candidate satellites are obtained. Based on these results, a CRLB-oriented greedy satellite-selection strategy is proposed to account for SCNR-dependent reliability and geometric complementarity with the terrestrial sensing configuration. The proposed strategy consistently outperforms benchmarks and approaches exhaustive-search performance with substantially lower complexity. Monte Carlo simulations validate the analytical approximations for both models.