Fundamental Limits of Cooperative Integrated Sensing and Communications over Low-Earth Orbit THz Satellite Channels

Abstract

Terahertz inter-satellite links enable unprecedented sensing precision for Low Earth Orbit (LEO) constellations, yet face fundamental bounds from hardware impairments, pointing errors, and network interference. We develop a Network Cram\'er-Rao Lower Bound (N-CRLB) framework incorporating dynamic topology, hardware quality factor $\Gamma_{\text{eff}}$, phase noise $\sigma^2_\phi$, and cooperative effects through recursive Fisher Information analysis. Our analysis reveals three key insights: (i) hardware and phase noise create power-independent performance ceilings ($\sigma_{\text{ceiling}} \propto \sqrt{\Gamma_{\text{eff}}}$) and floors ($\sigma_{\text{floor}} \propto \sqrt{\sigma^2_\phi}/f_c$), with power-only scaling saturating above $\text{SNR}_{\text{crit}}=1/\Gamma_{\text{eff}}$; (ii) interference coefficients $\alpha_{\ell m}$ enable opportunistic sensing with demonstrated gains of 5.5~dB under specific conditions (65~dB processing gain, 50~dBi antennas); (iii) measurement correlations from shared timing references, when properly modeled, do not degrade performance and can provide common-mode rejection benefits compared to mismodeled independent-noise baselines. Sub-millimeter ranging requires co-optimized hardware ($\Gamma_{\text{eff}}<0.01$), oscillators ($\sigma^2_\phi<10^{-2}$), and appropriate 3D geometry configurations.