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 $\sigma<sup>2_\phi$, 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 ($$\sigma_{\text{floor}} \propto \sqrt{\sigma<sup>2_\phi}/f_c$$), with power-only scaling saturating above $$\text{SNR}<em>{\text{crit}}=1/\Gamma</em>{\text{eff}}$$; (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 ($\Gamma_{\text{eff}}&lt;0.01$), oscillators ($\sigma<sup>2_\phi&lt;10<sup>{-2}$), and appropriate 3D geometry configurations.