Fundamental Limits of THz Inter-Satellite ISAC Under Hardware Impairments

Abstract: This paper establishes a theoretical framework for analyzing the fundamental performance limits of terahertz (THz) Low Earth Orbit (LEO) inter-satellite link (ISL) Integrated Sensing and Communications (ISAC) systems. We develop a unified, end-to-end signal model that, jointly captures the effects of extreme orbital dynamics, cascaded non-ideal hardware impairments, and micro-radian beam pointing errors. Through Bayesian Cram\'er-Rao Lower Bound (BCRLB) analysis, we derive the ultimate sensing accuracy for range and range-rate, revealing a quadratic ($1/f_c<sup>2$) improvement in estimation variance with carrier frequency, which is ultimately floored by signal-dependent hardware distortion. For communication, we show that system performance is not power-limited but hardware-limited, deriving a closed-form capacity ceiling under the joint effect of phase noise and PA nonlinearity: $$C_{\text{sat}} = \log_2(1 + e<sup>{-\sigma_\phi<sup>2}/\Gamma_{\text{eff}})$$, where $\Gamma_{\text{eff}}$ is a proposed hardware quality factor. Our numerical results, based on state-of-the-art component data and the identified trade-offs, suggest that favorable operational conditions may exist in the sub-THz frequency range (200-600 GHz) where the quadratic sensing gain with frequency is balanced against hardware quality degradation. Power Amplifier (PA) nonlinearity emerges as the dominant performance bottleneck, exceeding other impairments by one to two orders of magnitude.