CisLunarSense: Opportunistic ISAC for Debris Detection at the Lunar Gateway

We propose CisLunarSense, an opportunistic integrated sensing and communication (ISAC) framework that exploits the Lunar Gateway's Ka-band relay for monostatic debris detection, addressing the absence of cislunar space situational awareness infrastructure beyond the reach of ground-based radars. Using NASA/ESA-documented system parameters with author-selected sensing settings and a CR3BP-based 9:2 near-rectilinear halo orbit model, we derive the orbit-phase-dependent Cram\'{e}r--Rao bound under OFDM inter-carrier interference, quantify a 36~dB cislunar sensing advantage over a ground-based Ka-band reference, and design a velocity-adaptive processor with mode switching at 337~m/s. Gateway operational debris ($v_\mathrm{rel} < 50$~m/s) is detectable within 700~km with over 30~minutes of warning; external threats ($v_\mathrm{rel}$ up to 500~m/s) remain detectable within 400--630~km. An orbit-phase-adaptive allocation reduces the sensing duty cycle from 60\% to 19\%, increasing relay throughput from 44 to 90~Mbps. A closed-form sensing outage probability for $K$-CPI non-coherent integration under Swerling~I fluctuation shows that the 10\%-outage detection range reaches 91\% of the deterministic maximum at the nominal operating point $K = 16$.