Distortion is Not Noise: On the Limits of the Kappa Model for Monostatic ISAC

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Abstract
Hardware impairments affect sensing and communication asymmetrically in monostatic integrated sensing and communication (ISAC): the transmitter can monitor its own distorted waveform for sensing, whereas the remote communication receiver cannot. The aggregate k distortion model treats impairments as unknown noise, which is appropriate for communication but pessimistic for monostatic sensing. We derive power-amplifier-aware sensing Cramér–Rao bounds (CRBs) and a phase-noise-aware CRB that reveals an irreducible velocity-error floor, and quantify when k-based bounds overestimate sensing degradation. Simulations validate the analysis and show robustness to practical digital pre-distortion (DPD) template errors (less than 1 dB overhead at −25 dB normalized mean square error (NMSE)).

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