Bending-Aware Spectrogram Correlation for W-Band Quadcopter Detection: A Physics-Informed Non-Coherent Detection Framework

Small multi-rotor UAVs are difficult radar targets: their radar cross-section is low and aspect-dependent, and their slow body motion overlaps with birds and clutter in Doppler processing. We address W-band (94 GHz) detection with a physics-informed, non-coherent framework that exploits blade flexibility. A compact three-dimensional micro-Doppler model combines counter-rotating rotor kinematics, hub-dependent spatial phase, and a first-order out-of-plane bending term; the rigid rotational signature scales with (Formula presented.) and the bending contribution with (Formula presented.) in elevation (Formula presented.). Near zenith, where rigid micro-Doppler collapses toward DC, bending repopulates an observable low-velocity band. Detection uses cosine similarity between magnitude spectrograms, which is robust to the tested oscillator impairments. With a calibrated false-alarm rate ( (Formula presented.) ) and unknown target rotor phase, the detector reaches (Formula presented.) at SNR (Formula presented.) dB and stays stable for carrier-frequency offsets up to 500 (Formula presented.) and phase random walk up to (Formula presented.)   (Formula presented.) /sample, where an uncompensated matched filter fails; it also retains detection against simulated bird-and-clutter micro-Doppler in the background-dominated regime where an energy detector collapses. A consistency check against measured single-blade no-IQ W-band records reproduces the one-sided time–frequency periodicity under a matched product-detector operator. The result is an interpretable, training-free baseline for phase-limited W-band UAV sensing.