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 cosβ and the bending contribution with sinβ in elevation β. 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 (PFA=0.01) and unknown target rotor phase, the detector reaches Pd≈0.9 at SNR ≈-14 dB and stays stable for carrier-frequency offsets up to 500 Hz and phase random walk up to 0.2 rad/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.