Enhanced Arctangent Demodulation Algorithm for Periodic Motion Sensing with Quadrature Doppler Radar System

Accurate displacement measurement with Doppler radar necessitates the incorporation of phase demodulation techniques. However, these techniques are prone to phase ambiguity, as target displacements frequently surpass a quarter wavelength. In this paper, we introduce an enhanced arctangent (EATAN) demodulation algorithm to tackle the phase ambiguity challenge in quadrature Doppler radar systems for detecting a target with periodic motions. The EATAN algorithm seamlessly integrates arctangent operation, phase difference calculation, phase compensation, and phase accumulation to achieve a more precise phase reconstruction. Simulations conducted on a 24 GHz radar system demonstrate that the proposed EATAN algorithm can accurately track periodic motions with amplitudes up to 10 m (i.e., 800 wavelengths) and frequencies exceeding 20 Hz. Compared to other state-of-the-art demodulation methods, the EATAN method exhibits a more extensive demodulation range, higher demodulation accuracy, and improved noise robustness. Experimental detection of the driver nodding vibrations and pendulum motions corroborate the effectiveness of the EATAN method and indicate its vast potential for application in diverse contexts.