Large Displacement Motion Interferometry With Modified Differentiate and Cross-Multiply Technique

Millimeter-wave radar interferometry is superior in detecting small displacement motions owing to its short wavelength. However, it is subject to phase ambiguity as the target displacement may often exceed a quarter wavelength. In this article, a modified differentiate and cross-multiply (MDACM) technique is proposed to tackle the phase ambiguity issue for accurate reconstruction of the phase history in millimeter-wave interferometry. In addition, to resolve the imperfections of the interferometric radar system, an MDACM-based integral phase reconstruction approach is presented, which seamlessly integrates alternating current (ac)-coupling-induced distortion correction, $I/Q$ mismatch correction, and direct current (dc) offsets’ calibration. Without causing any phase ambiguity, the proposed technique acts as a black box to take in the raw $I/Q$ signals and correct all the hardware imperfections, and it outputs the desired displacement motions with micrometer accuracy. The simulation results show that the proposed technique can not only linearly recover the displacement motions across a wide range in different noise conditions without any phase ambiguity but also improve the stability by 11 times under ac-coupling-induced distortion. With a custom-designed 120-GHz interferometric radar sensor, experiments were carried out to validate various scenarios including mechanical vibrations and gesture sensing. The experimental results show that the proposed technique can accurately track not only deep subwavelength motion of only $1~\mu \text{m}$ but also multiwavelength displacement of >40 times of the wavelength at 120 GHz.