Utilizing microwave continuous-wave Doppler radars to wirelessly detect mechanical vibrations have been attracting more and more interests in recent years. In this paper, aiming to solve the null point and nonlinear issues in small-angle approximation-based Doppler radar sensors and eliminate the codomain restriction in the arctangent demodulation approach, we propose and investigate an extended differentiate and crossmultiply (DACM) algorithm. With an additional accumulator, the noise performance of the original DACM algorithm is improved. Moreover, the amplitude information of the vibration can be directly retrieved from accumulation without involving any distance-dependent issue. Experimental validations show that the proposed algorithm can fully recover the vibration patterns with the measured noncalibrated amplitude agreeing well with the known precalibrated data. Application examples of mechanical fault detection and human vital sign detection are demonstrated, showing a wide range of potential applications of this algorithm.Index Terms-Arctangent demodulation, differentiate and cross multiply (DACM), noncontact vibration measurement, nonlinear phase modulation, radar sensor.

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