This paper presents a 79 GHz ultra-wideband sensor monitoring the instantaneous heart-rate (HR) of moving persons. The sensor uses three approaches for the instantaneous HR monitoring: block-based motion/movement compensation of multiple persons, multiresolution analysis and Burg method for instantaneous HR analysis. The first approach normalizes and/or compensates for motion/movement of moving persons where the consecutive received signal, called radar range-profile, is stored on a block-by-block basis and the motion/movement within each block is then normalized as stationary. The second approach uses multi-resolution analysis (MRA) in order to remove most of the breathing signal from the received vital-sign waveform (HR and breathing). And the third approach estimates the instantaneous HR using Burg method. Measurement was conducted in order to investigate the usefulness of our suggested HR monitoring system including the above three approaches. The estimated HR is also compared with an optical pulse wave sensor (finger PPG) in order to confirm the accuracy.