Vital information wireless sensing is an interesting alternative to conventional techniques based on contact sensors. The evolution of radar technologies enables the proposal of cost-effective and compact radar sensors designed for diverse health monitoring, diagnostics, and Internet of Medical Things (IoMT) applications. It is possible to observe respiratory rate (RR), heart rate (HR), cardiac rhythm, blood pressure waveform (BPW), and emerging biometrics from the phase of radar echo signals. However, recognition and separation of the signals of interest from other interfering motion is a challenge, taking into account the diversity of signal patterns depending on subjects, health and observation conditions. In this context, we propose a novel wireless vital sensing system with a self-designed 120 GHz Frequency-Modulated Continuous Wave (FMCW) Radar. The developed sensor, based on a Radar System-on-Chip (RSoC), uses a real-time Repetitive Waveform Adaptive Matched Filter (RWAMF) maximizing Signal-to-Interference-plus-Noise Ratio (SINR) for reliable cardiac rhythm and BPW observations. The radar design has been optimized for vital sensing with a very short wavelength providing excellent sensitivity to micro-motion and a centimetric range and transversal resolutions to reject clutter and unwanted motions. The superior performance of our solution has been validated and evaluated experimentally on different subjects and measurement conditions with our own acquired vital signal database.