According to the World Health Organization, approximately 15 million neonates are born prematurely each year, which is more than 1 in 10 newborns. Premature birth disrupts the normal development of the neonate in the womb, which can result in various complications and health issues, necessitating continuous monitoring of vital signs to assess their health status. Currently, the predominant monitoring approach involves the use of contact-wired sensors, which offer precise readings but are accompanied by specific drawbacks. One notable limitation is the utilization of strong adhesives to attach the sensor to the neonate's skin, causing pain and stress during removal. Additionally, the wired sensor hinders skin-to-skin contact care, which is proved to be crucial for the neonate's growth and development. To address these drawbacks, a non-contact wireless approach using FMCW radar is proposed in this thesis project. The main aim is to develop a processing pipeline to monitor the vital signs of neonates with the radar. The core concept involves estimating the vital signs from the phase information corresponding to the chest movement of the monitoring target. This will be achieved through the implementation of an algorithm based on the short-time Fourier transform. Furthermore, this study also explores an approach to detect body movement, select near-steady state data segment and determine the range bin that is most relevant for the vital signs estimation. The proposed pipeline aims to provide a more comfortable and efficient monitoring system for neonates, potentially overcoming the limitations of conventional contact-wired sensors and promoting better care for their overall well-being and development.