Continuous and accurate monitoring of human vital signs is an important part of the healthcare industry, as it is the basic means by which the clinicians can determine the instantaneous status of their patients. Doppler-based noncontact vital signs (NCVS) sensor systems can monitor the heart and respiration rates without touching the patient, but it has been observed that that the accuracy of these NCVS sensors can be diminished by reflections from background clutters in the measurement environment, and that high directivity antennas can increase the sensing accuracy. Therefore, this work explores a NCVS sensor with continuous data taken inside an anechoic chamber where the background cluttering is negligible. In addition, a high directivity custom-made beam-steerable phased array antenna system is used to improve the performance and functionality of the 2.4GHz NCVS sensor we have built. We believe this work is the 1st systematic study using Doppler-based phased array systems for NCVS sensing performed in a clutter-free anechoic chamber.