The accuracy of a radar for sensing vital signs is generally affected by system noise, including the phase noise of the frequency synthesizer and the intermodulation of the vital sign signals. System noise becomes particularly serious when vital sign radars operate in the millimeter wave (mm-wave) band because the phase noise performance of mm-wave frequency synthesizers is generally inferior to that of microwave frequency synthesizers. To address the problem of system noise, a polar cross-correlation function (CCF) and a low-noise mm-wave frequency synthesizer were developed. The polar CCF can suppress both the intermodulation of vital sign signals and the phase noise of the radar system. The low-noise mm-wave frequency synthesizer further reduces the system phase noise by injection- and frequency-locked loop (IFLL) and loop bandwidth (BW) optimization. Experiments demonstrated that the proposed IFLL and loop BW optimization reduce the phase noise of a 24 GHz vital sign radar by more than 28 dB within the loop BW. The proposed polar CCF can further reduce the noise floor and intermodulation of the detected vital sign signals by 24 dB and 17 dB, respectively. These noise reductions reduced the standard deviation (SD) of the sensed respiration rate (RR) and heart rate (HR) by more than half, making the implemented 24 GHz vital signs radar system more reliable and accurate.