Remote vital sign detection using Doppler radar has gained increasing interest over the years. However, challenges remain in improving radar system sensitivity to extend the detection range. In this article, we analyze noise contributions in a dual-PLL low-IF Doppler radar system and identify RF leakage/coupling as a major component of the system noise floor. This effect results in negligible SNR improvement when the transmit output power is increased beyond a certain threshold. By applying RF leakage/coupling cancellation through phase and magnitude adjustments, we demonstrate significant improvements to radar system performance. Furthermore, we propose and validate an automatic RF leakage cancellation scheme. The proposed technique is shown to achieve a vital-sign-sensing range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4$</tex-math> </inline-formula> m under a very low transmit power of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-$</tex-math> </inline-formula> 31 dBm and with a high confidence level of three beats per minute against the ground truth measured by an oximeter sensor.