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We consider using a Doppler radar for accurate noncontact vital sign detection. The Doppler radar first captures and downconverts the wireless signal that is phase modulated by the physiological movements, and then identifies the human heartbeat and respiration rates by processing the baseband signal. When nonlinear Doppler phase modulation is employed to monitor vital signs without contact, one of the challenges that we encounter is the presence of undesired harmonic terms and intermodulations other than the sinusoids of interest. A spectral estimation algorithm is needed to accurately estimate the sinusoidal frequencies before identifying the heartbeat and respiration rates. The conventional periodogram cannot reliably separate the rich sinusoidal components since it suffers from smearing and leakage problems, particularly for the case of limited data samples. A parametric and cyclic optimization approach, referred to as the RELAX algorithm, is instead suggested to mitigate these difficulties. Both simulated and experimental results are provided to validate the superiority of using the RELAX algorithm for accurate noncontact vital sign detection.