Ultra-wide Band(UWB) radar has emerged a useful and safe technology in non-contact vital sign monitoring. Many literatures have described the feasibility of this application, even in the case the pulse radiates through the wall. The background clutter is an important issue because the intensity of it is usually larger than the desired signal. There are two major schemes. One is to estimate the time delay of the transmitted pulse using the wavelet transform or something else. We will use the matched filter to explain the phenomenon and the difficulty with the existence of the background clutter. The other scheme is to sample the waveform directly and observe the variation of the waveform at a certain time delay. Due to the weakness of the signal of heartbeat, the SNR is the higher the better. In this thesis, a modified method which can efficiently utilize the received data by taking multiple time delays of data for estimation is proposed.

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