This paper presents a new system for the detection of human respiration behind obstacles using impulse ultra-wideband (UWB) radar. In complex environments, low signal-to-noise ratios (SNRs) as they can result in significant errors in the respiration, heartbeat frequency, and range estimates. To improve the performance, the complex signal demodulation (CSD) technique is extended by employing the signal logarithm and derivative. A frequency accumulation (FA) method is proposed to suppress mixed products of the heartbeat and respiration signals and spurious respiration signal harmonics. The respiration frequency is estimated using the phase variations in the received signal, and a discrete short-time Fourier transform (DSFT) is used to estimate the range. The performance of the proposed system is evaluated along with that of several well-known techniques in the literature.