Through-wall respiration detection using Ultra-wideband (UWB) impulse radar can be applied to the post-disaster rescue, e.g., searching living persons trapped in ruined buildings after an earthquake. Since strong interference signals always exist in the real-life scenarios, such as static clutter, noise, etc., while the respiratory signal is very weak, the signal to noise and clutter ratio (SNCR) is quite low. Therefore, through-wall respiration detection using UWB impulse radar under low SNCR is a challenging work in the research field of searching survivors after disaster. In this paper, an improved UWB respiratory signal model is built up based on an even power of cosine function for the first time. This model is used to reveal the harmonic structure of respiratory signal, based on which a novel high-performance respiration detection algorithm is proposed. This novel algorithm is assessed by experimental verification and simulation and shows about a 1.5dB improvement of SNR and SNCR.