Respiration rate monitoring using ultra-wideband (UWB) radar is preferred because it provides contactless measurement without restricting the person’s privacy. This study considers a novel non-contact-based solution using a single-input multiple-output (SIMO) UWB impulse radar. In the proposed system, the collected radar data are converted to several narrow-band signals using the generalized Goertzel algorithm (GGA), which are used as the input of the designed phased arrays for position estimation. In this context, we introduce the incoherent signal subspace methods (ISSM) for the direction of arrivals (DOAs) and distance evaluation. Meanwhile, a beam focusing approach is used to determine each individual and estimate their breathing rate automatically based on a linearly constrained minimum variance (LCMV) beamformer. The experimental results prove that the proposed algorithm can achieve high estimation accuracy in a variety of test environments, with an error of 2%, 5%, and 2% for DOA, distance, and respiration rate, respectively.