In this paper, we present a comprehensive scheme for wireless monitoring of the respiratory movements in humans. Our scheme overcomes the challenges low signal-to-noise ratio, background clutter and high sampling rates. It is based on the estimation of the ultra-wideband channel impulse response. We suggest techniques for dealing with background clutter in situations when it might be time variant. We also present a novel methodology for reducing the required sampling rate of the system significantly while achieving the accuracy offered by the Nyquist rate. Performance results from simulations conducted with pre-recorded respiratory signals demonstrate the robustness of our scheme for tackling the above challenges and providing a low-complexity solution for the monitoring of respiratory movements.