UWB impulse radar for vital signs sensing ? A modeling framework for arbitrary periodic heart and lung motion

The Impulse Radio Ultra-wideband (IR-UWB) vital signs application is typically characterized by a periodic transmitted waveform and a periodic delay modulation caused by periodic chest displacement. We present closed-form spectral coefficients for the chest-reflected IR-UWB signal as it arrives at the radar receiver, assuming a planar chest model. We assume the chest displaces according to arbitrary periodic motion of the heart and lungs. Our base model assumes a periodic train of transmitted impulses. We call our approach a "framework" because our model can be put with any burst waveform that is transmitted periodically (such as a pseudo-random binary sequence), any multi-layer model of the chest, and any receiver signal processing model, to provide a complete model of the post-processed radar received signal. We describe in the paper how each of these extensions can be done in a straightforward way with our model, without having to re-derive the coefficients of the base model. Our model is more general than existing models, which lack closed form expressions or have various constraints, such as sinusoidal chest displacement, zero phase, or unavoidable aliasing.