Multi-λ Unlimited Sampling for RADAR Vital Sign Monitoring

In this paper, we take a computational sensing approach to solve the recovery of vital signs from FMCW radar measurements when they are perturbed by large Random Body Movements (RBMs), spanning hundreds of range bins, up to meters. Classic methods employ a sequential processing: (i) global peak detection, (ii) phases retrieval, (iii) unfolding, (iv) vital signs estimation. While estimating, and then unfolding a variable phase, in which the vital signs are embedded, makes sense for continuous wave radar, fitting this processing pipeline on the more complex FMCW architecture is sub-optimal. By recovering a single phase, linked to a single wavelength λ, a breadth of information from the whole transmitted bandwidth is lost. In this paper, we push the boundaries of vital sign recovery by leveraging what we call a multi- λ or multi-wavelength approach for FMCW radars. We show that this new processing pipeline and unfolding algorithm yield perfect reconstruction at any sampling rate and for any amplitude of RBM, while tracking the human subject across different range bins. The results are demonstrated using Monte-Carlo simulations and exhibit machine precision like recovery of -250 dB.