Unlimited Sampling for Radar-based Vital Sign Monitoring

This paper tackles the contactless recovery of vital sign information from backscattered signals using a radar device. These sensors do not require any physical contact with the patient, which makes them extremely suitable for healthcare applications such as the long-term monitoring of patients or elderly care. In this context, the information regarding the breathing and heart rate is embedded within the phase of the received radar signal and inherently suffers from a
$2\pi$
ambiguity. For sensors operating at millimeter-wave, common recovery methods rely on algorithms that unwrap the phase. These methods, however, do not possess strong recovery guarantees and often fail when encountering quick phase variations (e.g., random body movements and larger chest displacements). This can hinder accurate estimation and possibly prevent the proper medical diagnosis. This paper proposes to do away with these limitations by using the framework of Unlimited Sampling (US) to address the recovery of the signal embedded in the phase. Compared to other unwrapping algorithms, the US framework provides perfect recovery guarantees in practical settings. Furthermore, we show through simulations that the US-based recovery algorithm greatly extends the resilience of the recovering process when encountering random body movements at comparable sampling rates.