## 1 Introduction
There are also many advantages of using this technology for biomedical applications [16, 17, 21, 22]. Since UWB technology radiates and consumes low power, it works well with other instruments, and it is robust to narrowband and multipath interferences due to its large bandwidth [18]. UWB monitoring of breathing and heart rate has been studied in [15, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36] as an alternative to Doppler-based systems. From the pioneering work presented by [PERSON] [15] some other works ([15, 25, 26, 27, 31, 32]) have shown the feasibility of estimating the breathing rate using a wireless, contactless and non-invasive respiratory monitoring system based on low-cost commercial UWB radars that can be used in PSG studies and home respiratory applications. An analytical framework to analyze respiration rate estimation from a received UWB waveform has been presented in [27]. Other works have been focused in the detection of breathing and heart rate simultaneously using UWB radars [25, 31, 32]. These works show that the estimation of heart beat is a challenge because it could be masked by two undesirable phenomena: the noise and the intermodulation between the breathing and the own heart signals [35]. In order to reduce these interferences due to the harmonics of the breathing signal on the heart signal, a harmonic filter has been proposed in [35]. The interest of contactless monitoring systems using both radar systems has increased in the last years. Using UWB or Doppler radars, the breathing signal can be detected with reasonable accuracy even behind walls [28, 29, 35], which is especially important in rescue applications. Furthermore, wearable UWB sensors have been proposed for vital sign monitoring [30] and body area network applications [37]. The main drawback of UWB radars for vital sign monitoring is the lack of low-cost integrated circuits (IC), whereas Doppler radars can be implemented using standard microwave components. Due to the lack of UWB ICs the first demonstrations often used hybrid microwave solutions [15, 31, 32] or high-cost laboratory equipment such as wideband oscilloscopes and pulse generators [27]. Nowadays the situation has changed. Commercial development kits [38, 39] have appeared in the last years. Several groups have recently developed CMOS integrated circuits that implement UWB radar solutions for vital sign monitoring [30, 33, 34, 40]. However, there are some open challenges to which this manuscript intends to contribute. Long-duration signals must be analyzed in apnea studies. Some random motions can therefore affect the breathing rate estimation. These intervals must be detected in order to mitigate these sources of errors. Furthermore the amplitude of chest displacement changes with time. As a result, when detecting the event when breathing ceases, a dynamic method to estimate the decision threshold is required. A previously proposed UWB system for monitoring breathing [35] uses two antennas pointed towards the chest-one for transmission and the other for reception. The performance of these systems depends on their orientation [41, 42, 43], but unfortunately they are also sensitive to the movement of the subject. Since one fixed antenna is used, if the human subject is not facing the antenna at a sufficiently small angle, the backscattered signal comes mostly from the side of the body and not from the chest area, resulting in poor estimation accuracy [43]. During sleep, the patient may turn and sleep on his side or backwards. The major challenge for a practical application of night breathing monitoring system is the noise signal produced by the body motion. Multi-static radars have previously been proposed for target tracking problems and localization (see for instance [44, 45]). The main contributions of the paper are described below. First, a moving averaging filter to dynamically remove quasi-static clutter to enhance the breathing signal detection is proposed.