## 1 Introduction  
Obstructive Sleep Apnea (OSA) is the most common form of sleep-related breathing disorder (SRBD). OSA is characterized by repetitive obstruction of the upper respiratory tract during sleep, resulting in oxygen desaturation and frequent awakening. Its clinical importance is increasingly recognized [1; 2; 3; 4]. Sleep apnea affects sleep duration and quality, leading to chronic partial sleep deprivation, with the consequent widely acknowledged impaired neurocognitive function and daytime performance, increased risk of metabolic and cardiovascular diseases [1] (e.g., hypertension, coronary heart disease, life-threatening arrhythmias and strokes) and motor vehicle accidents [2], and diminished quality of life. Large prospective cohort community-based studies have demonstrated that sleep apnea increases risk of death [4]. Although OSA is a worldwide problem, affecting around 4% of men and 2% of women [4], the majority of affected individuals remain undiagnosed. The standard diagnostic tool for OSA is Polysomnography (PSG), which measures a wide range of parameters, including brain waves (EEG), eye movements, skeletal muscle activation, ECG/heart rate, airflow, respiratory effort, and blood oxygen saturation using a wide range of sensors. However, PSG requires costly measurement devices and labor-intensive set-up work for the electrode hook-ups, which often also disturb sleep. The technique also involves lengthy analysis requiring highly specialized staff. There is therefore growing interest in alternative approaches to the diagnostic assessment of OSA. Contact-type approaches include Respiratory Inductive Plethysmography (RIP) [4]. In this approach, the respiration rate is measured by measuring changes in the chest and/or abdominal volume by fastening belts around these areas. Thoracic-abdominal elastic belts measure changes in the body circumference during the respiratory cycle, detecting the change in the inductance of the belt due to the respiratory effort. This is an invasive technique for respiratory monitoring and this method requires accurate positioning and tightness of the belt. Other techniques are the electrocardiogram method [5], the nasal temperature probe [6], the contact-type microphone for audio analysis to monitor tidal volumes from human breathing activity [7], capacitive textile sensors [8] and pressure sensor arrays [9]. The main disadvantage of these technologies [4; 5; 6; 7] is their physical contact with the patient, which in some cases may be quite uncomfortable or impractical. Moreover, contact-type approaches often fail to monitor continuously because the devices can be unconsciously moved by the patient during sleep. All these methods require special beds or mattresses which can affect the patient's sleep. The recording may therefore not be a true indicator of the patient's daily sleep patterns. Doppler radars have been used in wireless sensor applications for decades [10; 11; 12; 13]. The first example of a radar-based vital sign monitoring system was developed in the mid-1980s [14]. Since then, there have been several works that report the utilization of Doppler radars for cardiopulmonary [10; 11; 12] and life detection to locate humans trapped in earthquake rubble [13]. On the other hand, vital sign monitoring using micropower impulse radar was proposed by [PERSON] [15]. Since then, the interest in ultra-wideband (UWB) radars for biomedical applications [16; 17] is increasing. Since the legalization of UWB by the FCC in 2002, UWB technology has awaken great interest in wireless communication [18; 19; 20] and radar sensor applications [21, 22, 23, 24]. This technology has unique features due to its extremely wide bandwidth. UWB wireless systems are generally based on the transmission and reception of sub-nanosecond pulses without carriers, or on the transmission of modulated short pulses with carriers. These wireless systems are simple, cheap, low-power and permit high data rates [18, 19].