Recent years have witnessed advances of Internet of Things (IoT) technologies and their applications to enable contactless sensing and elderly care in smart homes. Continuous and real-time respiration monitoring is one of the important applications to promote assistive living for elders during sleep and attracted wide attention in both academia and industry. Most of the existing respiration monitoring systems require expensive and specialized devices to sense chest displacement. However, chest displacement is not a direct indicator of breathing and thus false detection may often occur. In this paper, we design and implement a real-time and contactless respiration monitoring system by directly sensing the exhaled airflow from breathing using ultrasound signals with off-the-shelf speaker and microphone. Exhaled airflow from breathing can be regarded as air turbulence, which scatters the sound wave and results in Doppler effect. Our system works as an acoustic radar which transmits sound wave and detects the Doppler effect caused by breathing airflow. We mathematically model the relationship between the Doppler frequency change and the direction of breathing airflow. Based on this model, we design a Minimum Description Length (MDL) based algorithm to effectively capture the Doppler effect caused by exhaled airflow. We conduct extensive experiments with 25 participants (7 elders, 2 young kids and 16 adults, including 11 females and 14 males) in four different rooms. The participants take four different sleep postures (lying on one's back, on right/left side and on one's stomach) in different positions of the bed. Experiment results show that our system achieves a median error lower than 0.3 breaths/min (2%) for respiration monitoring and can accurately identify Apnea. The results also demonstrate that the system is robust to different respiration styles (shallow, normal and deep), respiration rate variation, ambient noise, sensing distance variation (within 0.7 m) and transmitted signal frequency variation