Annually, a significant number of premature infants suffer from apnea, which can easily cause a drop in oxygen saturation levels, leading to hypoxia. However, infant cardiopulmonary monitoring using conventional methods often necessitates skin contact, and they are not suitable for long-term monitoring. This article introduces a non-contact technique for infant cardiopulmonary monitoring and an adjustable apnea detection algorithm. These are developed using a custom-designed K-band continuous-wave biomedical radar sensor system, which features a DC-coupled adaptive digital tuning function. By using radar technology to detect chest motions without physical contact, it is feasible to extract significant biological information regarding an infant's respiration and heartbeat. The proposed algorithm utilizes an adaptively adjusted threshold and personalized apnea warning time to automatically measure the total number of apneic events and their respective durations. Experiments have been conducted in clinical environment, demonstrating that both the accurate cardiopulmonary signals and the apneas of varying durations can be effectively monitored using this method, which suggest that the proposed technique has potential applications both inside and outside of clinical settings.