Disturbed sleep has become more common in recent years. To improve the quality of sleep, undergoing sleep observation has gained interest as a means to resolve possible problems. In this paper, we evaluate a non-restrictive and non-contact method for classifying real-time sleep stages and report on its potential applications. The proposed system measures heart rate (HR), heart rate variability (HRV), body movements, and respiratory signals of a sleeping person using two 24-GHz microwave radars placed beneath the mattress. We introduce a method that dynamically selects the window width of the moving average filter to extract the pulse waves from the radar output signals. The Pearson correlation coefficient between two HR measurements derived from the radars overnight, and the reference polysomnography was the average of 88.3% and the correlation coefficient for HRV parameters was the average of 71.2%. For identifying wake and sleep periods, the body-movement index reached sensitivity of 76.0%, and a specificity of 77.0% with 10 participants. Low-frequency (LF) components of HRV and the LF/HF ratio had a high degree of contribution and differed significantly across the three sleep stages (REM, LIGHT, and DEEP; p <; 0.01). In contrast, high-frequency (HF) components of HRV were not significantly different across the three sleep stages (p > 0.05). We applied a canonical discriminant analysis to identify wake or sleep periods and to classify the three sleep stages with leave-one-out cross validation. Classification accuracy was 66.4% for simply identifying wake and sleep, 57.1% for three stages (wake, REM, and NREM) and 34% for four stages (wake, REM, LIGHT, and DEEP). This is a novel system for measuring HRs, HRV, body movements, and respiratory intervals and for measuring high sensitivity pulse waves using two radar signals. It simplifies measurement of sleep stages and may be employed at nursing care facilities or by the general public to improve sleep quality.