Objective: Ultra-wideband (UWB) radar technology has emerged as a promising alternative for creating portable and cost-effective in-home monitoring devices. Although there exists good evidence supporting its effectiveness in sleep monitoring, previous studies predominantly focus on younger, healthy participants. This research evaluates the applicability of commercial impulse UWB radar for sleep monitoring in older people and people with neurodegenerative disorders (NDDs). Methods: 47 older people (mean age: 71.2 ± 6.5, 18 with prodromal or mild Alzheimer's disease) participated in our overnight sleep trial with polysomnography (PSG) and UWB radar monitoring. Data processing based on multivariate empirical mode decomposition (MEMD) was employed to reconstruct cardiopulmonary activity and limb movements from radar signals. 29 features were extracted from the radar signals, and sleep stages were classified using a sequence-to-sequence neural network. Additionally, a cross-entropy-based approach was used to quantify uncertainties in the radar classification model and provide confidence in the classification. Results: The UWB radar system demonstrated high accuracy in detecting body movements, reconstructing respiratory patterns, and monitoring heart rate. For sleep stage classification, the results showed a Kappa coefficient of 0.63 and an average accuracy of 74.4% across wake, REM sleep, light sleep (N1 + N2), and deep sleep (N3) categories. Conclusion: The proposed method reliably monitors physiological changes during sleep, which suggests its potential as a cost-effective alternative to traditional sleep monitoring devices. Significance: The findings underscore the viability of UWB radar as a nonintrusive, forward-looking sleep assessment tool that could significantly benefit care for older people and people with neurodegenerative disorders.