Falls are among the most devastating events that can happen to an older person. Automatic fall detection systems aim to solve this problem by alerting carers and family the moment a fall occurs. This paper presents the development of an unobtrusive fall detection system using ultra-wideband (UWB) radar. The proposed system employed a ceiling-mounted UWB radar to avoid object occlusion and allow for flexible implementation. An innovative pre-processing method was developed to effectively enhance motion and reduce noise from raw UWB data. We designed a trial protocol composed of common types of falls in older population and activities of daily living (ADL). A fall detection algorithm based on convolutional neural networks was developed with simulated falls and ADLs obtained from ten participants following the trial protocol in a clear and cluttered living environment. The fall detection system achieved an accuracy of 93.97%, with a sensitivity of 95.58% and specificity of 92.68%.