This paper discusses fall detection technology, which is becoming increasingly important due to the increasing elderly population, which is expected to reach 2.1 billion by 2050. To address the data shortage and privacy issues of existing methods, this paper proposes an IoT-based fall detection as a service (FDaaS) framework. We design a service-oriented architecture that utilizes ultra-wideband (UWB) radar sensors to ensure privacy protection and minimal intrusion, and address the data shortage issue through a fall detection pre-trained transducer (FD-GPT) that uses data augmentation techniques. We develop a protocol to collect a comprehensive dataset of daily activities and fall events of the elderly, and generate a real dataset that accurately mimics the daily lives of real elderly people. We use this dataset to rigorously evaluate and compare various models. The experimental results show that the proposed method achieves 90.72% accuracy and 89.33% precision in distinguishing fall events from daily activities.