According to the World Health Organization and other authorities, falls are one of the main causes of accidental injuries among the elderly population. Therefore, it is essential to detect and predict the fall activities of older persons in indoor environments such as homes, nursing, senior residential centers, and care facilities. Due to non-contact and signal confidentiality characteristics, radar equipment is widely used in indoor care, detection, and rescue. This paper proposes an adaptive channel selection algorithm to separate the activity signals from the background using an ultra-wideband radar and to generalize fused features of frequency- and time-domain images which will be sent to a lightweight convolutional neural network to detect and recognize fall activities. The experimental results show that the method is able to distinguish three types of fall activities (i.e., stand to fall, bow to fall, and squat to fall) and obtain a high recognition accuracy up to 95.7%.