Falls are a major health concern for the elderly as it threatens their livelihood and independence. Nearly 50% of the older adults, aged over 65 years old, fall in a span of 5 years, with 62% sustaining injuries and 28% extensive protracting injuries. This paper presents a high accuracy contactless falls detection framework based on channel state information extracted from software-defined radios. The aim is to develop a system capable of detecting whether an individual subject is present within the sensing area, or if the subject is falling, and, finally, if the subject is performing one of three other activities, including sitting, standing, and walking. The results showed a promising detection accuracy of 95.6% and 98%, using the 10-fold cross-validation and train-test split methods, based on the Random Forest classifier, respectively. Furthermore, we present a real-time analysis of the system to highlight its capability to detect, analyze, and report falls in real-time.