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The global rise in the elderly population has increased the demand for effective fall detection in Ambient Assisted Living (AAL) environments. This paper introduces a novel and reliable fall detection system utilizing frequencymodulated continuous wave (FMCW) radar, designed to address privacy concerns, operate reliably in low-light conditions, and provide ease of installation. Data from two wall-mounted radars capture a variety of activities, including simulated falls, across five configurations to enhance model generalizability. Radar data processing employs the Fast Fourier Transform (FFT) and the Capon algorithm to generate Range-Azimuth and Range-Elevation maps, which serve as input features for a proposed 3D Convolutional Neural Network (3D CNN) model. This model achieves an accuracy of 94.33% and F1-score of 93.5%, combining high performance with adaptability across diverse environments and user needs. This work provides a robust solution for fall detection with significant potential for deployment in real-world elderly care settings.