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Falls have become a common health problem among older adults. In previous study, we proposed an acoustic fall detection system (acoustic FADE) that employed a microphone array and beamforming to provide automatic fall detection. However, the previous acoustic FADE had difficulties in detecting the fall signal in environments where interference comes from the fall direction, the number of interferences exceeds FADE's ability to handle or a fall is occluded. To address these issues, in this paper, we propose two blind source separation (BSS) methods for extracting the fall signal out of the interferences to improve the fall classification task. We first propose the single-channel BSS by using nonnegative matrix factorization (NMF) to automatically decompose the mixture into a linear combination of several basis components. Based on the distinct patterns of the bases of falls, we identify them efficiently and then construct the interference free fall signal. Next, we extend the single-channel BSS to the multichannel case through a joint NMF over all channels followed by a delay-and-sum beamformer for additional ambient noise reduction. In our experiments, we used the Microsoft Kinect to collect the acoustic data in real-home environments. The results show that in environments with high interference and background noise levels, the fall detection performance is significantly improved using the proposed BSS approaches.