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Phase fading is fatal to the performance of distributed acoustic sensors (DASs) influencing its capability of distributed measurement as well as its noise level. Here, we report the experimental observation of a strong negative correlation between the relative power spectrum density (PSD) at the heterodyne frequency and the noise floor of the detected phase for the heterodyne demodulated distributed acoustic sensor (HD-DAS) system. We further propose a weighted-channel stack algorithm (WCSA) to alleviate the phase fading noise via an e