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In this paper, we introduce a time varying smoothing factor for the noise update in the optimal filtering based on QR decomposition (QRD). Conventionally, the noise statistics are updated during noise-only periods and kept fixed during speech present periods in QRD-based multichannel noise reduction [G. Rombouts and M. Moonen, Sept 2003]. Instead of using this conventional scheme that needs an explicit voice activity detector (VAD), we adopt a time varying smoothing factor which is parameterized from the normalized cross correlation (NCC). In a multi-microphone based system, the NCCs between two microphones can be used for finding the direction of signals [M. Omologo and P. Svaizer, 1994]. Provided that we know the direction of the speech signal and the time delays between microphones are compensated, the NCCs can be considered as a measure for the speech presence probability. The NCCs are estimated for a given time interval, and they are averaged over the microphones and smoothed in time. Then the averaged value is mapped to a smoothing factor through a nonlinear function. The simulation results show that the proposed algorithm yields better performance compared to the conventional QRD-based noise reduction.