###### Abstract
[10] also extended the TF-GSC method to the DFT-GSC method for double talk scenarios to cancel the nonstationary interferences signal. [PERSON] et al. [11] estimated a room impulse response and a desired speech signal model jointly to reduce the computational complexity dramatically for specific applications. [PERSON] et al. [12] estimated the acoustical transfer function ratios in the presence of stationary noise and tracked the eigenvector adaptively to obtain better noise and interference reduction. The GSC method also could be optimized by using efficient complex value arithmetic to reduce the calculation complexity [13] and by introducing the external microphones into the local microphone array to improve the performance of the speech estimate [14]. The least mean square (LMS) algorithm is a common adaptive algorithm for the GSC method to estimate the noise signal. The LMS algorithm adjusts the filter coefficients to make the mean square of the error signal (difference between the canceling signal and the received noise signal) lowest [15,16]. The stochastic gradient descent method has been used to ensure that the error signal can be decreased iteratively in real-time, which was derived by [PERSON] and [PERSON] [17] in 1960. Several modified LMS algorithms were proposed for some practical consideration. [PERSON] and [PERSON] [18] introduced the normalized LMS (NLMS) algorithm to make the algorithm convergence speed independent of the reference signal power, because the step size of the filter coefficient updating was inversely proportional to the reference signal power. [PERSON] and [PERSON] [19] proposed the correlation LMS algorithm, which adjusted the step size of the filter coefficient updating to be proportional to the cross-correlation coefficient between the reference signal and the error signal. This means that when the reference signal and the error signal are uncorrelated, the step size will be too small to update the weight coefficients of the adaptive filter. This step size control scheme makes the adaptive algorithm more robust to disturbances, such as the system-measured noise. [PERSON] et al. [20] proposed the leaky LMS algorithm, in which a leakage factor was added to the adaptive weight update path. The leakage factor could avoid the overflow of the unconstrained weight to increase the stability of the algorithm. Some studies [21; 22; 23] introduced post-filtering methods to the microphone array for additional noise reduction to the beamforming output signal. Some studies [24; 25; 26] decomposed the multichannel signal into two subspace domains, the desired signal subspace domain and noise signal subspace domain, based on statistic features (like the singular value decomposition of the covariance matrix of the multichannel signal). The signal in the noise subspace domain was removed or suppressed, and the desired signal was restored from the desired signal subspace domain. Some researchers [27; 28] attempted to extract the desired signal that had been contaminated by noise without a signal model or transmission model, which can be referred to as blind source separation or independent component analysis, most of which were based on the statistic features or a neural network. This research is mainly in the laboratory stage because of the complexity of calculation and the feasibility in actual environments. The distortion of the enhanced signal consists of two parts: the residual noise and the distortion of the desired signal, which means that the desired signal is damaged. Most researchers attempted to reduce the residual noise of the output of the microphone array. In contrast, the desired signal is sometimes a nonstationary signal, as in speech application. The varying speech signal may damage the desired signal and degrade the denoising performance of the adaptive algorithm. Some researchers [29] employed the voice activity detection (VAD) method to make the algorithms only to be adjusted in speech-absent frames and avoid the affection of a varying speech signal.