## 2 The Proposed Method  
### The Conventional GSC Method  
The GSC algorithm can be separated into two transmission paths: the primary path and auxiliary path, as shown in Figure 1. The primary path generates a denoising signal with residual noise by the fixed beamforming method. The auxiliary path estimates the noise component in the output signal of the primary path. \(\omega_{m}\) is the weight vector to make the microphone array signal \(x(n)\) aligned in the look direction to suppress noise from the other direction. \(y_{m}(n)\) is the sum of the aligned signals as the beamforming output signal of the primary path. The auxiliary path estimates the noise component \(y_{b}(n)\) in the beamforming output signal of the primary path as the cancelling signal. The cancelling signal will be removed from the beamforming output signal. Hence, the enhanced signal \(y_{out}(n)\) consists of the desired signal, and the residual noise signal is obtained. The block matrix (BM) is adopted to generate the reference noise signal, excluding the desired signal from the noisy signal, in the auxiliary path for estimating the noise  
neglected. Therefore, \(\rho(k)\) is equal to the cross-correlation coefficient between the estimated noise signal \(y_{b}(k)\) and the residual noise signal \(n_{residual}(k)\) as expressed in Equation (4). This means that if the \(\rho(k)\) is small, the residual noise is nearly uncorrelated with the estimated noise, so the weight coefficient will be changed only slightly. Otherwise, the weight coefficient will be changed considerably to reduce the residual noise rapidly. Figures 3 and 4 illustrate the influence of the varying speech signal on the estimated noise signal. The input original of a speech signal was extracted from the TIMIT database [33], and the noise signal was the white noise obtained from the NOISEX-92 database [34]. Figure 3a shows the original speech and noise signal, in which the signal-to-noise ratio (SNR) was equal to \(-5\) dB (the ratio of the energy of the whole speech signal and the energy of the noise signal during the same time). Detailed information about the experiment implementation is depicted in Section 3. Figure 3b presents the cross-correlation coefficient between the estimated noise signal and the output signal with the conventional GSC method and the GSC-CC method. The negative peak of the cross-correlation coefficient with the conventional GSC method was generated when the amplitude of the speech signal increased suddenly (Figure 3b), which implies the phenomenon of over-subtraction. Figure 4 compares the energy of the estimated noise frame with different methods. Figure 4b displays the partially enlarged view of Figure 4a from the 50 th to the 100 th frame. The energy of the estimated noise frame with the conventional GSC method would increase when the energy of the speech frame was much more than the actual noise frame. The GSC-CC method could flatten the energy curve of the estimated noise frame, which is consistent with the trend of the energy curve of the original white noise signal. This means that the distortion of the enhanced speech signal was reduced for the desired signal, and it was damaged less when the amplitude of the speech signal changed. Figure 3: (**a**) Clean speech signal and white noise signal; (**b**) cross-correlation coefficient with different methods. Figure 2: Block diagram of the GSC method with the cross-correlation coefficient. The GSC-CC method could decrease the overestimation of the noise efficiently when the desired speech signal amplitude was increased suddenly (Figure 4). On the other hand, the figures also show that the energy curve of the estimated noise frames with the GSC-CC method was lower than the conventional GSC method. As the correlation coefficient was less than or equal to one, the step size of the adaptive filter of the GSC-CC method was smaller than the GSC method. Consequently, the energy of the residual noise signal with the GSC-CC method was higher than the conventional GSC method.