###### Abstract  
The generalized sidelobe canceller (GSC) method is a common algorithm to enhance audio signals using a microphone array. Distortion of the enhanced audio signal consists of two parts: the residual acoustic noise and the distortion of the desired audio signal, which means that the desired audio signal is damaged. This paper proposes a modified GSC method to reduce both kinds of distortion when the desired audio signal is a non-stationary speech signal. First, the cross-correlation coefficient between the canceling signal and the error signal of the least mean square (LMS) algorithm was added to the adaptive process of the GSC method to reduce the distortion of the enhanced signal while the energy of the desired signal frame was increased suddenly. The sidelobe pattern of beamforming was then presented to estimate the noise signal in the beamforming output signal of the GSC method. The noise component of the beamforming output signal was decreased by subtracting the estimated noise signal to improve the denoising performance of the GSC method. Finally, the GSC-SN-MCC method was proposed by merging the above two methods. The experiment was performed in an anechoic chamber to validate the proposed method in various SNR conditions. Furthermore, the simulated calculation with inaccurate noise directions was conducted based on the experiment data to inspect the robustness of the proposed method to the error of the estimated noise direction. The experiment data and calculation results indicated that the proposed method could reduce the distortion effectively under various SNR conditions and would not cause more distortion if the estimated noise direction is far from the actual noise direction. microphone array; generalized sidelobe canceller; cross-correlation; sidelobe neutralization +
Footnote †: journal: Applied  
17 May 2021  
total power of the final output signal. [PERSON] [3] developed the MVDR method that extended the constraint in the MVDR method to linear equations. Therefore, the weight coefficients could be adjusted adaptively based on the constraints. This method is referred to as the linearly constrained minimum variance (LCMV) method. The constraints could be independent of the LCMV method to simplify the algorithm. [PERSON] and [PERSON] [4] proposed the generalized sidelobe canceller (GSC) method in 1982. The GSC method consisted of three parts. The first part is the same as a conventional beamforming method to reduce the noise roughly. The second part is a block matrix to generate a reference noise signal by removing the desired signal from the original multichannel signals. The third part is an adaptive filter to estimate the noise component of the first part's output signal. Then, the estimated noise is subtracted from the output signal of the first part to obtain a cleaner desired signal. The GSC method converts the optimization goal of the LCMV method from the optimal weights with constraints to the optimal weights without constraints. Therefore, the simple adaptive algorithm could be adopted to reduce the residual noise in the final output signal. The three parts of the GSC method could be optimized individually to improve the aggregate denoising performance of the adaptive algorithm. [PERSON] et al. [5] and [PERSON] et al. [6] modified the block matrix to decrease the sensitivity of the GSC method to a mismatch between the estimated and actual direction of arrival (DOA) of the desired signal. The robustness of the GSC method was increased by reducing the leakage of the desired signal into the reference noise signal [7]. [PERSON] et al. [8] considered the complicated acoustic environments and proposed a transfer function GSC (TF-GSC). The block matrix of the TF-GSC method was modified with the transfer function ratio (between different microphones in an array) to adapt the GSC method to reverberation conditions. [PERSON] et al. [9] combined the TF-GSC with an acoustic echo cancellation to improve the performance of the algorithm in noisy and reverberant environments. [PERSON] et al.