## 4 Conclusions  
This paper proposed a modified GSC method to reduce the distortion of the enhanced signal using cross-correlation and sidelobe neutralization. The GSC-MCC method was proposed first by adding the cross-correlation coefficient between the cancelling signal and the error signal to the filter weight update path to control the distortion of the enhanced desired signal when the energy of the desired signal was increased suddenly. The beamforming sidelobe pattern was presented and combined with the conventional GSC method (refer to the GSC-SN method) to improve the denoising performance of the GSC method by reducing the noise component in the beamforming output signal of the GSC method. Finally, the GSC-SN-MCC method was proposed by combining the two methods to take advantage of them.  
The experiment was performed in the anechoic chamber, and the experimental data showed that the proposed method could reduce the enhanced signal distortion effectivity on different noise levels (the SNR range was between \(-20\) and \(20\) dB). The performance of the proposed method was better when the SNR condition was almost \(0\) dB. The simulated calculation was conducted to reveal the influence of the inaccurate estimated noise directions on the denoising performance of the proposed method. The calculation results showed that the proposed method could work effectively when the estimated noise direction was near the actual noise direction. Even if the estimated noise direction was far from the actual noise direction, the peak of the enhanced signal distortion would be decreased successfully, while the average of the enhanced signal distortion would still be similar  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Estimated Noise Direction/Degree** & **GSC** & **GSC-CC** & **GSC-SN** & **GSC-SN-MCC** \\ \hline \(-60\) & 100\% & 22.38\% & 105.90\% & 24.68\% \\ \(-30\) & 100\% & 22.38\% & 97.81\% & 23.04\% \\ \(0\) & 100\% & 22.38\% & 100\% & 22.38\% \\ \(30\) & 100\% & 22.38\% & 94.42\% & 21.15\% \\ \(60\) & 100\% & 22.38\% & 103.73\% & 20.55\% \\ \(90\) & 100\% & 22.38\% & 93.10\% & 18.44\% \\ \(120\) & 100\% & 22.38\% & 103.00\% & 23.60\% \\ \(150\) & 100\% & 22.38\% & 89.81\% & 21.52\% \\ \(180\) & 100\% & 22.38\% & 98.23\% & 23.62\% \\ \(-150\) & 100\% & 22.38\% & 93.95\% & 22.44\% \\ \(-120\) & 100\% & 22.38\% & 102.58\% & 25.06\% \\ \(-90\) & 100\% & 22.38\% & 96.50\% & 23.57\% \\ \hline \hline \end{tabular}  
* Normalized to result of the GSC method.  
\end{table}
Table 4: Distortion of the 83 rd frame with different methods in various estimated noise directions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Estimated Noise Direction/Degree** & **GSC** & **GSC-CC** & **GSC-SN** & **GSC-SN-MCC** \\ \hline \(-60\) & 100\% & 105.34\% & 112.55\% & 100.87\% \\ \(-30\) & 100\% & 105.34\% & 106.33\% & 91.93\% \\ \(0\) & 100\% & 105.34\% & 100\% & 88.07\% \\ \(30\) & 100\% & 105.34\% & 92.92\% & 76.27\% \\ \(60\) & 100\% & 105.34\% & 92.80\% & 68.32\% \\ \(90\) & 100\% & 105.34\% & 83.98\% & 59.01\% \\ \(120\) & 100\% & 105.34\% & 95.71\% & 80.68\% \\ \(150\) & 100\% & 105.34\% & 90.56\% & 76.15\% \\ \(180\) & 100\% & 105.34\% & 97.76\% & 82.98\% \\ \(-150\) & 100\% & 105.34\% & 94.29\% & 79.13\% \\ \(-120\) & 100\% & 105.34\% & 105.59\% & 93.54\% \\ \(-90\) & 100\% & 105.34\% & 102.98\% & 88.94\% \\ \hline \hline \end{tabular}  
* Normalized to result of the GSC method.  
\end{table}
Table 3: Average of the distortion–noise ratio with different methods in various estimated noise directions.  
to the conventional GSC method, which indicates the feasibility of the proposed method in practice.  
[PERSON]-[PERSON] gave academic guidance to this research work and revised the manuscript. [PERSON] designed the core methodology of this study, programmed the algorithms, carried out the experiments, and drafted the manuscript. Both authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.