## 4 Applications in Multi-Channel Speech Coding and Enhancement
### Application in Multi-Channel Speech Enhancement  
In order to verify the accuracy of the MASS more comprehensively, we propose a multi-channel speech enhancement for the microphone array speech simulated by the proposed MASS, which is the integration of the weighted prediction error (WPE)-based dereverberation method [30] and complex Gaussian mixture model-based minimum variance distortionless response (CGMM-MVDR) beamforming method [31] (called WPE-CGMM-MVDR). Figure 13 shows the block diagram of the WPE-based dereverberation method, the CGMM-MVDR beamforming method, and the proposed WPE-CGMM-MVDR method using Figure 13a-c, respectively. The inputs of the system consist of noisy speech, clean speech with reverberation, or noisy speech with reverberation of microphone array that are simulated by the MASS. For dereverberation performance evaluation, such as Figure 13a, the input microphone array clean speech with reverberation goes through the WPE-based dereverberation module, which achieves the purpose of removing the reverberation part after 20 iterations. For the denoising performance evaluation, such as Figure 13b, a beamformer that uses a novel steering vector estimation method based on time-frequency masks is employed. The time-frequency masks are used to avoid inaccurate prior knowledge such as array geometry and plane wave propagation assumption. Thus, it provides a robust steering vector estimation. Here, the time-frequency masks are estimated by using a spectral model based on the CGMM. For the microphone array noisy speech with reverberation, such as Figure 13c, the WPE-based dereverberation and the CGMM-MVDR beamforming are integrated together to implement a complete speech enhancement system that can also finish dereverberation and denoising tasks.  
Figure 13: The block diagram of the multi-channel speech enhancement method: **(a)** Weighted prediction error (WPE)-based dereverberation method; **(b)** complex Gaussian mixture model-based minimum variance distortionless response (CGMM-MVDR)-based denoising method; **(c)** WPE-CGMM-MVDR-based dereverberation and denoising method.  
After the multi-channel speech enhancement experiments, the enhanced speech is obtained. The PESQ, STOI, SSNR, and LSD are used to evaluate the quality of the enhanced speech as well. The average evaluation results of Target 1 to Target 20 are shown in Figure 14. Among them, the test results of noisy speech, clean speech with reverberation, and noisy speech with reverberation come from reference microphone 0 in Figure 3.  
Through Figure 14, we can clearly see the multi-channel speech enhancement results of the microphone array speech obtained by the proposed MASS. Experimental results show that whether it is dereverberation, denoising, or dereverberation plus denoising at the same time, the speech enhancement effect is still obvious even at a low SNR level. This phenomenon is consistent with the characteristics of the corresponding speech enhancement method. Therefore, we can draw a conclusion that the speech simulated by the proposed MASS method can be used in the research of multi-channel speech enhancement.