## 3 Simulation and Analysis of Microphone Array Speech
### Comparison with Other Speech Simulation Methods  
In order to further verify the effectiveness of the proposed MASS method in real acoustic environment, the comparison of the MASS with the existing multi-channel speech simulation method (called MCS) [19] and SMARD method [6] is shown in this subsection. The noisy speech dataset of microphone array with reverberation simulated by the three methods is used for training a convolutional neural network (CNN)-based multi-channel speech enhancement method [19], respectively. Then three trained CNN models representing three different microphone array speech simulation methods are obtained. Three trained CNN models are tested using the microphone array speech in the real environment, and the CNN model with the best test results is expressed as the corresponding microphone array speech simulation method that can better simulate the real acoustic environment.  
To ensure the generality of the experiment, the same parameters and configurations are set in three different microphone array speech simulation methods, so that the three datasets describing the same  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Theoretical TDOA** & **Simulated TDOA** \\ \hline
1.3113 samples & about 1.3 samples \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the time difference of arrival (TDOA) for theoretical and simulated values.  
Figure 9: The spatial coherence of noise signals of microphone array.  
acoustic environment are obtained. The acoustic environment described in the dataset is similar to that in Figure 3. The only difference is that a four-channel uniform linear microphone array with a distance of 5 cm is used, which is to match real microphone array data during the testing. Each position of target speech source matches 20 different speech segments that are randomly selected from the TIMIT corpus [17]. The dataset uses four types of the SNR levels (e.g., \(-\)5 dB, 0 dB, 5 dB, and 10 dB) of babble noise and seven types of reverberation time (e.g., as 200 ms, 300 ms, 400 ms, 500 ms, 600 ms, 700 ms, and 800 ms), and the total duration is about 10 hours. During the test, clean speech of microphone array with reverberation is obtained from the real recorded speech in LibriSpeech corpus [20] by using three microphone array speech simulation methods, and then the final real speech for the testing is obtained by adding the real recorded meeting room noise signals in the DEMAND dataset [8]. In the test set, each position of target speech source is equipped with five different speech segments, with the SNR levels of \(-\)5 dB, 0 dB, 5 dB, and 10 dB, and reverberation time of 300 ms, 500 ms, and 700 ms. The test set duration is about 1 hour.  
The average results of all the speech on all the target speech source positions in real speech data are shown in Table 3. The improvements of perceptual evaluation of speech quality (PESQ) [21]\(\Delta\)P and short-time objective intelligibility (STOI) [22]\(\Delta\)S are used to test the corresponding results. As can be seen from Table 3, the CNN model trained by the proposed MASS method (called CNN_MASS) can achieve better speech enhancement effect than that trained by the MCS method (called CNN_MCS) or trained by the SMARD method (called CNN_SMARD). Especially in the case of low SNR levels, the simulation of isotropic spherically diffuse noise field in the proposed MASS method can better describe the real acoustic environment, so it can obtain a higher amount of improvement in the use of real data testing.  
Therefore, based on the above analysis, the proposed MASS can well simulate the room acoustic environment with isotropic spherically diffuse noise, so as to simulate the required speech signals of microphone array for the research of related fields. In the next section, the multi-channel speech coding and enhancement methods are further used to verify the proposed MASS.