## 3 Simulation and Analysis of Microphone Array Speech
### Analysis of the Simulated Microphone Array Speech  
With the room shape, target speech sources, and microphone array parameters described above, we can build the required microphone array speech by setting noise signal (such as babble noise), SNR level, absorption factor, which reflects the RT\({}_{60}\), and other parameters. The clean target speech used is randomly selected from TIMIT corpus [17]. Figure 5 depicts a real RIR with the RT\({}_{60}\) of 500 ms and Figure 6 shows the simulated RIRs between Target 1 and each microphone when the RT\({}_{60}\) is 500 ms. From the RIRs shown in Figure 6, we can clearly see that the simulated RIRs have similar positive and negative values as the real ones and obviously show the three features, direct path, early echoes, and reverberation, are similar to those in Figure 5. So, the speech signals of microphone array obtained by the RIRs can simulate the real microphone array speech well. Figure 7 shows the spectrograms of clean speech, noisy speech, clean speech with reverberation, noisy speech with reverberation, and noise signals of microphones array for Target 1 when the RT\({}_{60}\) is 500 ms and the SNR level is 5 dB. Figure 4: The abstracted meeting room acoustic environment with 20 target speech sources and a uniform linear microphone array. Figure 5: The real room impulse response (RIR) for the RT\({}_{60}\) of 500 ms.  
From Figure 7, we can watch various types of speech and noise signals in each microphone. As a whole, due to the close distance between each microphone, the speech signals between each channel are very similar, but when we carefully observe their time-domain waveforms, we can clearly see their differences. In order to verify whether the simulated microphone array speech conforms to the sound wave propagation model, we draw a segmental time-domain waveform of clean speech of microphone array  
Figure 6: The RIRs between Target (Tar.) 1 and each microphone (Mic.) when the RT\({}_{60}\) is 500 ms.  
Figure 7: The spectrograms of clean speech, noisy speech, clean speech with reverberation, noisy speech with reverberation, and noise signals of microphone (Mic.) array for Target 1 when the RT\({}_{60}\) is 500 ms and the signal-to-noise ratio (SNR) level is 5 dB. in Figure 8a and a segmental comparison waveform with Target 1 in Figure 8b. The selected speech waveforms are enlarged for observing the relationship of each waveform. Through Figure 8, we can clearly see that there is a large amplitude attenuation and propagation delay between Target 1 and the speech signals of microphone array. In addition, we also find that amplitude attenuation and propagation delay between the microphones are small. According to sound wave propagation model given in [18], the speech signals of microphone array and target speech signals have the following approximate relationship:  
\[x_{i}(t)=\sigma s_{j}(t-\tau)=\frac{10}{\sqrt{4\pi q_{ij}}}s_{j}(t-\frac{q_{ij} }{c}) \tag{10}\]  
where \(\sigma\)and \(\tau\)represent amplitude attenuation factor and propagation delay, respectively. \(x_{j}(t)\) and \(s_{i}(t)\) represent speech signal of the \(i\)th microphone and the \(j\)th target speech source, respectively. \(q_{ij}\) is the  
Figure 8: Time-domain waveform comparison; (**a**) clean speech signals of microphone array; (**b**) clean speech signals of microphone array together with the Target 1.  
distance from the target speech source \(j\)th to the \(i\)th microphone. Based on Equation (10) and time-domain waveform shown in Figure 8, we can quantitatively analyze the accuracy of time difference of arrival (TDOA) for microphone array.