# Interaural Coherence Estimation for Speech Processing in Reverberant Environment
## 3 Numerical Experiment and Results
### IC Estimation Performance Comparison with Conventional Method
In each reverberation environment, the maximum values of the averaged \(\text{MAC}_{\text{total}}\) of the conventional method were 0.0008, 0.0255, and 0.0524 lower than the averaged \(\text{MAC}_{\text{total}}\) of the proposed method with the optimal parameters. Thus, the estimation performance of the proposed method was better in each reverberation environment compared to the conventional method with optimal \(\alpha\). In the previous numerical experiment of determining parameters, \(L_{\text{T}}\) and \(\beta\) with STFT using a longer window and longer hop lengths were determined. Based on these parameters, the performance of the proposed method was also compared with that of the conventional method using STFT with a 64-ms Hamming window, 16-ms hop length, and 1024-point FFT. The average \(\text{MAC}_{\text{total}}\) according to \(\alpha\) was calculated for the same 1680 speech samples, and the results obtained for the conventional and proposed methods are shown in Figure 5. They are similar to the results obtained using short STFT variables, and \(\alpha\) for the maximum of the averaged \(\text{MAC}_{\text{total}}\) was the optimal value for the conventional method. It was 0.65 in 0.37 s of \(\text{RT}_{60}\), 0.40 in 0.69 s of \(\text{RT}_{60}\), and 0.25 in 0.79 s of \(\text{RT}_{60}\). In each reverberation environment, the maximum values of the averaged \(\text{MAC}_{\text{total}}\) of the conventional method were 0.0236, 0.0494, and 0.0017 higher than the averaged \(\text{MAC}_{\text{total}}\) of the proposed method with the optimal parameters. Therefore, when large STFT variables were applied, the conventional method achieved better performance for the environment with reverberation. Although the proposed method with the optimal \(L_{\text{T}}\) and \(\beta\) had higher \(\text{MAC}_{\text{total}}\) than the conventional method using STFT with 512-point FFT, the \(\text{MAC}_{\text{total}}\) only represents the overall estimation performance of the IC. By comparing the ICs for each time-frequency bin of reverberation speech, we tried to identify the characteristics of the bins where each method accurately estimated the coherence. The IC estimation method was applied to an utterance with 0.79 s of \(\text{RT}_{60}\) environment where the difference of the \(\text{MAC}_{\text{total}}\) was largest. Spectrograms of the clean speech and the reverberant speech using STFT with a 25-ms Hamming window, 10-ms hop length, and 512-point FFT are represented as (a) and (b) in Figure 6. Due to the effect of reverberation, the time-frequency bins of the direct speech were not exactly known in the spectrogram of the reverberation speech. In this case, the clean speech was known; thus, the bins of the direct speech could be determined using it, and the binary mask of the direct speech is represented as (c) in Figure 6. For the reverberant speech, the ICs were calculated by applying the proposed method  
Figure 4: Averaged \(\text{MAC}_{\text{total}}\) using short-time Fourier transform (STFT) with a 25-ms Hamming window, 10-ms hop length, and 512-point FFT for 1680 speech samples of conventional and proposed methods in (**a**) 0.37 s, (**b**) 0.69 s, and (**c**) 0.79 s of \(\text{RT}_{60}\). and the conventional method, and each result was as shown in (d) and (e) of Figure 6. It is difficult to visually compare the difference between the estimated coherences. To solve this problem, the difference in the coherence accuracy (\(\Gamma^{2}\) in the direct speech bins and \(1-\Gamma^{2}\) in the diffuse speech bins) of each method was calculated as shown in (f) of Figure 6. If the difference of the coherence accuracy is greater than zero, the proposed method estimated the IC more accurately; otherwise, the conventional method estimated the IC more accurately. It can be seen that the light-colored bins, which were larger than zero, almost matched the direct speech mask in (c). Among the figures, the difference in coherence accuracy was larger at the boundary between direct and diffuse speech bins.