# Iteratively Refined Multi-Channel Speech Separation
## 4 Results  
### Analysis of Iterative Results  
The separation results of our proposed method at different stages are shown in Table 2. Here, \(\hat{y}_{q,1}^{(n)}\) denotes the speech signal from each speaker on the first microphone after the TFDPRNN module at the \(n^{\text{th}}\) stage, and \(\hat{z}_{q}^{(n)}\) denotes the speech signal from each speaker after the MVDR beamformer at the \(n^{\text{th}}\) stage. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dataset** & **Number of Samplers** &
\begin{tabular}{c} **Total Duration** \\ **(h)** \\ \end{tabular} \\ \hline Training & 20,000 & 30 \\ Development & 5000 & 10 \\ Testing & 3000 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of data used for training, development, and testing. From Table 2, we can see that after the first iteration, the SDR performance of \(\hat{z}_{q}^{(n)}\) increased by 17.46% and the SI-SDR performance of \(\hat{z}_{q}^{(n)}\) increased by 22.66%. This shows that the first iteration brought high gains to our model. However, after the second iteration, although some improvement was still observed with each iteration, the performance improvements of \(\hat{z}_{q}^{(n)}\) in SDR and SI-SDR were very slow, with an increase of less than 1%. This indicates that as the number of iterations increased, the estimation of the SCM became more accurate and gradually approached the inherent upper performance limit of MVDR beamforming. On the other hand, \(\hat{y}_{q,1}^{(1)}\) improved by about 51% over \(\hat{y}_{q,1}^{(0)}\) in SDR and SI-SDR, and \(\hat{y}_{q,1}^{(2)}\) also improved by about 11% over \(\hat{y}_{q,1}^{(1)}\) on these two metrics. In the subsequent stages, although the performance continually improved, the rate of improvement was less than 2%. The performances of \(\hat{y}_{q,1}^{(n)}\) and \(\hat{z}_{q}^{(n)}\) on the SIR and PESQ improved after each iteration. The STOI performance of \(\hat{y}_{q,1}^{(n)}\) and \(\hat{z}_{q}^{(n)}\) remained at about 0.99. Overall, the performance of our model obviously improved during the iteration process. In order to describe the results of the method graphically, Figure 3 shows a comparison of the spectrograms for a single speaker. They include the original clean speech signal, the original reverberant speech signal, the mixed speech signal, the output signals of the neural network at different stages, and the output signals of the beamformer at different stages, respectively. The colors in the spectrogram correspond to the energy levels of the spectral components. Observing the output spectrograms of neural network in the left column, it is clear when the processing stage increased, the clarity and quality of the spectrograms gradually improved. For example, compared with the spectrogram of the original reverberant signal, it can be observed that certain spectral components in the spectrogram of the first neural network were reduced (e.g., the red circles). After iterative processing, these signal components gradually recovered in the spectrogram of the second neural network. In the speech spectrogram in the right column, the separation effect of the beamformer at different stages can be observed; there were no significant changes or improvements. When comparing the speech spectrograms in the left and right columns, we can see that the output spectrograms processed by the neural network exhibited relatively higher clarity compared with those processed by the beamformer. This comparison reveals the potential advantages of neural networks in processing speech signals. In general, the iteration of MVDR and post-separation is fully employed for promoting their individual optimization, which ultimately improves overall performance. In addition, the outputs of MVDR and post-separation can both be used as the final output of the model. However, the performance of the output of post-separation was better than that of the MVDR beamformer, according to Table 1, so the former was used as the final output of the model.