# Adaptive Speech Separation Based on Beamforming and Frequency Domain-Independent Component Analysis
## 4 Simulations and Experiment
### Simulations
In our simulation, the angle interval could not be less than 45\({}^{\circ}\), otherwise it can be considered that the effective separation function is lost. Figure 6: Signal-to-interference ratio (SIR) improvement with separation under dual sources in Room A. (**a–d**) correspond to SET1-SET4, respectively. In Simulation II, three sources were chosen from the given sources in Figure 5 and were used to conduct speech separation with the proposed algorithm. The selected sources composition is Source 1 located in 90\({}^{\circ}\), Source 3 located in 150\({}^{\circ}\), and Source 2 located in 270\({}^{\circ}\). The localization result of the preprocessing step is 91\({}^{\circ}\), 149\({}^{\circ}\), and 270\({}^{\circ}\) in Room A and 92\({}^{\circ}\), 153\({}^{\circ}\), and 269\({}^{\circ}\) in Room B, respectively. The separation evaluation is shown in Figures 8-10, where the horizontal axis is the usage ratio of ICA; the vertical axis is the SIR improvement by using the proposed method. In this simulation, with increasing the usage ratio of ICA, the SIR improvement of the proposed algorithm is not always increasing as expected, it fluctuates at some positions. Furthermore, the increasing speed of SIR improvement is slower than that of the previous simulation. The reason is that for multiple components at a frequency bin, when the dimension of ICA iteration is determined by the PCA and it is less than the number of real sound sources, the iterative convergence of ICA could reach a bad point, causing the SIR improvement decreases. Therefore, a modification has been made to the frequency with multiple components, where the PCA is still used to reduce dimensionality; however, the ICA iteration dimension is equal to the number of real sound sources when the result number of PCA is less than the number of sound sources. Therefore, the threshold of PCA does not influence the effective convergence of ICA. The final separation result of the modified algorithm is shown in Figures 8 and 9, where the problem in Figure 7 has been solved. The SIR improvement \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multirow{2}{*}{**Source**} & \multirow{2}{*}{\
\begin{tabular}{c} **True** \\ **Position** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Positioning** \\ **Result in** \\ **Room A** \\ \end{tabular} } & \multicolumn{2}{c}{**Improved**} & \multicolumn{2}{c}{**Positioning**} & \multicolumn{2}{c}{**Improved**} \\  & & & **Result in** & **Performance in** & **Result in Room** & **Performance in** \\  & & & **Room A** & **Room A** & **B** & **Room B** \\ \hline SET1 & S1, S2 & 90\({}^{\circ}\), 270\({}^{\circ}\) & 90\({}^{\circ}\), 270\({}^{\circ}\) & 16.3 dB, 14.2 dB & 89\({}^{\circ}\), 269\({}^{\circ}\) & 13.0 dB, 12.3 dB \\ \hline SET2 & S1, S4 & 90\({}^{\circ}\), 0\({}^{\circ}\) & 89\({}^{\circ}\), 0\({}^{\circ}\) & 16.8 dB, 14.4 dB & 89\({}^{\circ}\), 0\({}^{\circ}\) & 12.3 dB, 12.6 dB \\ \hline SET3 & S1, S3 & 90\({}^{\circ}\), 150\({}^{\circ}\) & 91\({}^{\circ}\), 149\({}^{\circ}\) & 16.6 dB, 14.7 dB & 93\({}^{\circ}\), 152\({}^{\circ}\) & 8.4 dB, 9.4 dB \\ \hline SET4 & S1, S3 & 90\({}^{\circ}\), 135\({}^{\circ}\) & 91\({}^{\circ}\), 133\({}^{\circ}\) & 10.2 dB, 11.2 dB & 92\({}^{\circ}\), 135\({}^{\circ}\) & 5.5 dB, 4.8 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results by proposed method under dual sources in Room A and Room B.  
Figure 7: SIR improvement with separation under dual sources in Room B. (**a–d**) correspond to SET1-SET4, respectively. increases with increasing the usage ratio of ICA, and its maximal value is larger than 16 dB in Room A, 8 dB in Room B when ICA is employed 20%. In Simulation III, all sources were chosen in Figure 5, and conducted speech separation with the proposed algorithm.