# Adaptive Speech Separation Based on Beamforming and Frequency Domain-Independent Component Analysis
## 4 Simulations and Experiment
### Simulations  
In Simulation I, two sources are randomly chosen from the given four sources in Figure 5 and speech separation is conducted with the proposed algorithm. Because the proposed method can switch between ICA and beamforming according to mixing conditions at each frequency bin, its influence on separation performance should be researched. Therefore, the SIR improvement was calculated with Equation (33) when the usage ratio of ICA increases from 0% to 100%, and the simulated result is shown in Figure 6 for Room A and Figure 7 for Room B, where the horizontal axis denotes the usage ratio of ICA in percentage; the vertical axis denotes the SIR improvement by using the proposed method. The selected source compositions are SET1 in which Source 1 located in 90\({}^{\circ}\)and Source 2 located in 270\({}^{\circ}\), SET2 in which Source 1 located in 90\({}^{\circ}\)and Source 4 located in 0\({}^{\circ}\), SET3 in which Source 1 located in 90\({}^{\circ}\) and Source 3 located in 150\({}^{\circ}\), and SET4 in which Source 1 located in 90\({}^{\circ}\)and Source 3 whose theoretical position is decreased to 135\({}^{\circ}\). In Figure 6 for Room A, (a) is the separation result for SET1 when the localization result is 90\({}^{\circ}\) and 270\({}^{\circ}\); (b) is the separation result for SET2 when the localization result is 89\({}^{\circ}\) and 0\({}^{\circ}\); (c) is the separation result for SET3 when the localization result is 91\({}^{\circ}\) and 149\({}^{\circ}\); and (d) is the separation result for SET4 when the localization result is 91\({}^{\circ}\) and 133\({}^{\circ}\). Figure 5: Distribution of sound sources to evaluate the proposed speech separation algorithm. In Figure 7 for Room B, (a) is the separation result for SET1 when the localization result is 89\({}^{\circ}\) and 269\({}^{\circ}\); (b) is the separation result for SET2 when the localization result is 89\({}^{\circ}\) and 0\({}^{\circ}\); (c) is the separation result for SET3 when the localization result is 93\({}^{\circ}\) and 152\({}^{\circ}\); and (d) is the separation result for SET4 when the localization result is 92\({}^{\circ}\) and 135\({}^{\circ}\). Table 2 contains the simulated result of different cases. From the simulation results, the following conclusions can be obtained. 1. The localization result of our preprocessing method is accurate, and the largest deviation from the actual position is 3\({}^{\circ}\) in Room B. The accuracy of the localization algorithm has a slight relationship with indoor environment due to the reverberation. 2. Increasing the usage ratio of ICA improves the performance of our proposed algorithm. When ICA is employed more than 30%, the algorithm performance tends to be flat, suggesting that nearly 70% of the frequency components in the mixed signal are dominated by a single sound source and the other components contain signal mixtures. 3. The separation performance obtained by the DSB could be better than FDICA in some frequency bins. In Figure 6b,d and Figure 7a, the improved SIR obtained by the proposed method with the ratio of FDICA less than 30% is better. However, the situation of these frequency bins is hard to distinguish. 4. The indoor environment has a strong impact on separation performance. In Room A, the highest SIR improvement is about 16.8 dB, whereas for the lowest case, it is 10.2 dB. In Room B, the highest SIR improvement is about 13.0 dB, whereas the lowest SIR improvement is 4.8 dB. The intensity of the reverberation increases as the size of room decreases, so that the performance of separation degrades. 5. The angle between two sources is 180\({}^{\circ}\), 90\({}^{\circ}\), 60\({}^{\circ}\), and 45\({}^{\circ}\). Therefore, the performance of our proposed algorithm decreases with angle interval because of the use of the initialization of ICA separation matrix. The performance of separation is more susceptible to the angle between sources in the smaller room.