# An Efficient Multistage Approach for Blind Source Separation of Noisy Convolutive Speech Mixture
## 5 Performance Evaluation  
In this section, the separation performance of the proposed model is compared with various multistage BSS approaches with different source priors such as multivariate super-Gaussian [31], Student's T [42], and generalized Gaussian distributions [32]. The two proposed multistage models use the BSS approach to separate the estimated speech signals from the noisy convolutive mixture followed by the MMSE filtering technique to de-noise the signals. For the performance evaluation of first model, we generated 20 different noisy convolutive speech mixtures with the help of a simulated room model by randomly selecting speech signals from a pool of 10 source speech signals (five male and five female). We varied SNR and RT to obtain the average results where the SNR varies between \(-2\) to 10 dB with window length = 512, NFFT = 1024, and RT = 100 msec. The average results are presented in Table 1 in terms of SDR, showing that the proposed model gains an enhancement of 0.3 dB for \(\hat{S_{1}}\) and 0.5 dB for \(\hat{S_{2}}\). Moreover, the proposed model is compared with the literature, showing its effectiveness with optimum gains of 0.2 and 1 dB for both estimated speech signal \(\hat{S_{1}}\) and \(\hat{S_{2}}\), respectively. Additionally, RT was varied from 40 to 200 msec with a window length = 512, FFT frame length = 1024, and SNR = 4 dB. The noisy reverberant mixtures were fed to the proposed model and the other multistage BSS methodologies [31; 32; 42]. The average objective analysis results are presented in Table 2, which shows performance gains for the proposed model of 0.3 and 0.4 dB for \(\hat{S_{1}}\) and \(\hat{S_{2}}\) in comparison with other BSS approaches. The proposed approach also shows significant performance improvements of 3.81 and 2.9 dB for the estimated source signals \(\hat{S_{1}}\) and \(\hat{S_{2}}\), respectively, from the multistage BSS  
Figure 8: Normalized energy in different frequency bins of observed mixture 2. Figure 7: Normalized energy in different frequency bins of observed mixture 1.  
having a source prior [42]. The objective analysis is also compared with [32], in which the proposed method shows optimum improvements of 0.16 and 0.2 dB for \(\hat{S}_{1}\) and \(\hat{S}_{2}\), respectively. For the performance evaluation of the second model, the noisy reverberant mixtures were de-noised by using the MMSE filtering technique in the first stage. In the second stage, the estimated speech signals were separated from the de-noised mixture using the BSS method. The average results based on objective analysis by varying SNR are shown in Table 3. It can be seen in Table 3 that the proposed model shows a performance improvement of 0.2 dB for both \(\hat{S}_{1}\) and \(\hat{S}_{2}\) in comparison with other multistage BSS approaches. The results in Table 3 show that the proposed approach achieved significant performance improvements of 0.7 and 0.8 dB in comparison with the Student's T method [42] for estimated source signals \(\hat{S}_{1}\) and \(\hat{S}_{2}\), respectively. Moreover, Table 3 demonstrates that the proposed approach shows 0.1 and 0.4 dB gains from [32] for \(\hat{S}_{1}\) and \(\hat{S}_{2}\), respectively. The objective evaluations with variable RT, having a window size = 512, FFT = 1024, and SNR = 4 dB, are provided in Table 4. From Table 4, the proposed model shows performance gains of 1.7, 2.14, and 0.21 dB for \(\hat{S}_{1}\) and 0.6, 1.63, and 0.4 dB for \(\hat{S}_{2}\) in comparison with [31; 32; 42], respectively. Experiments were also performed to cross verify the simulations where the window length, NFFT, and RT parameters were set to 512, 1024, and 100 msec, respectively. The five participants were asked to mark the MOS of the estimated speech signals extracted from the multistage BSS model with source prior [31; 32; 42] and the two proposed methods. The average MOS results from the first model are presented in Tables 5 and 6, with variable SNR and RT, respectively.