# Iteratively Refined Multi-Channel Speech Separation
## 4 Results
### Comparison with Reference Methods  
At present, there are two kinds of mainstream methods to address the task of multi-channel speech separation; one is the frequency domain-based separation method, the other is the time domain-based separation method. The most popular multi-channel speech separation methods are listed as follows:  
1. Filter-and-sum networking (FaSNet) [26] is a time-domain method that uses a neural network to implement beamforming technology. This method utilizes deep learning to automatically learn and optimize the weights and parameters of the beamformer. The core advantage of this method is its adaptability, allowing the network to adjust according to the complexity and diversity of the speech signal;
2. Narrow-band (NB) BLSTM [27] is a frequency-domain method using the BLSTM network, which is specially focused on narrow-band frequency processing and is trained by full-band methods to improve its performance. By processing each narrow-band frequency component separately in the frequency domain, this method can effectively identify and separate individual speakers in overlapped speech;  
Figure 3: Spectrographic comparison of the separated speech at different stages.  
* Beam-TasNet [9] is a classical speech separation method that combines time-domain and frequency-domain approaches. First, the time-domain neural network is used for pre-separation. Subsequently, these pre-separated speech signals are used to calculate the SCM of the beamformer. Finally, the separated signal is obtained by the beamformer;
* Beam-guided TasNet [19] is a two-stage speech separation method that also combines both time-domain and frequency-domain approaches. In the first stage, the initial speech separation is performed using Beam-TasNet. In the second stage, the network structure remains the same as Beam-TasNet, but the input includes the output from the first stage. This iterative process helps to further refine the separation of the initial speech.
* Beam-TFDPRNN [15] is our previously proposed time-frequency speech separation method, which, like Beam-TasNet, also uses a neural beamforming structure. This method has more advantages in the reverberant environment, because it uses a time-frequency domain network with more anti-reverberant ability for the pre-separation.  
The experimental results on the spatialized version of the WSJ0-2 mix dataset for the proposed method and current popular methods are shown in Table 2. It should be emphasized that the results of Beam-TasNet are directly cited from the original paper, while the result for beam-guided TasNet were obtained from our replicate test, the difference being about 0.2 dB from the original result.  
From Table 3, we can see that the performance of FaSNet and NB-BLSTM was not satisfactory. In comparison, the Beam-TasNet and Beam-TFDPRNN demonstrated good separation performance. The beam-guided TasNet further improved the performance of Beam-TasNet by employing an iteratively refined structure. The proposed method, iBeam-TFDPRNN, significantly outperformed the other methods. In addition, our proposed model included only 2.8M parameters, fewer than the parameters of most other methods. In conclusion, the method proposed in this paper demonstrated excellent performance compared with the reference methods.