# A Deep Learning Method for DOA Estimation with Covariance Matrices in Reverberant Environments
## 4 Learning Strategies and Network Architectures
### Segmentation Strategy  
As shown in Section 4.1, there are 468 different classes in the regular strategy. Too many classes can bring interference to learning and testing. Thus, this part proposes the segmentation strategy for predigestion. For the azimuth, the entire space is considered, which is a major contributor to too many classes. The azimuth space can be processed with the segmentation strategy. The entire space is equally divided into \(Q\) sub-spaces. Thus, the task is finished in parallel with \(Q\) independent networks. This strategy can decompose the excessive number of classes in the task into \(Q\) parts so that the number of the total classes in each part is reduced, thereby reducing the interference induced by classes. Figure 4 shows the example of the space division when \(Q=3\), and the experiments in this paper are conducted in the case of \(Q=3\). The color-rendered part is the corresponding sub-space, and the white area is the irrelevant space compared to the coloring space.  
Take Figure 4a as an example. The pink part is the first sub-space used for the first CNN. The space range for the pink part is from 0\({}^{\circ}\) to 120\({}^{\circ}\), thus, 169 classes can be obtained for the first CNN. As the other blank parts are irrelevant spaces, a new class is needed in this subtask. This class represents irrelevant sound, which means that the signal comes  
Figure 4: Schematic diagram of space division. (**a**) is the first sub-space, which ranges from 0\({}^{\circ}\) to 120\({}^{\circ}\). (**b**) is the second sub-space, which ranges from 120\({}^{\circ}\) to 240\({}^{\circ}\). (**c**) is a perspective view of (**b**). (**d**) is the third sub-space, which ranges from 240\({}^{\circ}\) to 360\({}^{\circ}\).  
Figure 3: The process for DOAs estimation and architecture in detail. Conv \((x,y,z)\) indicates that the size of the convolution core is \(y\times z\), and the number of the filters is \(x\). \(N_{H}\) is the number of the nodes in the first FC layers. \(N_{C}\) is the number of the nodes in the second FC layer, which represents the number of classes.  
from irrelevant areas. This feature should be used as the input of the other two networks to determine the location, the signal does not appear in this sub-space. Thus, 170 classes are considered for the first sub-CNN. Similarly, the second sub-space, ranging from 120 to 240 deg, also has 170 classes. The third sub-space also has this, whose range is from 240 deg to 360 deg.  
Figure 5 shows the architecture of the network in the segmentation strategy with \(Q=3\). The specific structure of the sub-CNN is the same as the network structure of the CNN in the regular strategy to better compare the effectiveness of strategies.  
For testing, the input feature of one signal is sent to three sub-networks for detection at the same time, and the three networks output all the posterior probabilities of the whole space and judge the position of the signal through the principal of the maximum posterior probability. In particular, when the maximum probability appears in the irrelevant class, the entire corresponding sub-space will no longer be considered.