# Blind Detection of Broadband Signal Based on Weighted Bi-Directional Feature Pyramid Network
## 3 Deep Learning-Based Target Detection
### Improved Loss Function  
The standard Intersection over Union (IOU) loss function is shown in Equation (7) below when the prediction frame A does not intersect with the real frame B, i.e., \(\Lambda\cap\texttt{B}=\mathcal{O}\) when the loss function has no gradient. In addition, the IOU may be different when the prediction frame and the real frame have the same size, and the IOU loss function cannot distinguish between these two cases.  
\[\text{IOU\_Loss}=1-\text{IOU}=1-\frac{A\cap B}{A\cup B} \tag{7}\]  
In order to overcome the above problems, new IOU loss functions have been continuously developed by researchers, and their development has resulted in Generalized-IOU (GIOU), Distance-IOU (DIOU), Complete-IOU (CIOU) and Efficient-IOU (EIOU), which are loss functions that can effectively improve the target detection performance [27; 28; 29; 30]. Among them, EIOU is the current relatively advantageous one, which is developed based on DIOU and CIOU. The formulas of DIOU and CIOU loss functions are as follows.  
\[\text{DIOU\_Loss}=1-(\text{IOU}-\frac{\rho^{2}(b,b^{gt})}{c^{2}}) \tag{8}\]  
\[\text{CIOU\_Loss}=1-(\text{IOU}-\frac{\rho^{2}(b,b^{gt})}{c^{2}}-\alpha\gamma) \tag{9}\]  
where, \(\alpha=\frac{\gamma}{1-\text{IOU}+\gamma}\), \(\gamma=\frac{A}{\pi^{2}}\left(\arctan\frac{b^{gt}}{b^{gt}}-\arctan\frac{w}{h} \right)^{2}\), \(b\) and \(b^{gt}\) respectively are the middle points of the prediction box and the real box; \(w\) and \(w^{gt}\) respectively are the width of the prediction box and the real box; \(h\) and \(h^{gt}\) respectively are the height of the prediction box and the real box; \(\rho\) is the Euclidean distance between the two middle points; \(c\) is the diagonal distance of the best that can include the prediction and real box.  
Figure 7: Schematic diagram of the improved neck network structure.  
As shown in Equation (10) below, EIOU takes into account not only the centroid distance and aspect ratio but also the real differences in width and height of the target and anchor boxes. The EIOU loss function directly minimizes these differences and accelerates the convergence of the model.  
\[\text{EIOU\_Loss}=1-(\text{IOU}-\frac{\rho^{2}(b,b^{st})}{c^{2}}-\frac{\rho^{2} (w,w^{st})}{c_{w}^{2}}-\frac{\rho^{2}(h,h^{st})}{c_{h}^{2}}) \tag{10}\]  
When the SNR is too low, the overall texture of the time-frequency image becomes blurred, and the detection frame obtained by the target detection model for the signals with the time-domain aliasing relationship with each other is more prone to false detection or omission of detection. In Section 3.2, we describe the method to enhance the neck network by replacing the PANet module with a BiFPN module. The introduction of the BiFPN module allows the original model to discover more features, thereby adding more candidate sample frames. However, this improvement increases the number of correctly detected sample frames but also increases the number of false detections or missed detections. Compared with the previous CIOU loss function, the EIOU loss function takes into account the overlapping area, the distance between the center points, and the real difference in length, width, and side length. Based on CIOU, the fuzzy definition of aspect ratio and the problem of sample imbalance in bounding box regression are solved. Therefore, It is believed that the introduction of the EIOU loss function can inhibit the increase in false detection frames caused by the introduction of the BiFPN module to a certain extent.