# Sep-RefineNet: A Deinterleaving Method for Radar Signals Based on Semantic Segmentation
## 3 System Framework and Method
### Frequency Characteristic Matrix  
The frequency characteristic matrix (FCM) is a method we propose to encode the PRI of pulse streams. This method avoids the threshold judgment and pulse sequence search process of the traditional deinterleaving algorithm and reduces the manual participation in the sorting. The situation that all the pulses of radar emitter are missed due to a potential PRI not exceeding the threshold is prevented.  
The encoding method of FCM is presented as follows. First, the TOA in PDW is extracted, and the obtained TOA sequence is divided into a TOA vector with a length of 512 and a width of 1. Then, the TOA vector is subjected to a 10-order self-correlation difference to obtain the PRI transformation matrix (TM). The value of the \(TM_{(i,j)}\) is the \(j\)-th pulse minus the \(i\)-th pulse of the TOA vector. Count the frequency of potential PRI in the TM. Considering the measurement error of TOA, the allowable error in statistics is 10 \(\upmu\)s. Finally, the frequency of different potential PRI is written into the corresponding FCM to complete the feature encoding of the pulse stream. Before feeding it to Sep-RefineNet to learn the FCM features, it needs to be standardized. The standardized value of FCM is shown in Equation (7).  
\[f_{(i,j)}=255\times\left[\frac{FCM_{(i,j)}-min(FCM)}{max(FCM)-min(FCM)}\right] \tag{7}\]  
Mapping the feature elements of FCM to [255; 0], the maximum value is 255, and the minimum value is 0, which can better help the neural network learn the semantic feature of PRI. When the length of the pulse stream is less than 512, the subsequent position is filled with zeros. The encoding process of the FCM is presented in Figure 3.  
Figure 2: The system framework of radar signals deinterleaving.  
After obtaining the FCM constructed by the potential PRI, the paired label matrix is obtained in Figure 4.  
According to the corresponding position of the pulse in the pulse streams, the category label of the radar emitter to which it belongs can be marked, and the paired FCM and label matrix can be obtained. During the experiment, in order to add a verification step when decoding the position, the FCM and label matrix are both symmetrical about the diagonal. After the FCM is symmetric, the PRI of the radar emitter has clearer semantic features of texture and structure. After the label matrix is symmetric, it can be compared whether the label at the symmetrical position is correct, so as to verify the post-processing algorithm of deinterleaving. The visualization of the FCM and label matrix is presented in Figure 5.  
Figure 4: The result of label matrix: (**a**) PRI transform matrix; (**b**) generated label matrix.  
Figure 3: Encoding process of FCM: (**a**) PRI transformation matrix obtained by the self-correlation difference of the TOA sequence; (**b**) the statistical potential PRI; (**c**) generated frequency characteristic matrix.  
The position decoding method of the FCM is as follows. First, the label of each element in the prediction matrix is obtained, and then, the elements with different predicate results in symmetrical positions are eliminated to ensure the accuracy of deinterleaving. Obtain the symmetric position of the same label in the prediction matrix, and select the coordinates of the original TOA pulse stream as a set; then, the set of radar pulse sequences with the same label can be obtained, and complete the signal deinterleaving. This method encodes and decodes the received pulse stream to complete the deinterleaving of radar signals, avoiding the dependence of traditional methods on threshold judgment and pulse sequence search, and relies on the FCM to reflect the characteristics of different PRI in the position and between elements for the texture and structural features. Finally, combined with Sep-RefineNet to segment the pixel-level semantic features of FCM, the deinterleaving of radar signals is intelligently completed.