# Blind Recognition of Frame Synchronization Based on Deep Learning
## 3 Test and Analysis  
To evaluate the ability of blind recognition algorithm for frame synchronization based on deep learning (BRFS-DL) to recognize frame lengths, the data set is configured with five different physical frame lengths of [50; 60; 70; 80; 90] and each frame length utilizes the same 11-bit Barker code as the synchronization code. When constructing the matrix \(H\), the matching radius \(d=10\), and the starting position of the extracted data sequence is randomly determined. The search range of \(L_{\pi}\) is set to [160; 400] considering the interpolation factor of 4. The simulation results are shown in Figure 5.  
When evaluating the ability of BRFS-DL to recognize frame synchronization codes, the data set is set up with four different synchronization codes with length of [7; 11; 13; 15]. Each category has the same frame length \(L=50\), the number of columns of the matrix \(H\) is set to \(n\in[190,210]\). The simulation results are shown in Figure 6.  
To verify whether BRFS-DL can simultaneously recognize the frame length and synchronization code, a data set is created with four different frame lengths [50; 60; 70; 80] and three different synchronization codes with length of [11; 13; 15], totaling 12 different categories. A negative sample category is also included. The matrix \(H\) is constructed with \(d=10\) and search range of \(L_{\pi}\) is set to \([160,360]\). The simulation results are shown in Figure 7.  
Using three network models trained on the above three datasets for recognition prediction, the error rate of the original binary data sequence is set to \(0.02m\), \(m=[0,1,2,...,20]\), and each network was subjected to 200 random experiments for each error rate. In each experiment, the data sequence was first interpolated and then multiple matrices \(H\) were constructed using the same interpolated data sequence, with the number of columns of \(H\) increasing by \(d_{i}=5\) within the range of \(n\). Each matrix was transformed into an RGB image by combining its respective scaling factor, and fed into the trained network model for recognition. For every image, the recognition result includes a category and probability. We count the number of times (\(N_{i}\)) the sequence is recognized as being in each category (\(C_{i}\)) and the maximum probability (\(P_{i}\)) of being judged to be in that category, denoted by \(\{C_{1},N_{1},P_{1},C_{2},N_{2},P_{2},\ldots,C_{p},N_{p},P_{p}\}\). If there is only one category \(C_{i}\) satisfying \(N_{i}=max\{N_{1},N_{2},\ldots,N_{p}\}\), then we take (\(C_{i}\)) as the recognition result. If there are multiple categories satisfying \(N_{i}=max\{N_{1},N_{2},\ldots,N_{p}\}\), the category with the highest classification probability among them is chosen as the recognition result for this experiment. Following, we simulate our algorithm and compare it with the method proposed in reference [13; 25] and reference [12] which is implementated with FPGA in reference [32]. Reference [12] constructed matrices with varying column numbers and computed their first-order cumulants. Decision thresholds were set based on frame structure characteristics to distinguish between synchronous bit columns and data bit columns, enabling recognition of frame length and synchronization codes. Reference [13] utilized high-order cumulant to detect the burst signal in time domain, and then completed the frame synchronization recognition by combining the code domain information. Reference [25] transformed digital sequences into images with column number equal to frame length and then trained the neural network to recognize the frame length. The frame length recognition results are shown in Figure 5. When the error rate is less than 0.2, BRFS-DL achieves a recognition accuracy of 100%. Furthermore, even when the error rate is as high as 0.25, the recognition accuracy of BRFS-DL remains above 90%. Figure 6 shows the performance comparison between BRFS-DL and the algorithm in reference [12] in frame synchronization code recognition.