# Blind Recognition of Frame Synchronization Based on Deep Learning
## 3 Test and Analysis
It can be observed that when the error rate is less than 0.2, the recognition accuracy of BRFS-DL algorithm reaches 100%. In addition, even when the error rate is up to 0.25, the recognition accuracy of BRFS-DL algorithm is still above 95%. The performance comparison of the four methods for comprehensive recognition of frame length and frame synchronization code is depicted in Figure 7. When the error rate is 0.15, the blind recognition method of frame synchronization in time-code domain proposed in Reference [13] achieves a recognition probability of about 22%, and the convolutional neural network-based physical layer cutting method in Reference [25] has a recognition probability of about 40%. In contrast, our algorithm achieves a recognition accuracy of 100%. Moreover, when the error rate is around 0.25, the recognition accuracy still exceeds 90%. In contrast, the first-order cumulant and error elimination method presented in reference [12] exhibits a rapid decline in recognition performance at this error rate and fails to accurately recognize frame synchronization. The main reason for the good recognition performance of BRFS-DL is that it transforms the feature of frame length into a scaling factor and combines it with the sequence to create a striped RGB image for neural network training. By employing flat-top interpolation on the original data and setting an appropriate matching radius \(d\), the diversity of the dataset is enhanced. In contrast, the recognition methods in references [12; 13] require setting suitable thresholds to make decisions based on  
Figure 5: Comparison of frame length recognition performance between BRFS-DL and reference [12] ([PERSON], 2021). Figure 6: Comparison of frame synchronization code recognition performance between BRFS-DL and reference [12] ([PERSON], 2021). the computed first or higher-order cumulants, however, it is difficult to find a threshold that fits all scenarios at the same time. Furthermore, the recognition method in reference [13] relies on the autocorrelation characteristics of frame synchronization codes to correct the data in the analysis matrix, which limits its applicability in high bit error rate environments. Reference [25] also employs the idea of converting sequences into images and using neural networks for recognition. However, it requires that the number of columns in the matrix be strictly uniform with the frame length during data compression, which is equivalent to setting the matching radius to 0 in our method. Additionally, it lacks the process of flat-top interpolation. Therefore, our method improves recognition accuracy while reducing computational complexity. In constructing the training set, we used a matching radius of \(d\) and column number increment of 1, which means that all the matrices whose column number is within the range \([L-d,L+d]\) are used to generate positive samples. In each experiment, we generate multiple images of varying sizes for the fixed binary sequence. Theoretically, as long as one of the images has a matrix column number within the range \([L-d,L+d]\), we can obtain the correct recognition result. In realization, the increment of the matrix column number \(d_{i}\) is less than \(d\), which means that at least two positive samples will definitely appear in one experiment, providing us with more grounds for post-selection, enabling us to reach more accurate decision results. It is obvious that the recognition accuracy will increase as \(d_{i}\) decreases, but this comes at the cost of increased computational complexity. It's a trade-off between computational complexity and accuracy. Even with the maximum \(d_{i}=2d+1\), the computational complexity of our method will still be significantly higher than the traditional algorithms, due to the millions of parameters in the neural network model.