# A Novel Data-Aided Frame Synchronization Method Based on Hough Transform for Optical Communications
## 4 Simulation Results and Discussion  
In this section, the performance of HT-based data-aided frame synchronization method is analyzed. Simulations are conducted over a 56 Gbps QPSK coherent optical transmission system built in Optisystem. The BER of received bit stream is first calculated at the receiver, and then the frame synchronization algorithm is applied to attain synchronization before payload extraction.  
The frame length \(L\) in simulation is set to 1024 bits, while the frame synchronization word \(S\) is 0 xA53C, 16 bits in length. The payload \(D\) is generated randomly. Details of how the proposed algorithm works are shown first, and then its performance in different situations is analyzed. Finally, a comparison between our proposed algorithm and the algorithm proposed in [24] is made.  
First, the workflow of HT-based blind recognition algorithm is presented at BER = \(2\times 10^{-2}\). \(r\), the rows of image space, is set to 100 and the search range of \(l\) is [500,5000]. Figure 5 above gives the running results of Step2-Step4 of the algorithm at \(l\) = 1024. It can be seen from the Step 2-result that there is obvious image noise in the synchronization-word columns, which is circled with a red frame. From the Step3-result, we can find that the noise is eliminated after edge extraction, and the  
Figure 4: Binary image of interception matrix \(C\). (**a**) \(l\ \
eq\ kl\); (**b**) \(l\ =\ kl\).  
Then, the value of \(\alpha\) is discussed at different BER, and we have also explored the influence of the selection of \(r\) on the value of \(\alpha\). For each BER level, 20 simulations are conducted, and \(\alpha\) takes the mean. The curves of \(\alpha\) versus BER for different values of \(r\) are shown in Figure 8. When \(r\) takes 20, the value of \(\alpha\) is greater than 1, as BER exceeds 0.2, which means that the frame parameters cannot be recognized correctly. When \(r\) exceeds 50, our algorithm still works at BER = 0.3. On the other hand, when \(r\) exceeds 200, the value of \(r\) has little influence on \(\alpha\). Hence, the optimal value of r should be between 100 and 200, taking into account both the amount of calculation and the accuracy of identification. In addition, it can be seen from Figure 8 that the value of \(\alpha\) decreases first, and then turns to increase as BER increases, which reflects the ability of our algorithm to suppress noise from another aspect. When the value of \(r\) increases, the turning point of \(\alpha\) moves towards higher BER.  
Finally, the recognition accuracy, which is defined as the ratio of the times of recognizing correctly to the total times, is compared between our proposed algorithm and the autocorrelation-based recognition algorithm proposed in [24]. A total of 100 simulations are carried out for each BER level. The value of \(\alpha\) takes 0.8 and \(r\) is set to 100 in the comparison simulation, according to Figure 8. The results are shown in Figure 9.  
Figure 8: Value of \(\alpha\) versus bit error rate (BER) under different \(r\). \(r\), the columns of interception matrix \(C\).  
Figure 7: Result of frame synchronization word recognition in Step10. The enlarged part is the synchronization-word columns.  
As shown in Figure 9, the HT-based blind recognition algorithm outperforms the autocorrelation-based blind algorithm. When the BER is over 0.1, the recognition accuracy of the AC-based algorithm is lower than 0.5, while that of the HT-based algorithm is still 1. The recognition accuracy of HT-based algorithm starts to gradually decrease at BER = 0.18 and deteriorates sharply at BER = 0.22. Actually, the recognition accuracy is related to the value of \(\alpha\). Apparently, our algorithm has a better error resilience performance.