# Preamble-Based Noncoherent Synchronization in Molecular Communication: A Machine Learning Approach
## 5 Simulation Results
The SCW concentration summation intervals were set to \(2T_{p}\), \(4T_{p}\), and \(8T_{p}\), respectively, to compute the LCW. By determining the max value of the LCW, the starting position of the received preamble signal at the receiver can be identified, and this can be compared with the transmitted signal to ascertain the occurrence of errors. In Figure 6, error increases due to channel effects as the distance grows. Increasing the SCW interval enhances \(P_{\mathrm{sync}}\) performance. However, while \(\mathrm{NMSE_{avg}}\) is smaller for shorter transmission distances, it can increase with greater distances. Thus, we can see that enlarging the SCW can improve synchronization performance, it might also elevate the average timing error. Consequently, depending on the signal, it is essential to set an appropriate value for the SCW. Figure 5: Synchronization probability with distance for different SCW widths prior to training. In MC channels, it is observed that errors increase sharply as the distance grows. To mitigate this, ML training is employed. Post ML training, the accuracy for each distance, \(r\), based on the correct data and preamble signal data are evaluated, along with the accuracy when distance data are mixed in. For testing, cross-entropy was utilized as the cost function, and Gradient Descent was employed to minimize the cost. The data values used for training are presented in Table 1. Train data refers to the number of data used for training, and validation data refers to the number of data used to evaluate it. Test data represents the number of data used in the test based on the learned model. Figure 7 depict the accuracy based on transmission distance when the size of SCW is \(4T_{p}\). While the data exhibits fluctuations due to random noise, it converges within a certain range as the epochs increase, indicating improved synchronization performance post-training. It is observed that the accuracy is higher after training for shorter transmission distances. Figure 7c displays the synchronization accuracy post-training across epochs for mixed data with \(r=1\) to 5. When training with mixed data from different transmission distances, it exhibited an accuracy of approximately 0.6. This indicates an improvement in performance compared to the case when \(r=1\) before training. Overall, it can be observed that the accuracy is higher after ML training compared to before. When the distance of the training data exceeds \(r=5\), the learning process was hindered due to the delay phenomenon and ISI in the MC channel. This indicates that by adjusting SCW when the communication distance is closer, synchronization performance can be controlled, and additionally improved performance can be achieved through ML training. Figures 8 and 9 represent the performance of \(P_{\text{sync}}\) and \(\text{NMSE}_{\text{avg}}\) after learning, respectively. When \(r=5\), the \(\text{NMSE}_{\text{avg}}\) value was measured to be higher when the SCW width was \(4T_{p}\), compared to when it was \(2T_{p}\). This seems to be because the time difference increases when errors occur as the SCW width increases. This indicates that while increasing the SCW width generally improves the performance of \(P_{\text{sync}}\), it may also increase the NMSE value, suggesting the need to set the SCW width appropriately for the situation. The ML-based receiver showed overall improvements in \(P_{\text{sync}}\) and \(\text{NMSE}_{\text{avg}}\) after training with \(2T_{p}\), \(4T_{p}\), and \(8T_{p}\). This is because ML can learn and mitigate the difficult-to-model nonlinear characteristics of the channel. Therefore, it was found advantageous to employ data learning through ML when applying preamble-based synchronization methods in MC. Figure 6: Average normalized mean square error with distance for different SCW widths prior to training. Figure 8: Synchronization probability with distance for different SCW widths after training. Figure 7: Train and validation accuracy based data.