# Preamble-Based Noncoherent Synchronization in Molecular Communication: A Machine Learning Approach
## 5 Simulation Results  
In this paper, we first examined the performance of the preamble signal in conventional MC channels. Subsequently, through ML training, we evaluated the extent to which synchronization accuracy is improved. This study assumes that molecular propagation takes place through diffusion in air. In addition, the diffusion coefficient \(D\) is considered constant throughout this analysis, simplifying the computation and modeling. The total pulse position count (\(N_{p}\)) is 8. In the current study, we use two metrics to verify the robustness of the proposed synchronization scheme, namely synchronization probability \(\big{(}\mathrm{P_{syn}}\big{)}\) and average normalized mean square error \(\big{(}\mathrm{NMSE_{avg}}\big{)}\). These metrics are chosen because they directly measure the key aspects of synchronization performance: \(\mathrm{P_{syn}}\) assesses the success rate of synchronization, while \(\mathrm{NMSE_{avg}}\) provides a measure of temporal accuracy. While other metrics such as bit error rate (BER) and throughput are commonly used in communication systems, they are more pertinent to data transmission performance rather than synchronization. In our study, the focus is specifically on the synchronization process. BER, for instance, evaluates the accuracy of data detection, and is heavily influenced by transmission errors rather than synchronization precision. Similarly, most of the MC performance metrics are related to the stochastic nature of molecule transmission, but are less effective for quantifying synchronization accuracy. Thus, \(\mathrm{P_{syn}}\) and \(\mathrm{NMSE_{avg}}\) were deemed sufficient and appropriate for capturing the essential performance characteristics of our \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values** \\ \hline Distance (\(r\)) & 1–10 cm \\ Learning rate & 0.1 \\ Unit number & 400 \\ Hidden layer & 2 \\ Train data & 80,000 \\ Validation data & 20,000 \\ Test data & 100,000 \\ Epoch & 5000 \\ Diffusion coefficient (\(D\)) & 0.43 cm\({}^{2}\)s\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Default simulation parameters. synchronization scheme. The softwares used for the simulations are MATLAB R2023b, PyCharm 2023.1, Python 3.8.8, and TensorFlow 2.10.0. In the context of the CSK-based CEMC system, \(\mathrm{P_{syn}}\) can be defined as the likelihood that the receiver correctly aligns its timing with the transmitted preamble signal within a specified accuracy. That is, synchronization means that the receiver accurately detects the timing of the start of the preamble based on the concentration of molecules received. In particular, it involves detecting the correct timing of concentration changes of molecules that signify the start or specific parts of a message (similar to aligning to a phase or a specific waveform in EM communication). On the other hand, \(\mathrm{NMSE_{avg}}\) measures the accuracy of estimating the start time of the transmission or the concentration levels of molecules, normalized by the duration of transmission. In particular, it quantifies the average squared difference between the estimated and true synchronization points, normalized to the magnitude of the preamble duration. Mathematically, it can be represented as [18]  
\[\mathrm{NMSE_{avg}}=E\Bigg{[}\left(\frac{|\hat{t}_{\mathrm{syn}}-t_{\mathrm{ syn}}|}{T_{tx}}\right)^{2}\Bigg{]}. \tag{14}\]  
A lower \(\mathrm{NMSE_{avg}}\) indicates that, on average, the synchronization time estimated by the receiver closely matches the actual synchronization time, relative to the duration of the message being transmitted. Conversely, a higher error indicates a less accurate synchronization. Figures 5 and 6 depict the before-training \(P_{\mathrm{sync}}\) and \(\mathrm{NMSE_{avg}}\) performances as a function of distance, respectively. Before training, the entire transmission time of a single preamble signal in conventional MC channels was set to \(16T_{p}\), and the performance was evaluated for the case of sending two consecutive signals.