# Preamble-Based Noncoherent Synchronization in Molecular Communication: A Machine Learning Approach
## 3 Proposed Preamble-Based Synchronization Scheme  
### Pulse-Based Preamble  
As previously mentioned, preamble-based synchronization refers to estimating timing by transmitting a preamble signal before the actual transmission signal. In diffusion-based MC, blind synchronization [13] is another prominently used scheme. In [13], ML criterion was adopted for blind synchronization algorithm, which involves maximizing the log of the probability density function for the received signal, which is conditioned on the unknown signal, and an unknown delay. The study considers a Molecule Shift Keying (MoSK) receiver with a bank of chemical receptors, each designated to detect one of different molecule types. Considering non-decision directed estimation, where the receiver does not have prior knowledge of the transmitted data, the estimation metric is obtained by averaging over the likelihood function of the possible information symbols. To refine the delay estimation iteratively, a gradient-based update algorithm is used, approximating the derivative of the likelihood function. This approach shares similarities with the early-late gate technique, but direct implementation is infeasible due to the lack of symmetry in the metric derivative for diffusion-based noise. Moreover, the authors assumed that the propagation delay is a fixed unknown value, and did not discuss how to synchronize the time. Reference [34] presents another blind synchronization scheme, where transmitterencodes its clock reading into messenger molecules and releases them. The updated clock at the receiver is then calculated as a sum of transmitted clock reading and the propagation delay. On the other hand, our proposed method relies on collecting the preamble molecules for synchronization. Its non-coherent approach makes the computation simpler and less complex, leading to much higher resource efficiency. Due to simple structure and low computational burden, the proposed method is better suited for resource-constrained unpredictable nanonetwork environments and nanomachines.  
The structure of the preamble signal is depicted in Figure 2. The sequence of rapid, distinct bursts of molecules (high concentration) are released \(N_{p}\) times with a value of \(Q_{s}\). As the time corresponding to one concentration segment of the preamble signal is denoted as \(T_{p}\), the entire concentration segment duration becomes \(T_{s}=N_{p}T_{p}\), resulting in an overall transmission time of \(T_{tx}\) equal to \(2T_{s}\). Representing the signaling part as \(s(t)\), it can be expressed as follows [18]:  
\[s(t)=\sum_{k=0}^{N_{p}-1}p_{k}(t-kT_{p}). \tag{5}\]  
Note that there is an guard interval of period \(T_{s}\), which provides a buffer period that will allow the preamble molecules to disperse, thus reducing the probability of ISI with the subsequent emissions. In addition, guard interval facilitate better timing analysis by providing clear breaks between preambles, which help the receiver in determining the timing and duration of incoming signals.  
If the preamble signal \(s(t)\) is transmitted \(N\) times, the set of preamble signals can be expressed as follows [18]:  
\[x(t)=\sum_{k=0}^{N-1}s(t-kT_{tx}). \tag{6}\]