# Preamble-Based Noncoherent Synchronization in Molecular Communication: A Machine Learning Approach
## 2 Concentration-Encoded Molecular Communication  
### Transmitter  
In CEMC, information is encoded based on the concentration of the molecules used in the transmission. This is analogous to how traditional digital communication systems might use voltage levels or light intensity to encode data. The primary method of transmission in CEMC is diffusion [25], where molecules diffuse through a medium (like air or liquid) from a transmitter to a receiver. At the receiver's end, the concentration of molecules is measured. If the concentration exceeds a certain threshold, it is decoded as one binary state (e.g., '1'), and if it falls below the threshold, it is decoded as another binary state (e.g., '0'). The most fundamental and widely used CEMC method is concentration shift keying (CSK), similar to conventional on-off Keying (OOK), where the concentration \(Q\) represents bit '1', and no concentration represents bit '0'. Mathematically, it can be represented as  
\[Q(t)=\begin{cases}Q_{s}&\text{if }0\leq t\leq T_{p}\\ 0&\text{otherwise}\end{cases}, \tag{1}\]  
where \(T_{p}\) is the time period for which the concentration is released. The interval \([0,T_{p}]\) during which \(Q(t)=Q_{s}\) is the transmission of bit '1'. On the other hand, \(Q(t)=0\), corresponds to a binary '0'.  
As molecules approach the receiver, they interact with specific receptors, triggering a minimal but detectable chemical pulse. This interaction, essential for the molecular concentration detection, is governed by the ligand-receptor binding dynamics [26; 27]. Notably, some of the molecules remain unbounded, and introduce noise, which contributes to ISI. It is also pertinent to address that, over time, the accumulation of residual molecules can further exacerbate the noise, complicating the detection process. Such ISI may result in the received signal deviating from the transmitted one. To accurately represent the stochastic nature of ligand-receptor binding process (LRBP), the probability of these events can be modeled by a normal distribution with equal mean and variance [28]. This is because a normal distribution with the same mean and variance has features that can well explain the stochastic fluctuations of various natural phenomena. Moreover, Normal distributions are mathematically easy to handle, and provide intuitive and reliable results for learning and interpretation of ML models. This probabilistic approach allows for a more precise quantification and analysis of molecular concentrations at the receiver. Note that other methods, such as chaos theory [29; 30] and dynamical systems [31; 32], can also be used to model the stochastic nature of LRBP. However, in this study, we judged that the normal distribution was most appropriate to explain the gradual distribution of noise occurrence patterns over time.  
Figure 1 shows the block diagram of the preamble-based synchronization method. In this method, a signal with a specific pattern is transmitted before the data to be sent, allowing for the estimation of the signal timing. The preamble signal to be sent is generated in the form of pulses using the concentration of molecules. When such a signal passes through the channel and reaches the receiver nanomachine, the molecular concentration of the received signal can be measured through the LRBP process. After the LRBP, the molecules are accumulated, and a decision is based on the received concentration.  
Figure 1: Block diagram of preamble-based synchronization in MC system.