# Convolutional Neural Network (CNN)-Based Frame Synchronization Method
## 2 System Model  
In this study, we consider a synchronized communication network, in which a Tx transmits signals to an Rx at predesignated time \(t_{s}\). The Tx packet consists of the preamble and data in the front and end of the packet, respectively, as shown in Figure 1. In this scenario, the Tx transmits a packet at \(t_{s}\), yet the packet arrival time has some deviation due to clock offset and propagation delay between the Tx and the Rx. As the time deviation is bounded within a certain time window with size \(W\) by designing the system depending on the amount of clock offset and the distance, we can assume that the packet arrival time falls within the time window \([0,\ldots,W-1]\). The preamble consists of the BPSK modulated signals and its length is denoted by \(L\). Here, we note that any modulation scheme is applicable to the proposed technique, which will be introduced shortly.  
Figure 1 shows the overall block diagram of frame synchronization. It is assumed that the received signal is Q-times oversampled compared to the transmitted symbol rate. The received analog signal and its sampled digital signal, respectively, can be represented as  
\[r(t) = \sum_{k=-\infty}^{\infty}s(k)p(t-kT-t_{0})+w(t), \tag{1}\] \[r[n] = r(t)|_{t=nT/Q}, \tag{2}\]  
where \(T\) is the symbol duration, \(s(k)\) is the Tx symbol (first \(L\) symbols are the preamble), \(p(t)\) is the impulse response of the pulse shaping filter, \(w(t)\) is white Gaussian noise, and \(t_{0}\) is the packet arrival time that should be found at the Rx. In conventional frame synchronizers, \(t_{0}\) is found via the correlation between the preamble \(s(k)\) and the received signal \(r[n]\). As the sampling frequency of the received signals is Q-times higher than that of \(s(k)\), the correlation in the correlator in Figure 1 can be obtained as  
\[z[n]=\left|\sum_{l=0}^{L-1}r[n-lQ]s^{*}[L-l-1]\right|^{2}, \tag{3}\]  
and thus, the structure of the correlator is as shown in Figure 2.  
As the sampling frequency is \(Q/T\), the packet arrival time \(t_{0}\) corresponds to \(n_{0}=\lceil t_{0}\frac{Q}{T}\rceil\) in the correlator output, where \(\lceil\cdot\rceil\) denotes a ceiling operation. Therefore, \(n_{0}\) is the starting point of the packet and it should be found at the Rx.  
Figure 3 shows an example of the correlator output, where the window size is 10,000, i.e., \(W=10,000\). The maximum of the correlator output occurs at \(n=7,913\), i.e., \(n_{0}=7,913\). If  
Figure 1: Overall block diagram of the conventional correlation-based frame synchronization.  
Figure 2: Structure of the correlator and frame synchronization based on the maximum correlation in Figure 1.  
exists within the time window, searching the maximum value of the correlator output \(z[n]\) within the window will be one of the best policies and it is described as follows,  
\[\hat{n}_{0}=\arg\max_{\{n\}}z[n],\forall n\in[0,W-1]. \tag{4}\]  
In this synchronized network case, it is advantageous that frame synchronization can be performed without SNR estimation. Throughout this paper, this correlation-based method is called a conventional method.