# Robust Symbol Timing Synchronization for Initial Access under LEO Satellite Channel
## 2 Transmission Model Description
### Demodulator Structure for DVB-RCS2 Linear Modulation  
Figure 4 illustrates a high-level functional block diagram of the TDMA burst demodulator for the DVB-RCS2 standard. In the next part, we briefly review the functionality of each block. The received signal is bandpass filtered, sampled, and digitally down-converted to baseband signal through an Analog Digital Convertor (ADC) block. The continuous time version of the received signal can be modeled as follows:  
\[r(t)=\sum_{k}a_{k}p(t-\tau-kT)e^{[2\pi\Delta f+\phi(t)+\phi_{\mathrm{o}}]}+w(t), \tag{1}\]  
where \(T\) is symbol duration, \(\tau\) is a time delay, \(\Delta f\) is Carrier Frequency Offset (CFO) or Doppler shift offset, \(\phi(t)\) is time-varying phase noise such as Wiener processor Doppler rate, and \(\phi_{\mathrm{o}}\) is arbitrary initial phase offset, respectively. \(a_{k}\) can be a sequence of modulated transmission symbols that contain preamble, distributed pilot, and postamble symbols. \(p(t)\) is the composite of channel impulse response reflecting pulse shape, static channel, and Matched Filter. The variable \(k\) means symbol time index, and \(w(t)\) is a complex AWGN channel.  
We assume that complex I/Q baseband samples are stored in digital memory, and a channelizer process like Figure 4 is performed. The serialized baseband signal from multicarrier signals passes through a Matched Filter (MF). The burst detector block consists of a Unique Word (UW) detector and coarse frequency recovery. UW detector simply is a correlation process using differential, non-coherent, and coherent schemes depending on an amount of CFO, which refers to the difference between the actual carrier frequency of a received signal and nominal carrier frequency of a transmitted signal due to Doppler or inaccuracy of clock generator. Coarse frequency recovery block roughly estimates CFO through the reuse of functional block in the process of differential UW detector and reduces the amount of a large CFO. In the UW detection process, coarse STR can be achieved so that the starting point of the burst in a timeslot is roughly determined. Strictly speaking, we can first identify the burst start position in a timeslot by symbol time index counter. Of course, if the correlator used for the burst detector may have multiple samples per symbol, the start position can be more accurate in a sample time index, but the receiver complexity should be increased. As the burst detector operates in a sample time without the information of an accurate sampling point with maximum Signal-to-Noise Ratio (SNR) in a symbol time duration, the CFO and the timing offset estimate can be less precise. Subsequently, the fine STR is to obtain the exact sampling time using the Oerder and Meyer (O&M) algorithm [19] with four samples per symbol, and fine frequency recovery is accomplished  
Figure 4: Demodulator structure of linear modulation for DVB-RCS2 standard.  
Figure 3: Channel model for return link transmission.  
with the _FFT_ or the Mengali and Morelli algorithm [20]. To elaborate further on the STR scheme, also known as symbol synchronization or clock recovery, is a critical process in digital communication systems that involves accurately determining the timing or phase of received signals.  
Next, SNR and signal level are estimated in the level control block, and carrier phase recovery is operated by the second DA/Decision-Directed (DD) PLL algorithm or Colavolpe Barbieri Caire (CBC) algorithm [2; 3]. For bit conversion from a symbol, the Log-Likelihood Ratio (LLR) for each bit from the constellation label is computed in a soft de-mapper block, and the erroneous information bits by the channel are corrected by a 16-state duo binary turbo decoder.