# Robust Symbol Timing Synchronization for Initial Access under LEO Satellite Channel
## 2 Transmission Model Description  
### Transmission Structure for DVB-RCS2 Linear Modulation and Channel Model  
The burst format for linear modulation of the DVB-RCS2 standard is depicted in Figure 1. It can be constructed according to the preamble, pilot field, and postamble symbol length flexibly by FLS configuration information. In Figure 1, the Half Guard Time (HGT) that can be described as a specific period of time inserted between consecutive data transmissions to avoid the overlapping with packets due to timing jitter and delay is the allocated time to avoid inter-burst interference by timing uncertainty. Preamble symbols are typically used to detect the presence and the start position of a burst within the timeslot, and they are also used to estimate the channel error using pilot field and postamble. The user field represents the modulated symbols with QPSK, 8 PSK, and 16 QAM constellations. The presence and contents of the preamble, pilot field, and postamble are determined by FLS from a Gateway. If pilot fields are required, they should be periodically inserted, and one pilot field needs to be followed by user field symbols. The postamble is appended after the final user field symbol is placed in the burst. The set of burst design parameters is {nSymbol, PreambleLength, PostambleLength, UserFieldLength, PilotFieldLength}, and it is signaled by the Broadcasting Composite Table (BCT) of the FLS SI through a forward link [8], where the GW sends to UTs via satellite transponder. In Annex A of the RCS2 specification [8], the list of reference waveforms (essential set) is tabularized, and it is a mandatory requirement that UTs shall have the capability to produce them. As we can see in Figure 1, each timeslot consists of a single burst and HGT at both each start and edge of the burst. The GT should be minimized because it should not waste resourcesin the TDMA system. However, it should be at least necessary and be allocated when considering network synchronization timing errors, UT and satellite motion, beam footprint size, transmission power switch on/off transient time, and more. Therefore, the length of HGT in the symbol time unit is, in general, determined by system parameters such as symbol rate, clock timing jitter, and drift by Doppler and NCR, which is a vital component in network synchronization providing a common timebase from GW to synchronize with UTs and extra. For LEO satellite systems, the maximum Doppler shift and drift can be calculated from the carrier frequency, elevation angle, and altitude of the LEO satellite. For example, the maximum Doppler shift \(\pm\)420 kHz and Doppler rate \(\pm\)260 Hz/s and around \(\pm\)20 \(\upmu\)s timing offset per one second can occur in case of 20 GHz frequency and 1200 km altitude. Furthermore, the maximum differential delay between GW and UTs in a beam can be determined by LEO antenna beamwidth, satellite altitude, and UT's position, and it amounts to 3.18 ms [18]. Figure 2 shows the transmission structure of each UT toward the return link. It supports the construction of configurable burst format of DVB-RCS2 physical layer and up-conversion in low Intermediate Frequency (IF) or L-band frequency band directly. As we can see in Figure 2, the composite chain of the channel model is not aligned with the reality in order. For example, the Solid State Power Amplifier (SSPA) block should be placed after the up-conversion block. For simplicity, it works at a lower operational clock rate. In addition, each UT has an independent burst Timing Offset of Arrival (ToA), which refers to the difference in the arrival times of signals when compared to a reference time in an HGT interval, sampling clock drift, and carrier offset with uniform distribution every transmission time.