# Performance Analysis of NB-IoT Uplink in Low Earth Orbit Non-Terrestrial Networks +
## 1 Introduction
### Related Work  
The 3 GPP considers common Doppler shift pre-compensation to solve the high Doppler shift [21]. This method offsets the same frequency for the received signal from all devices within the satellite beam coverage. Here, the frequency is estimated using the signal from the coverage center. Thus, the user equipment (UE) at the coverage edge suffers from a large residual Doppler shift even after the common Doppler shift compensation. The receiver must compensate for this to enable communication in the beam coverage. Currently, the residual Doppler shift compensation for NB-IoT uplinks ranges up to approximately 950 Hz [22; 23]. The 3 GPP proposes residual Doppler shift values for each satellite altitude and beam diameter. Table 1 summarizes the maximum Doppler shift and the residual Doppler shift after pre-compensation when an LEO satellite is at an altitude of 600 km [21]. The smallest residual Doppler shift they specify is 1.05 ppm for a beam diameter of 50 km, which amounts to 2100 Hz for the center frequency of 2 GHz. Therefore, additional solutions are needed to counterbalance the residual Doppler shift in NB-IoT receivers. Two approaches have been studied for residual Doppler shift compensation mainly. The first approach is reducing the beam coverage of an LEO satellite. The authors of [24; 25] solved the issue of Doppler shift compensation using the first approach. [PERSON] et al. [24] addressed the maximum residual Doppler shift of LEO satellites with resource allocation. The system model assumes that an LEO satellite is at an altitude of 1000 km and has a beam diameter of 200 km. The beam coverage is divided into ten areas to satisfy the 950 Hz compensation range of the NB-IoT receiver. As a result, the maximum residual \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Frequency band & S-band (2 GHz) \\ Satellite altitude & 600 [km] \\ Maximum Doppler shift & 24 [ppm] \\ Residual Doppler shift & 1.05 [ppm] for 50 km beam diameter \\ after & 1.88 [ppm] for 90 km beam diameter \\ pre-compensation & 15.82 [ppm] for 1000 km beam diameter \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum Doppler shift and the residual Doppler shift after pre-compensation. Doppler shift in one region decreases, making it possible to compensate for. [PERSON] et al. [25] described the residual Doppler shift as an equation after compensating for the common Doppler shift. After that, the maximum beam coverage size of the satellite is proposed for each altitude of the satellite. The second approach is increasing the compensation range for the Doppler shift of the NB-IoT receiver. There are two methods to accomplish this in OFDM-based communication systems [5; 15; 21]. The first method is to increase the subcarrier spacing (SCS). Currently, the maximum SCS for NB-IoT is 15 kHz. The Doppler shift compensation ranges are up to approximately 950 Hz, obtained by multiplying the SCS and frequency offset [13]. Although SCS expansion increases the compensation range [22; 23], it also increases the bandwidth. It is not suitable for an NB-IoT receiver with a narrow bandwidth. The second method involves adding the channel estimation symbols. In the NB-IoT standard, these are called the demodulation reference signal (_DMRS_) symbols. They are arranged at regular symbol intervals, with the property that the narrower the gap, the more accurate the channel estimation becomes. In the NB-IoT, one _DMRS_ symbol is placed per slot. Therefore, placing two or three _DMRS_ symbols per slot results in a narrower spacing and, thus, more accurate channel estimation [13]. _DMRS_ symbol addition is also used in vehicle-to-everything (V2X) research. For vehicles, because of their high speed, a Doppler shift occurs. A _DMRS_ symbol is added to solve this, which increases the receiver's Doppler shift compensation range [26]. In addition, [27] analyzed the performance according to the number of _DMRS_ symbols in the NR physical uplink control channel (PUCCH).