# Positioning-Based Uplink Synchronization Method for NB-IoT in LEO Satellite Networks
## 4 Simulation Analysis  
The accuracy of the NPSS detection algorithm directly affects the acquisition of TDOA observation values and the subsequent synchronization precision. Figure 13 compares the detection performance of the proposed MSA algorithm with the maximum likelihood (ML) algorithm under various signal-to-noise ratios and Doppler frequency offsets. The results indicate that the MSA algorithm can achieve a timing error within one symbol duration even under negative SNR conditions and maintains reliable detection performance under severe Doppler shifts. Although the MSA algorithm demonstrates superior detection capability compared to the ML algorithm, it incurs a higher computational complexity.  
Figure 14 presents the distribution of uplink TA estimation errors under different SNR conditions for three distinct scenarios using the proposed BOS scheme. In the three-satellite and two-satellite visibility cases, favorable satellite geometry results in lower positioning errors and narrower TA ambiguity ranges, allowing successful uplink synchronization even at low SNR levels. However, in the single-satellite scenario, the weak satellite geometry significantly degrades positioning accuracy, causing the BOS scheme to reach the threshold of acceptable TA estimation accuracy at around \(-4\) dB. Nevertheless, single-satellite visibility is relatively rare in the Iridium constellation and thus does not significantly impact the overall performance of the BOS approach.  
Figure 15 illustrates the uplink synchronization success rates under different visible satellite scenarios. In the Iridium constellation, the proportions of triple-satellite, dual-satellite, and single-satellite visibility are approximately 6:3:1. Based on this distribution, the proposed scheme achieves an uplink synchronization success rate of 98% even under negative SNR conditions.  
Figure 16 compares the RMSE of the proposed TDOA-based positioning method with the CRLB. The results demonstrate that the proposed method achieves positioning accuracy close to the CRLB under low SNR conditions, indicating its effectiveness as a reliable localization approach.  
Figure 13: Comparison diagram of NPSS detection algorithms.  
Figure 17 shows the positioning error over a 50-min period in the Nanjing and Tokyo regions under an SNR of \(-2\) dB using the proposed algorithm. It can be observed that while the error fluctuates significantly over different time windows, it generally remains around 200 m. Figure 18 illustrates the impact of the NB terminal's sleep duration \(T\) on TA estimation under the dual-satellite visibility scenario. A clear negative correlation is observed. However, an excessively large \(T\) value would increase power consumption during the synchronization process. Therefore, we choose 100 s as the sleep duration.  
Figure 14: Comparison of TA values under different scenarios.  
Figure 15: Synchronization accuracy under different scenarios.  
Figure 19 presents a comparison of energy consumption between the GNSS-based scheme and the proposed BOS scheme under different satellite visibility scenarios. It is evident that the GNSS-based approach incurs significantly higher energy consumption compared to the BOS scheme. The three-satellite case exhibits the lowest power consumption, as only a single measurement is required to complete uplink synchronization. Overall, the BOS scheme achieves an energy saving of approximately 15% to 40% compared to the GNSS-based method.  
Figure 16: Comparison between positioning method and the Cramér-Rao lower bound.  
Figure 17: Positioning accuracy at different times and in different regions.