# High-Precision Ranging Method of 5G NR Co-Band PRS in Industrial Internet Scenarios
## 4 Simulation Results And Errors Analysis
### Simulation and Analysis  
For coarse synchronization, we can only estimate the integer time error of sampling units. For a particular snapshot, we set a delay of 3887 samples with a sampling rate of 122.88 MHz. We evaluated the performance of coarse synchronization at SNR values of 10 dB, 30 dB, and 50 dB, respectively (see Figure 5). It can be observed that as the SNR increases from 10 dB to 50 dB, the accuracy of the estimation using the traditional ML-based method [26] increases from 13% to 62%. Therefore, the traditional method can only determine the STO by selecting the maximum probability from multiple estimations. The method proposed in this paper still achieves 99% accuracy even at an SNR of 10 dB. For indoor areas, the time delay extension is generally at the hundred nanosecond level. For this reason, the multipath delay of Rice channel is set to [0, 6, 10, 40] samples, and the average gain is [0 dB, \(-2\) dB, \(-5\) dB, \(-10\) dB]. The \(K\) factor of Rician fading is set to 4, which represents the power ratio between direct and scattered components, while keeping other settings constant. At this time, as the SNR increases from 10 dB to 50 dB, the estimation accuracy of the traditional ML-based method increases from 9% to 34%. While the accuracy of the proposed method decreases to 52% and 92% for 10 dB and 30 dB SNR conditions, it maintains full accuracy in the 50 dB SNR case (see Figure 6). It can be seen that the Rician channel has a greater impact on coarse synchronization. Therefore, to ensure accurate estimation of the FFT window positions, it is recommended to estimate multiple OFDM symbols simultaneously and select the position with the highest probability. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Carrier Frequency & 3.4 GHz \\ Subcarrier Spacing & 30 kHz \\ FFT Points \(N\) & 4096 \\ Cyclic Prefix & Normal \\ Number of RB & 200 \\ PRS Resource Set Period \(T_{\text{P}\text{S}}^{\text{PRS}}\) & 4 \\ PRS Resource Repetition \(T_{\text{P}\text{S}}^{\text{PRS}}\) & 4 \\ Number of PRS Symbols \(L_{\text{P}\text{S}}\) & 12 \\ Comb Size \(K_{comb}^{\text{PRS}}\) & 2 \\ Factor \(\beta_{\text{P}\text{S}}\) & 0.01 \\ \hline \end{tabular}
\end{table} 
Table 1: Specific configuration of Co-Band PRS parameters. For the multipath delay estimation, the simulation is still performed in the aforementioned Rician channel with a fixed noise level of 30 dB. The \(\hat{\theta}\) is estimated by averaging  
Figure 5: Coarse synchronization estimation under Gaussian noise. Figure 6: Coarse synchronization estimation under Rician channel. 10 symbols to ensure the accuracy. On this basis, the performance of multipath delay estimation without removing the communication signal is analyzed, as shown in Figure 6(a). Because the power of the communication signal is 40 dB higher than that of the localization signal, and the Co-Band PRS signal uses only a 20 RB bandwidth, its correlation characteristics are not excellent. Since there is no way to detect the first arrivals, the ranging information is invalid for the localization user at this point. Of course, we further explored the power limit of the positioning signal, and we found that the first-arrival path is weakly detected when the positioning signal is 16 dB lower than the communication signal (Figure 6(b)), but the estimated channel implicit response is still inaccurate. Next, we explored the effect of Co-Band PRS signals on communication signals. Since the Co-Band PRS power is extremely low, it has almost no impact on the bit error rate (BER) of the communication signal, as shown in Figure 7(a). For this reason, we first consider signal detection of the communication signal. Then, we calculate the pilot signal that only contains the Co-Band PRS using Equation (17). At this stage, we can accurately estimate the main path and three multipaths of the Rician channel (Figure 7(b)). This further confirms that interference cancellation techniques can eliminate the interference of communication signals on the positioning signals.