# A Novel Time Delay Estimation Algorithm for 5G Vehicle Positioning in Urban Canyon Environments
## 4 Simulation Results
### Simulation Results  
Figure 7a,b show, respectively, the cumulative distribution functions (CDF) of the NC-MUSIC ranging error in UMi and UMa scenarios. In the simulation experiment, the signal bandwidth is 20 MHz, 50 MHz and 100 MHz, the time of cancellation is 1. It can be seen from the figures that the bandwidth is the main factor affecting the ranging error. The larger bandwidth is, the higher corresponding sampling rate, the higher time resolution, and the higher ranging accuracy are. Tables 3 and 4 are, respectively, the direct path identification rate of NC-MUSIC in UMi and UMa scenarios. The direct path identification rate means the probability that the result of time delay estimation is equal to the direct path delay. The direct path identification criteria stipulates that if the time difference between the estimated time delay and the first arrival time delay of the receiver signal in the channel does not exceed a sampling time, it is considered that the estimated delay accurately identifies the direct path. It can be seen from the tables that bandwidth and direct path identification rate do not show a simple positive correlation or negative correlation, and analysis shows that the greater bandwidth results in a higher time resolution. When there is a NLOS path with strong power and the time delay is similar to the direct path, the correlation calculation before NLOS cancellation cannot distinguish this NLOS path, so it is impossible to cancel this NLOS path. When the time delay is estimated with super resolution, this NLOS path will severely affect the direct path and submerge the peak of direct path, because of the phenomenon in Figure 1, thus this NLOS path will be mistaken as the direct path, leading to the decrease of the direct path identification rate. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Scenario & UMi, UMa \\ Carrier frequency & 3.5 GHz \\ Bandwidth & 20 MHz, 50 MHz, 100 MHz \\ Subcarrier spacing (kHz) & 15 kHz for 20 MHz and 50 MHz, 30 kHz for 100 MHz \\ Transmit power & 23 dBm \\ Base station noise figure & 5 dB \\ UE noise figure & 9 dB \\ Pts & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of the simulation system. Figure 7: (**a**) CDF of the NC-MUSIC ranging error in UMi scenario with 20 MHz, 50 MHz and 100 MHz bandwidth; (**b**) CDF of the NC-MUSIC ranging error in UMa scenario with 20 MHz, 50 MHz and 100 MHz bandwidth. Figure 8a,b show, respectively, the cumulative distribution functions (CDF) of the NC-MUSIC ranging error in UMi and UMa scenarios. Tables 5 and 6 show, respectively, the direct path identification rate of NC-MUSIC in UMi and UMa scenarios. In the simulation experiment, the signal bandwidth is 100 MHz, while the direct path identification rate of one time cancellation and two time cancellation is similar. However, after three times of cancellation, the range error significantly increases and the identification rate of direct path decreases, the reason is analyzed as follows: in the third cancellation, the first two times of the direct path of NLOS signal were mistakenly cancelled, resulting in a large delay estimation error. In the UMa scenario, the direct path identification rate of two times of cancellation is higher than the direct path identification rate of one time of cancellation and three times cancellation. The main reason for this is that there are two NLOS paths with similar time delay. In correlation, only one of the two NLOS paths was identified and cancelled due to insufficient resolution. During the second NLOS cancellation, this NLOS path was identified and cancelled. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bandwidth** & **Direct Path Identification Rate** & **False Positive Rate** & **False Negative Rate** \\ \hline
20 MHz & 78.89\% & 0.83\% & 20.28\% \\
50 MHz & 76.81\% & 0.00\% & 23.19\% \\
100 MHz & 72.22\% & 0.56\% & 27.22\% \\ \hline \hline \end{tabular}
\end{table}