# Evaluation of 5G Positioning Performance Based on UTDoA, AoA and Base-Station Selective Exclusion
## 4 Simulation Results and Evaluation
### Performance Results  
To evaluate the 5G positioning performance in dense urban areas, two scenarios have been considered, as mentioned above. Scenario 1 considers a narrow BW of 20 MHz and scenario 2 considers a wide BW of 50 MHz, both at a carrier frequency of 4 GHz with \(-50\) ns or 50 ns Root-Mean-Square (RMS) network synchronization error, distributed randomly every four BS among all available BSs for positioning. Each UE considers a maximum of six BSs to calculate the position. For each of the scenarios, the impact of the angle accuracy of the additional AoA observables and the use of NLoS monitoring method has been analyzed. The positioning performance is first assessed from a geometric perspective. The additional use of AoA observables with the TDoA observables improves the geometry. This is typically assessed with the Geometric Dilution of Precision (GDOP). Since we are dealing with terrestrial deployment, we are only interested in the horizontal positioning and therefore in the Horizontal Dilution of Precision (HDOP). This parameter for the joint TDoA-AoA is calculated following the derivations in [24], defined as: \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **Scenario 1 FR1,** & **Scenario 2 FR1,** \\  & **20 MHz** & **50 MHz** \\ \hline \multirow{3}{*}{Channel model} & \multicolumn{2}{c}{Baseline Channel Model based on} \\  & common assumptions defined related to \\  & the channel models of 3 GPP TR 38.901 \\ \hline Carrier frequency & \multicolumn{2}{c}{4 GHz} \\ \hline System Bandwidth & 20 MHz & 50 MHz \\ \hline Reference Signal & \multicolumn{2}{c}{1-symbol PRS, SRS} \\ \hline Number of subcarrier & 1200 & 3300 \\ \hline Number of sites & \multicolumn{2}{c}{7 (3-sector each)} \\ \hline Antenna elements & \multicolumn{2}{c}{M = N = 11} \\ \hline Network synchronization assumptions & \multicolumn{2}{c}{Perfect sync. and realistic Sync. with T1 = 50 nsec} \\ \hline \multirow{3}{*}{Applied positioning algorithm} & UTDoA, AoA, RTT \\  & joint UTDoA-AoA, \\ \cline{1-1}  & joint UTDoA+FDE-AoA, \\ \cline{1-1}  & Gauss–Newton algorithm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. \[\text{HDOP}=\sqrt{\mathbf{P}_{1,1}^{-1}+\mathbf{P}_{2,2}^{-1}}, \tag{38}\]  
where  
\[\mathbf{P}=\text{k}_{\phi}^{2}\mathbf{G}_{\phi}^{T}\mathbf{G}_{\phi}+\text{k}_{ \phi}^{2}\mathbf{G}_{\phi}^{T}\mathbf{G}_{\theta}+\mathbf{G}_{\text{TDOA}}^{T} \mathbf{G}_{\text{TDOA}}, \tag{39}\]  
with \(\text{G}_{\phi}\), \(\text{G}_{\phi}\) and \(\text{G}_{\text{TDOA}}\) being the geometry matrix of elevation angles, azimuth angles and time delays, respectively, computed as in (25) and (19), \(\text{k}_{\phi}\) and \(\text{k}_{\theta}\) representing the relationship between variance of time delays with variance of angles (elevation and azimuth, respectively), defined as:  
\[\text{k}_{\phi}=\frac{\sigma_{\text{TDOA}}}{\sigma_{\phi}},\text{k}_{\theta}= \frac{\sigma_{\text{TDOA}}}{\sigma_{\theta}}. \tag{40}\]  
These coefficients serve to make the HDOP of AoA dimensionless and comparable to the HDOP of the TDOA. The HDOP value for the angle part can be obtained by extracting the first two terms of the sum in (39) and then using the result in (38). The same method also works for the calculation of HDOP for the time delay part separately. In this case, only the third term of the sum in (39) is needed. Smaller values of HDOP are preferred, meaning that small changes in the measurement will not result in large errors in the location output. The Cumulative Distribution Function (CDF) of the HDOP is shown in Figure 4 for UTDoA, AoA and the hybrid solution. The HDOP values below 2 are expected to provide precise position estimation. For the cases when AoA and TDoA are treated as a stand-alone positioning method, the HDOP value is independent of the values of \(\sigma_{\text{TDOA}}\), \(\sigma_{\phi}\) and \(\sigma_{\theta}\). In the hybrid approach, their ratio, defined in (40), is a factor that affects the HDOP values.