# A Comparative Study of 3D UE Positioning in 5G New Radio with a Single Station
## 4 Performance Comparison
### Performance Comparison of Positioning accuracy in Different Contexts
#### 4.2.1 Single Target Estimation Performance  
Firstly, Figure 5 is given to show how the level of SNR affects the estimation accuracy. The target is 3 m away from the base station, and the SRS is from the direction of \([20,20]\) in the azimuth and elevation dimension. The bandwidth assigned for the SRS is 2.88 MHz, which contains 192.15 kHz subcarriers with a comb-two structure. Ninety-six subcarriers contain the SRS message. The size of the URA for AoA estimation is \(8\times 8\). Both the EM and subspace methods provide accurate estimation in the high SNR region (>10 dB), and the EM algorithm shows better robustness in the low SNR region (0\(\sim\)10 dB). The reason for this phenomenon is that the iteration procedures (especially the M-step) in the EM algorithm effectively approach the maximum likelihood estimation.  
\begin{table}
\begin{tabular}{l l l} \hline \hline Angle step & 0.1 degrees & The AoA searching step in the EM and subspace-based estimation process. \\ \hline Time step & 1 ns & The ToA searching step. \\ \hline Observation time & 20 ms & Observation time set as 20 ms to enhance the performance and that equals 20 time slots when the subcarrier spacing is 15 kHz. \\ \hline Sampling frequency & 60 MHz & Assuming a 60 MHz bandwidth. Sixteen RBs are allocated to the UEs, and the sampling frequency can be selected as 60 Mhz. \\ \hline \hline \end{tabular}
\end{table}
Table 3: Positioning algorithms\({}^{\prime}\) parameters.  
Figure 4: Positioning accuracy of the EM and subspace algorithms in different SNR conditions.  
This 3D positioning accuracy is affected by the antenna scales and signal bandwidth. To better understand the antenna scale effect on the RMSE in both the EM and subspace approaches, Figure 6 shows the comparisons under different antenna scales. The signal bandwidth is 2.88 MHz, and the SNR is 9 dB. To achieve better angle estimation accuracy, zero-point-zero-five degrees are set as the angle increment size. With the fixed target position in both cases, the RMSEs of the position estimation decrease with the larger antenna scale. In this comparison, we assume both algorithms know the signal source distance and perform the angle-only estimation. It is evident that the subspace algorithm has the advantage on AoA recognition.  
ToA accuracy is related to the subcarrier space, while the number of SRS subcarriers is fixed at 96. In 5G NR, subcarrier spacing can be chosen from 15, 30, 60, and 120 kHz.  
Figure 5: Positioning accuracy of the EM and subspace algorithms in different SNR conditions.  
Figure 6: Positioning accuracy of the EM and subspace algorithms with known distance and estimated AoA.  
An \(8\times 8\) URA, 1 ns time step, and 9 dB SNR are used to figure out the subcarrier spacing impacts. Different subcarrier spacings will lead to different signal bandwidths. For the results shown in Figure 7, the performance of the \(8\times 8\) antenna array is shown under the 9 dB SNR. With the increasing of the subcarrier spacing, both the EM and subspace algorithms show improving positioning resolution. The EM algorithm outperforms the subspace algorithm in the larger subcarrier spacing cases (60 and 120 kHz), while the subspace algorithm outperforms the EM algorithm in the narrower subcarrier spacing cases (15 and 30 kHz).