# A Comparative Study of 3D UE Positioning in 5G New Radio with a Single Station
## 4 Performance Comparison
### Limitations and Discussion  
From the simulation results shown in Section 4.2, we can see that both the subspace and EM algorithms can successfully localize the SRS source by estimating the angle and delay. The EM algorithm outperforms the subspace algorithm in terms of the position RMSE. However, the current methods have their limitations, which need to be addressed in future work:  
* Computational load of the subspace algorithm: As can be seen from Equations (6), (10), and (11), the subspace algorithm involves two Kronecker operations and one covariance operation of the Kronecker product. These facts imply that the vector and matrix size will increase exponentially with the number of antenna elements and the subcarriers; moreover, the base station will have to allocate more computing resources for positioning information extraction. Therefore, the development of a computational efficient subspace-based algorithm will pave the wary for applying the subspace-based algorithms in practice.
* Multipath propagation: The orthogonality of the SRSs from different UEs avoids the mutual interference to achieve the high positioning capacity. However, the multipath distortions of the ToA parameter estimation is unavoidable because the multiple copies of the signal originated from the same SRS with a recognizable ToA difference are strongly correlated. As can be seen from the results in Section 4.2.2, the estimation RMSE of the position increases if there exists a copy of the SRS close to the UE. Hence, the multipath mitigation schemes with high spatial resolution are the problem to be solved in future work.
* UEs' mobility: The mobility of the UEs will cause position changes during the 20 ms observation time of the SRS in this work. By using the same codes that generated the results in Section 4.2, we find that the estimated position of a moving UE is located at the middle point between the two positions of that UE when the observation starts (0 ms) and ends (20 ms). For example, let us assume that the mobility of one target is 70 km/h. The radial distance between the positions when the SRS observation started at (0 ms) and ended at (20 ms) is then 0.39 m. Under no reflections and a line-of-sight scenario, the estimated position radial distance to the UE's final position is 0.19 m (around 0.39/2). This example shows that mobility related error exists, and it increases with UE speed. In order to reduce the performance reduction introduced by the mobility of UEs, reducing the observation time can be a straightforward approach.  
Figure 8: The impact of a nearby coherent source on the positioning accuracy.  
Non-line-of-sight positioning: Regarding the non-line-of-sight scenario, this work mainly has two issues that are addressed. The first one is related to the multipath propagation. Multipath indeed makes the estimation difficult as we discussed in the multipath part, when we showed how the nearby reflected signal decreased the estimation accuracy. Furthermore, the position estimation in this case is more challenging than for the line-of-sight, as it has a weak signal strength and a small ToA difference. The second issue is related to the fact that this design can directly estimate the incident angle rather than the reflection angle on the surface where reflection and scattering occur. Thus, this design shall utilize the environment reflection information and the UE's SRS to jointly calculate the target's position.
* Requirement of prior knowledge: Both the subspace and EM algorithms in this paper take advantage of the prior knowledge of the SRS and channel equalization to estimate the angle and propagation delay. However, the SRS is only sparsely distributed in the 5G NR frames. These facts limited the effective samples that can be used for positioning purposes. In addition, both algorithms need to know the number of signal sources to achieve good estimation accuracy. Thus, the blind source separation or blind estimation schemes are also promising topics to explore in the context of 5G NR signal-based positioning.