## 5 Simulation
### Critical Cases  
In real cases, the power of the MP received by a dual-polarization antenna is unpredictable; hence, the LHCP channel may provide invalid information of the MP signal. Table 6 shows two critical cases that may happen when the LHCP channel provides no or false information. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(B_{0}^{2}\) & \(DPG\) = 2 & \(DPG\) = 1.25 & \(DPG\) = 1.1 & RHCP-MEDLL \\ \hline \(-30\) dB & \(1.66\) m & \(1.71\) m & \(1.97\) m & \\ \(-15\) dB & \(1.90\) m & \(2.27\) m & \(2.70\) m & \(2.83\) m \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The RMSE of the DP-SIMLE algorithm as the DPG decreases. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Power of LOS Signal in LHCP Channel**} \\ \hline \(-30\) **dB** & \(-15\) **dB** & \(-12\) **dB** & \(-9\) **dB** & \(-6\) **dB** \\ \hline \(1.66\) m & \(1.91\) m & \(2.09\) m & \(2.36\) m & \(2.71\) m & \(2.83\) m \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The RMSE of the DP-SIMLE algorithm in the entire simulation as the power of the LOS signal in the LHCP channel increases. In the case described by the left part of Table 6, the LHCP antenna barely receives the MP signal; thus, the merging of the LHCP data provides almost no information of the MP signal, or even disturbance, because of the received LOS signal in the LHCP channel. Figure 12 shows the RMSE of the DP-SIMLE algorithm in this scenario if we disable the indicator in the initialization step. The DP-SIMLE without the indicator has a large variance around 200 s when the relative delay of MP1 to the LOS signal goes to the critical zone where DP-SIMLE is just able to distinguish the LOS signal from the MP signal. Actually, this increased variance is caused by the modeling error in the DP-SIMLE algorithm that ignores the LOS signal in the LHCP channel. However, this phenomenon disappears (1) as the received LOS signal power in LHCP channel \(B_{0}^{2}\) decreases (it completely disappears when \(B_{0}^{2}\) is less than \(-30\) dB) or (2) when the received MP signal power dominates in the LHCP channel (\(B_{1}^{2}\geq B_{0}^{2}\)). In order to tackle this problem, we design an indicator to detect whether the MP dominates the LHCP channel by measuring the distance between \(\widehat{l_{\text{RHCP}}}\) and \(\widehat{l_{\text{LHCP}}}\) as described in the initialization step in Section 4. Given the CCF of the received LOS and MP compound signal, we regard all of the MP signals as a composite one. In general the \(\hat{t}\) that maximizes this CCF is closer to the peak of the ACF of the signal that has higher power. Therefore, \(\widehat{l_{\text{RHCP}}}\) is close to the TOA of the LOS signal in RHCP channel, and \(\widehat{l_{\text{LHCP}}}\) is close to the composite MP signal if it dominates the LHCP channel. Usually, MP arrives at the antenna later than the LOS signal; hence, if the LHCP antenna receives more of the MP signal power than the LOS signal, \(\widehat{l_{\text{RHCP}}}<\widehat{l_{\text{LHCP}}}\); otherwise the received signal may not compatible with the signal model that ignores the LOS signal in the LHCP antenna. Enabling this indicator, the RMSE of the DP-SIMLE in this critical scenario is the same with that of RHCP-MEDLL. In the case described by the right part of Table 6, there is almost no multipath interference in the RHCP channel; however, the strong MP received by LHCP indicates the existence of MP, which is false information. The result of this critical case in Figure 12 shows that DP-SIMLE performs the same with RHCP-MEDLL in the entire simulation when the LHCP channel provides false information about the multipath.