# Influence of Noise-Limited Censored Path Loss on Model Fitting and Path Loss-Based Positioning +
## 7 Positioning Simulation Results
### Example 3
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \(P_{\text{pos}}\) & \multicolumn{2}{c}{100} & \multicolumn{2}{c}{95} & \multicolumn{2}{c}{90} & \multicolumn{2}{c}{85} & \multicolumn{2}{c}{80} \\ \cline{2-11}  & 50\% & 90\% & 50\% & 90\% & 50\% & 90\% & 50\% & 90\% & 50\% & 90\% \\ \hline OLS-OTP & 54 & 198 & 64 & 258 & 78 & 357 & 98 & 458 & 126 & 548 \\ \hline MLE-OTP & 42 & 117 & 50 & 183 & 61 & 270 & 74 & 341 & 96 & 436 \\ \hline OLS-MLE & 38 & 92 & 41 & 126 & 47 & 196 & 55 & 288 & 66 & 403 \\ \hline MLE-MLE & 40 & 98 & 45 & 148 & 53 & 244 & 63 & 329 & 78 & 421 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Positioning error, in meters, 50 th and 90 th percentiles of Example 3 (28 GHz) with variable LOS detection probability in the positioning phase \(P_{\text{pos}}\). Base stations have directional antennas (\(N=8\)) and the average number of contacted BSs is \(\overline{N}_{\text{BS}}=10\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(PL^{*}\) & \multicolumn{2}{c}{120 dB} & \multicolumn{2}{c}{125 dB} & \multicolumn{2}{c}{130 dB} & \multicolumn{2}{c}{135 dB} & \multicolumn{2}{c}{140 dB} \\ \cline{2-11} \(d_{\text{BS}}\) & \multicolumn{2}{c}{459 m} & \multicolumn{2}{c}{623 m} & \multicolumn{2}{c}{846 m} & \multicolumn{2}{c}{1164 m} & \multicolumn{2}{c}{1600 m} \\ \cline{2-11}  & 50\% & 90\% & 50\% & 90\% & 50\% & 90\% & 50\% & 90\% & 50\% & 90\% \\ \hline OLS-OTP & 168 & 434 & 234 & 595 & 316 & 801 & 425 & 1063 & 554 & 1396 \\ \hline MLE-OTP & 114 & 265 & 158 & 377 & 218 & 525 & 302 & 716 & 416 & 987 \\ \hline OLS-MLE & 114 & 279 & 154 & 361 & 206 & 500 & 283 & 683 & 395 & 950 \\ \hline MLE-MLE & 110 & 259 & 150 & 351 & 203 & 485 & 283 & 674 & 391 & 929 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Positioning error, in meters, 50 th and 90 th percentiles of Example 3 (2 GHz) with variable noise threshold level \(PL^{*}\). Base stations have omni-directional (\(N=1\)) BS antennas and the average number of contacted BSs is \(\overline{N}_{\text{BS}}=5\). Positioning error 50 th and 90 th percentiles are listed in Table 7 for noise cutoff levels varying from 120 dB to 140 dB at 2 GHz, \(N=1\), and \(\overline{N}_{\text{BS}}=5\). Since the average number of contacted BSs is fixed, the higher threshold levels lead to larger distance between the BSs. With larger \(PL^{*}\), and larger \(d_{\text{BS}}\), the errors are larger but quite stable when compared to \(d_{\text{BS}}\). For example, with MLE-MLE the median error is a constant 24% of the \(d_{\text{BS}}\). The improvement from OLS-OTP to MLE-MLE ranged from 29% (from 554 to 391 m with \(PL^{*}=140\) dB) to 36% (from 234 to 150 m with \(PL^{*}=125\) dB) for the median error and from 33% (from 1396 to 929 m with \(PL^{*}=140\) dB) to 41% (from 595 to 351 m with \(PL^{*}=125\) dB) for the 90 th percentile. Therefore, performance improvement by using MLE is not sensitive to the noise cutoff level. Positioning error 50 th and 90 th percentiles are listed in Table 8 for positioning-phase LOS detection probabilities \(P_{\text{pos}}\). The detection probability is varied from 100% to 80% at 28 GHz, \(N=8\), and \(\overline{N}_{\text{BS}}=10\). For simplicity, detection probability is 100% in the training phase and same PL model parameters can be used. LOS detection errors cause larger positioning errors since wrong PL model parameters are used. With worse \(P_{\text{pos}}\) the relative improvement from OLS-OTP to MLE-MLE increases for the median but decreases for the 90 th percentile. The improvement from OLS-OTP to MLE-MLE ranged from 25% (from 54 to 40 m with \(P_{\text{pos}}\) 100%) to 38% (from 126 to 78 m with \(P_{\text{pos}}\) 80%) for the median error and from 23% (from 548 to 421 m with \(P_{\text{pos}}\) 80%) to 51% (from 198 to 98 m with \(P_{\text{pos}}\) 100%) for the 90 th percentile. Therefore, the results demonstrate improved positioning performance when the noise-limited censored PL is taken into account also in the case of LOS detection errors.