# Influence of Noise-Limited Censored Path Loss on Model Fitting and Path Loss-Based Positioning +
## 7 Positioning Simulation Results
### Example 3  
In this section, we analyze the positioning results assuming the true PL follows the Example 3 distribution, given in Section 5.3, at 2 and 28 GHz. The OLS and MLE model fitting results for LOS and NLOS are presented in Section 5.3. The positioning is based on (4) with parameters from Table 2 and \(PL^{*}=120\) dB and 140 dB at 2 and 28 GHz, respectively. The noise threshold is varied for one 2 GHz case to test the performance with different cutoff values. The LOS probability (12) is used to determine the LOS/NLOS state for the BSs. For simplicity, we assume that the LOS detection probability is 100% and the appropriate LOS or NLOS model parameters are used. BSs with censored PL are assumed to be in NLOS. In practice, the LOS state needs to be detected [41; 42; 43]. One 28 GHz case is presented with 100%, 95%, 90%, 85%, and 80% LOS detection rates in the positioning phase. LOS detection error leads to using LOS model parameters in NLOS, or NLOS parameters in LOS, and therefore, severe overestimation or underestimation of the link distances, respectively. Two BS grid densities are considered, leading to an average of five or ten contacted BSs, and two BS antennas are considered, omnidirectional and eight directional beams with \(N=8\) and \(\theta_{\text{3 dB}}=45^{\circ}\). The numbers of detected LOS and NLOS BSs depend on the average total number of contacted BSs, BS antenna, frequency, and the noise threshold. For example, \(\overline{N}_{\text{BS}}=10\) and the eight-sector directional antennas (\(N=8\)) the average number of contacted LOS BSs is 1.2 or 2.1 at 2 and 28 GHz, respectively. At 2 GHz, BSs with censored PL around the OTP results are included if they lie within 1600 and 640 m (OLS-MLE and MLE-MLE, respectively). At 28 GHz, these numbers are 1300 and 480 m. For example, at 2 GHz in the case of \(\overline{N}_{\text{BS}}=5\) and \(N=8\), OLS-MLE includes an average of 17 censored BSs and MLE-MLE includes an average of only 2.2. Positioning error 50 th and 90 th percentiles are listed in Tables 5 and 6, and four of the error CDFs are presented in Figure 9. At 2 GHz, the improvement from OLS-OTP to MLE-MLE ranged from 27% (from 73 to 53 m with \(N=8\) and \(\overline{N}_{\text{BS}}=10\)) to 44% (from 139 to 77 m with \(N=8\) and \(\overline{N}_{\text{BS}}=5\)) for the median error and from 40% (from 434 to 259 m with \(N=1\) and \(\overline{N}_{\text{BS}}=5\)) to 52% (from 392 to 188 m with \(N=8\) and \(\overline{N}_{\text{BS}}=5\)) for the 90 th percentile. At 28 GHz, the improvement from OLS-OTP to MLE-MLE ranged from 25% (from 54 to 40 m with \(N=8\) and \(\overline{N}_{\text{BS}}=10\)) to 46% (from 107 to 58 m with \(N=8\) and \(\overline{N}_{\text{BS}}=5\)) for the median error and from 36% (from 394 to 253 m with \(N=1\) and \(\overline{N}_{\text{BS}}=5\)) (from 198 to 98 m with \(N=8\) and \(\overline{N}_{\text{BS}}=10\)) for the 90 th percentile. Even though the underlying PL model is quite different than in Examples 1 and 2, the influence of the noise-limited PL is the same. Usually the error percentiles in Tables 3-6 are lower for OLS-MLE than MLE-OPT. This indicates that including the censored PL is more critical in the positioning phase than in the training phase. Of course, if possible, the MLE-MLE method should be used when possible. The influence of including the noise-limited PL in the positioning phase is much greater from OLS-OTP to OLS-MLE compared to MLE-OTP to MLE-MLE. In other words, including the censored PL in positioning is especially effective for correcting or compensating for the difference between the OLS fitted model and the true PL distribution. When the PL model fits well, the influence of MLEpositioning is clearly smaller and can be mostly seen in the 90 th percentiles of MLE-OTP and MLE-MLE. For example, at 28 GHz with \(N=8\) and \(\overline{N}_{\text{BS}}=5\), the 90 th percentile error is reduced by 21% from MLE-OTP to MLE-MLE.