# Multipath Mitigation for BOC Signals Based on Prompt-Assisted-Offset Correlator
## 4 Performance Evaluation and Results
### Simulation Results
#### 4.3.2 Static Multipath Scenarios  
In practice, ranging errors include the noise error and multipath error. Moreover, multipath signals lead to variations in the SNR, thereby affecting the thermal noise error. It is difficult to separate the noise error from the multipath error. Thus, the root-mean-square error (RMSE) is used to evaluate the ranging performance of the four methods. According to Equations (27) and (29), when the multipath relative phase is 0 and \(\pi\), the subcarrier multipath error reaches its maximum value, while the carrier multipath error is almost 0. Figure 10 shows the RMSE envelop of the four methods for the BOC(15, 2.5) signal when the multipath relative phase is 0 and \(\pi\). The subcarrier RMSE varies with multipath relative delay in Figure 10a due to the multipath error. According to Equations (13) and (29), the carrier multipath errors of all four methods are 0 when the multipath relative phase \(\theta_{m}\) is 0 and \(\pi\). Therefore, the carrier errors shown in Figure 10b are noise errors. Since the PAOC technique has thermal noise performance loss compared with using the prompt correlator, the carrier RMSE of the PAOC-PAOC method in Figure 10b is larger than that of the OC-P and DBT methods. Moreover, the carrier RMSE varies with multipath relative delay in Figure 10b because the SNR is affected by multipath. According to Equations (27) and (29), when the multipath relative phase is \(\pm\pi/2\), the subcarrier multipath error reaches its minimum value, while the carrier multipath error reaches its maximum value. Figure 11 shows the RMSE envelop of four methods for the BOC(15, 2.5) signal when the multipath relative phase is \(\pm\pi/2\). When the multipath relative delay is greater than 1 chip, there is only thermal noise error and no multipath error in the RMSE. When the multipath relative delay is less than 1 chip, the RMSE of the DBT method contains both thermal noise error and multipath error. Comparing the RMSE in the two cases, it can be found that the multipath error is significantly larger than the thermal noise error. Moreover, Figures 10 and 11 show that the PAOC-PAOC method has better multipath mitigation performance than the other three methods. Figure 10: RMSE envelop of various methods for the BOC(15, 2.5) signal, where the multipath relative phase is 0 and \(\pi\): (**a**) subcarrier RMSE; (**b**) carrier RMSE. Both OC-P and OC-OC methods use the OC technique with the same forward offset in the SPLL, which suggests that they have the same subcarrier multipath performance. However, Figure (a)a shows that the subcarrier RMSE of the OC-P method is greater than that of the OC-OC method. This is because the OC-P and OC-OC methods use different techniques in the PLL, and the carrier error indirectly affects the subcarrier error. Figure (b)b shows that the carrier RMSE of the OC-P method is greater than that of the OC-OC method. The OC-OC method using the OC technique in the PLL not only directly improves the carrier multipath performance, but also indirectly improves the subcarrier multipath performance. Therefore, it is desirable to use multipath mitigation techniques in both the PLL and the SPLL to improve multipath performance. The area enclosed by the RMSE envelop can reflect the average ranging performance of the multipath mitigation methods, which is calculated as:  
\[Area(\tau_{max})=\int_{0}^{\tau_{max}}RMSE(\tau_{m})d\tau_{m} \tag{34}\]  
where \(\tau_{max}\) is the maximum multipath relative delay. Considering that multipath signals with relative delays greater than 1 chip do not cause multipath errors, \(\tau_{max}\) is set to 1.2 chips. Table 3 shows the area enclosed by RMSE envelopes of the four methods. When the multipath relative phase is \(\pm\pi/2\), the PAOC-PAOC method has the smallest subcarrier and carrier RMSE area. When the multipath relative phase is 0 and \(\pi\), the PAOC-PAOC method has the smallest subcarrier RMSE area but has a large carrier RMSE area.