## 5 Multipath Mitigation Results
### Scenario 3: High-Order BOC Signals  
Because of the excellent ranging accuracy and good spectral separability from the existing GNSS signals, some high-order BOC signals are adopted for military or safety critical applications. For example, the Chinese Beidou system employs the BOC(14,2) modulation of B1 frequency point as a new military signal and the Galileo system L1 PRS is a BOC(15,2.5) signal. However, these high-order BOC signals also bring a challenge that their auto-correlation functions have more secondary peaks compared with low-order BOC signals, such as BOC(1,1) signal, which makes it more difficult to track the LOS in a multipath environment. In this test, we mainly considered two high-order BOC signals, BOC(14,2) and BOC(15,2.5), to show the applicability of different multipath mitigation techniques on high-order BOC signals. Besides, in order to facilitate comparison and analysis, the setting of multipath  
Figure 12: Correlation functions in the presence of three multipath components.  
signal keeps consistent with the single-path channel scenario, except that the system sampling rate is set to 40 MHz due to the wider frequency spectrum of high-order BOC signals.  
Figure 14 shows the circumstance when the incoming signal is a BOC(14,2) modulated signal. The code rate of BOC(14,2) is 2.046 MHz. Because the time delay of the reflected ray is still 75 metres, equivalent to 0.51 code chip, the correlation peak of multipath signal shifts significantly to the right. Figure 15 indicates the performance of code delay estimation in the case of BOC(14,2). We can see that the CCRW method has the worst performance among all methods. When C/N\({}_{0}\) is 30 dB-Hz, the RMSE is more than 60 m. That is because high-order BOC signals have more correlation peaks compared with the low-order BOC signals. The CCRW methods try to suppress these secondary peaks, and meanwhile have to suffer a power loss of the main peak, which will cause significant ranging errors. So for this case, the CCRW methods cannot work well.  
Figure 14: Correlation function of BOC(14,2) signal in the presence of single multipath component.  
Figure 13: RMSE curves of averaging-FFT, MEDLL and CCRW methods in the presence of three paths.  
Interestingly, compared with the results in Figure 11, the RMSE curves of two aFFT methods even decrease slightly instead of going up. That's probably because of the good anti-multipath capacity of BOC(14,2) signal, but for MEDLL, the multi-peaks of BOC(14,2) still cause a RMSE increase compared with the BOC(1,1) signal.  
Further, the correlation function and RMSE curves of BOC(15,2.5) are shown in Figures 16 and 17, respectively. These results are quite similar to that of BOC(14,2). However, BOC(15,2.5) has a code rate of 2.5 \(\times\) 1.023 MHz, which is larger than the code rate of BOC(14,2), so the RMSE curves of different approaches are slightly lower than the curves in Figure 15.  
From all simulation results we present above, the proposed averaging-FFT method (\(L\) = 64) outperforms all other methods either in a single-path or multi-path channel and either for low-order or high-order BOC modulated signals. It means the proposed method has good universality and  
Figure 16: Correlation function of BOC(15,2.5) signal in the presence of single multipath component.  
Figure 15: RMSE curves of different methods for BOC(14,2) signal with single reflected path.  
robustness. It is feasible to perform multipath parameter estimation for arbitrary type of BOC(\(m\),\(n\)) signal with various numbers of reflected paths.