## 5 Multipath Mitigation Results
### Scenario 1: Single-Path Channel  
In this subsection, we tested the code tracking performance of the above three methods in the presence of a single multipath component. This test can be seen as a basic controlled trial whose results can be used to make a comparison with that obtained from the next two tests. The setting of simulation parameters is given in Table 3. A multipath component with attenuation of \(-3\) dB and delay of 75 m is added. The receiver intermediate frequency sampling rate is set to 20 MHz, which means the double-sided bandwidth is 20 MHz. Particularly, we choose two window sizes, \(L\) = 64 points and \(L\) = 128 points, to make a comparison with other methods, which helps us get a better understanding of the effect of window size \(L\). The total signal length herein is 40 ms and overlap rate is 50%. Generally, long-term data can be processed to achieve performance gain. However, for conventional anti-multipath techniques in correlation domain, such as CCRW technique, navigation bit transition is an issue that cannot be ignored and needs special treatment. But the IFFT-based method does not need to consider the effect of navigation bit transition, so long-term data as long as several seconds would be employed for multipath, which is also an advantage of the frequency processing technique over the conventional correlation domain anti-multipath techniques.  
Figure 10 shows the correlation function corresponds to the LOS component for this case. We can see that the correlation peak of the received signal is no more symmetry, which will bring errors to the conventional tracking loops, as well as the multipath mitigation methods based on measuring the correlation function.  
Figure 11 shows the RMSE curves of code delay estimation using different algorithms. The C/N\({}_{0}\) is varying from 30 dB-Hz to 40 dB-Hz. It can be seen that the aFFT method with \(L\) = 64 outperforms all other algorithms. Particularly when C/N\({}_{0}\) is 40 dB-Hz, the RMSE is just approximate 2.5 m; whereas  
for MEDLL and CCRW, the RMSE is around 6 m and 16 m. CCRW method, by contrast, has the worst performance. This is probably because CCRW method employs the correlation shape to estimate code delay. Since the correlation peak has been distorted in the presence of the multipath signal, the CCRW suffers from a significant bias even if without noise. Besides, we can also see that compared with \(L=64\), the RMSE of aFFT with \(L=128\) has a degradation of about 5 m to 8 m. This confirms the analysis in subsection entitled _Analysis of window length \(L\)_ that smaller \(L\) helps reduce the noise effect.  
Figure 11: RMSE curves of averaging-FFT, MEDLL and CCRW methods with C/N\({}_{0}\) varying from 30 dB-Hz to 40 dB-Hz.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Signal modulation type & BOC(1,1) \\ Signal length & 40 ms \\ Sampling rate & 20 MHz \\ Window length L & 64, 128 points \\ Window function & Hamming \\ Multipath attenuation (power) & \(-3\) dB \\ Multipath delay & 75 m \\ \hline \hline \end{tabular}
\end{table}
Table 3: Setting of Simulation Parameters.  
Figure 10: Correlation functions in the presence of single multipath component.