# A Design Method of Code Correlation Reference Waveform in GNSS Based on Least-Squares Fitting
## 3 Results
### Boc(2,1)  
The settings for BOC(2,1) signals are listed in Table 3. The code correlation reference waveform for each case also present at each code transition, and its value is determined by the sign of the next code at transitions.  
The CCRW diagrams of the BOC(2,1) signal for the infinite bandwidth case are shown in Figures 22 and 23. The structures are quite different from the BPSK and BOC(1,1) signal with infinite bandwidth. No regular patterns can be found for the BOC(2,1) signals. The resulting S-curves for the infinite bandwidth case are presented in Figure 24, compared to non-coherent W2 CCRW, the double-delta correlator and the results of the waveforms in [14]. It can be seen that the S-curve in [14] (named the HEU S-curve) has a half-size linear region with a doubled slope, compared to the others. The steeper slope in the linear region aims for the improvement of tracking precision. The S-curve proposed here has a slope and a linear region like the W2 waveform, and an offset in the right side and returns to zero in the left side. As a result, the LS S-curves have a better multipath mitigation capability then the Harbin Engineering University (HEU) S-curve for medium and long delayed multipath signals, but worse for the short delayed multipath signal. The HEU S-curve also has a wider pull-in region for the negative part.  
The resulting S-curves for the 8.184-MHz bandwidth case are presented in Figure 25, and the CCRW diagrams are shown in Figures 26 and 27. The gate width of the code correlation reference waveforms is 0.1 chips, indicating that the smaller bandwidth can increase \(\upmu\). The ideal S-curve can be reproduced in the linear region, but the non-coherent S-curve has a sharper slope due to the ACF of the BOC(2,1) signal. Furthermore, the non-coherent S-curve returns to zero more quickly and has larger fluctuations in the left side of the linear region. The fitted S-curves still avoid the false lock points, compared to CCRW W2 and the double-delta correlator.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & **Infinite Bandwidth** & **16.368 MHz** & **8.184 MHz** \\ \hline Fitting range (\(\pm\)chips) & 1 & 1 & 1 \\ Linear region (\(\pm\)chips) & 0.1 & 0.1 & 0.1 \\ Offset (chips) & 0 (coherent) & 0.02 (coherent) & 0.02 (coherent) \\  & 0.02 (noncoherent) & 0.03 (noncoherent) & 0.05 (noncoherent) \\ Waveform range (chips) & \(-\)0.5\(\sim\)0.5 (coherent) & \(-\)0.8\(\sim\)0.15 (coherent) & \(-\)0.8\(\sim\)0.2 (coherent) \\  & \(-\)0.8\(\sim\)0.2 (noncoherent) & \(-\)0.5\(\sim\)0.5 (noncoherent) & \(-\)0.4\(\sim\)0.4 (noncoherent) \\ Gate width (chips) & 0.01 & 0.05 (coherent), 0.02 (noncoherent) & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation parameters for the BOC(2,1) signal.  
Figure 22: Code correlation reference waveform diagram for the BOC(2,1) signal coherent discriminator (infinite bandwidth).  
Figure 23: Code correlation reference waveform diagram for the BOC(2,1) signal non-coherent discriminator (infinite bandwidth).  
Figure 24: Fitted S-curves for the BOC(2,1) signal (infinite bandwidth).  
Figure 25: Fitted S-curves for the BOC(2,1) signal (8.184-MHz bandwidth).