## 5 Performance Analysis  
### ACF and PSD  
The ACF and PSD are essential in signal simulation, performance evaluation, and acquisition and tracking algorithm design [28; 29]. We first derive the expressions of ACF and PSD for each type of ACE-BOC signal. Then, we selected several representative ACE-FHBOC signals in comparison with ACE-BOC. These signals are ACE-FHBOC(24:1:1,1), ACE-FHBOC(24:1:6,1), ACE-BOC(12,1), and ACE-BOC(15,10). ACE-FHBOC(24:1:1,1) has the same PSD main lobe bandwidth (MLB) as ACE-BOC(15,10), and its zero-crossing near the ACF main peak (ZCNM) is approximately equal to that of ACE-BOC(12,1). ACE-FHBOC(24:1:6,1) has the same MLB and ZCNM as ACE-BOC(15,10), and its spectrum compatibility is also similar to ACE-BOC(15,10). In general, there are two main approaches for processing an ACE-FHBOC: one is to process each signal component independently, and the other is to process the whole ACE-FHBOC signal with a wideband receiver to realize better performance. Under the assumption that an ACE-FHBOC signal has an ideal spreading code and infinite bandwidth, we derive the ACF and PSD of the whole ACE-FHBOC signal in Appendix B. The top panel of Figure 7 shows the normalized ACFs of the Type-I example signals. ACE-FHBOC(24:1:1,1) has the lowest ACF side peaks among the example signals, which means the lightest ACF ambiguity. The ACF side peaks of ACE-FHBOC(24:1:6,1) are lower than ACE-BOC(15,10). The ACF main peak of ACE-FHBOC(15,10) is the narrowest among the example signals, which means the best potential ranging performance among the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Resource Consumption** & **ACE-FHBOC** & **ACE-BOC** \\ \hline Minimum Subchip Rate & \(12\alpha_{M-1}/f_{0}\) & \(12\alpha/f_{0}\) \\ Minimum number of Bits of Direct Subcarriers Generator & 3 & 3 \\ LUT of Phase Rotation Generation Method & \(M\times 12\times 16\) LUT & \(12\times 16\) LUT \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Generation complexity comparison summary. Figure 6: Simulated and theoretical results for normalized ACF and PSD of ACE-FHBOC(10:1:1,1). example signals. The ACF main peak of ACE-FHBOC(24:1:1,1) is narrower than that of ACE-BOC(12,1). The bottom panel of Figure 7 shows the normalized PSDs of the Type-I example signals. The power in the PSD main lobes is evenly distributed within the bands for ACE-FHBOC(24:1:1,1), and the maximum value of PSD envelope is the smallest among the example signal. The PSD main lobes of ACE-BOC(12,1), ACE-BOC(15,10), and ACE-FHBOC(24:1:6,1) are offset from the band center. Table 3 lists the spectral separation coefficients (SSC) of the example signals with the legacy satellite navigation signals. ACE-FHBOC(24:1:1,1) has a larger cross-SSCs than ACE-BOC(15,10) and ACE-FHBOC(24:1:6,1), but has a smaller self-SSC. Thus, ACE-FHBOC(24:1:1,1) has a worse intersystem compatibility but a better intrasystem compatibility than ACE-BOC(15,10) and ACE-FHBOC(24:1:6,1). Figures 8 and 9 show the normalized ACFs of the Type-II and Type-III example signals, respectively. Interestingly, the ACFs of these signals are complex. The real parts are even functions and the imaginary parts are odd functions. \begin{table}
\begin{tabular}{c c c c c} \hline \(K_{XY}\) (dB/Hz) & **(12,1)** & **(15,10)** & **(24:1:1,1)** & **(24:1:6,1)** \\ \hline BPSK(1) & \(-92.2\) & \(-83.9\) & \(-82.4\) & \(-92.0\) \\ BPSK(10) & \(-86.5\) & \(-84.2\) & \(-78.3\) & \(-84.7\) \\ MBOC(6,1,1/11) & \(-92.2\) & \(-84.1\) & \(-78.5\) & \(-86.1\) \\ BOC(10,5) & \(-76.1\) & \(-79.4\) & \(-78.4\) & \(-78.1\) \\ Self & \(-66.7\) & \(-76.6\) & \(-78.6\) & \(-78.0\) \\ \hline \end{tabular}
\end{table} 
Table 3: SSCs of the example signals. Figure 7: Normalized ACFs and PSDs of the Type-I example signals. Figure 10 shows the normalized PSDs of the Type-II and Type-III example signals, respectively. It can be seen that the upper and lower sidebands are assigned different signal powers. Figure 8: Normalized ACFs of the Type-II example signals. Figure 9: Normalized ACFs of the Type-III example signals.