## 4 Simulation Experiment Comparison  
To validate the effectiveness and reliability of the BBC design and optimization method, six sets of BBC sequences were generated and optimized using the parameters listed in Table 3. The system sampling frequency was set to 80 MHz, the PRN rate \(f_{chip}\) was set to 1.6 MHz, the data code rate \(f_{data}\) was set to 25 kbps, and the PRN code length was 1024. Under these settings, \(n_{code}=64\). Six sets of BBC sequences were obtained using the parameters in Table 3, and their performance was compared with those of the original Weil sequences. The specific performance results for each indicator are shown in Figure 5 and Table 4. The maximum sidelobes of the correlation and maximum value ranges of the other indicators, along \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Parameters** & **Value** & **Remarks** \\ \hline \multirow{3}{*}{
\begin{tabular}{c} ranging \\ communication \\ system \\ \end{tabular} } & system frequency \(f_{s}\) & 80 MHz & \\  & PRN rate \(f_{chip}\) & 1.6 MHz & \\  & PRN length \(N\) & 1024 & \\  & data rate \(f_{data}\) & 25 kbps & \\ \hline \multirow{3}{*}{BBC design} & combination window \(n_{code}\) & 64 & \(n_{code}=f_{chip}/f_{data}\) \\  & variable \(T_{0}\) & 6 & \(T_{0}=\lfloor n_{code}/10\rfloor\) \\ \hline \multirow{3}{*}{BBC optimization} & weight \(z_{1}\), \(z_{2}\), \(z_{3}\) & 0.5, 0.25, 0.25 & \(z_{1}+z_{2}+z_{3}=1\) \\  & PRN target code count \(M_{0}\) & 6 & gravitational wave \\ \cline{1-1}  & & & design requirements \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation of each index parameter. with their averages, are presented (the mean is the actual data mean, not the center point of each range). It can be observed that the BBC sequences designed based on the Weil sequences, when compared to the original Weil sequences, show improved performance after optimization. Specifically, the mean value for the odd cross-correlation indicator remains the same as that of the original sequence at 95.33, while the average values for the even autocorrelation, odd autocorrelation, maximum spectrum amplitude, and even cross-correlation indicators are better than those of the original Weil sequence by 7.17, 2.83, 1.22, and 7.16, respectively. A comparison of various performance indicators shows that the BBC generation and optimization method can enhance the performance of the original sequence while modifying the balance and selecting the best-performing BBC sequences, thus verifying the effectiveness of this method. Furthermore, to verify that the BBC sequences can effectively eliminate the DC component during BPSK modulation, random data were encoded into six optimized BBC sequences based on the parameters in Table 3, followed by cumulative mean statistics. The results are presented in Figure 6, which illustrates the cumulative mean before and after data encoding. For a balanced signal, the cumulative mean should approach zero. In the figure, the horizontal axis represents each sample point in the signal, while the vertical axis represents the cumulative mean at each sample point. The six optimized BBC sequences are depicted in blue and red, with solid lines representing BBC sequences without encoded data and dashed lines representing BBC sequences with encoded data. To enhance clarity, the encoded sequences are displayed with inversion. It can be observed that the BBC sequences exhibit consistent trends before and after encoding, with only minor fluctuations near zero. As the sample size increases, the mean rapidly converges to zero, indicating \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & **Mean** & **Mean** & **Mean** & **Mean** & **Mean** \\  & **Even-Auto** & **Odd-Auto** & **Spectrum** & **Even-Cross** & **Odd-Cross** \\ \hline BBC & 59.33 & 98 & 64.81 & 58.67 & 95.33 \\ Weil & 65.50 & 100.83 & 66.03 & 65.83 & 95.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance Comparison Table of BBC and Weil Sequences.