## 4 Performance Analysis of the BOC Signal and BPSK Signal
### Acquisition Performance of the BOC Signal  
For the receiver of the traditional multinode switching, the switching process will be accompanied by signal reacquisition and retracking. According to [34], the BOC signal acquisition process and the clock cycles required in each stage are shown in Figure 8. Thus, all clock cycles of one acquisition are shown in Equation (15):  
\[T_{\text{acq}}=T_{\text{code}}+T_{\text{FFT}}+T_{\text{IFFT}}+T_{\text{mul}}+T _{\text{max}}+\Delta t \tag{15}\]  
where \(T_{\text{code}}\) represents the PN code period. \(T_{\text{FFT}}\) and \(T_{\text{IFFT}}\) are the time costs of the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) with 4096 points, respectively. \(T_{\text{mul}}\) is the time cost to multiply the FFT results of the local PN code and the FFT results of the receiving signal. \(T_{\text{max}}\) represents the time cost to search for the maximum value of the IFFT process. \(\Delta t\) is the time cost in other processes, which is less than 100 clock cycles. The system adopts \(f_{\text{s}}=80\) MHz, and the time of one acquisition is 0.6 ms.  
Since a single acquisition will increase false alarms and missed alarms, the receiver uses multiple detections to increase the acquisition success probability. For the Tong detector, the minimum detection times is 6 times. In addition, the Doppler frequency caused by relative motion is less than 12 kHz. In addition, we sh  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Distance between different nodes & Within 100 km \\ Relative movement speed & 1020 m/s \\ Radio frequency of VHF band & Uplink 200 MHz/ \\  & Downlink 300 MHz \\ Radio frequency of S band & Uplink 2.9 GHz/ \\  & Downlink 3.1 GHz \\ Maximum Doppler frequency of VHF band & Uplink 2550 Hz/ \\  & Downlink 3825 Hz \\ Maximum Doppler frequency of S band & Uplink 9860 Hz/ \\  & Downlink 10,540 Hz \\ Equivalent isotropically radiated power (EIRP) of VHF band & 45 dBm \\ Equivalent isotropically radiated power (EIRP) of S band & 47 dBm \\ VHF band receiving antenna gain & 8 dBi \\ S band receiving antenna gain & 28 dBi \\ \hline \hline \end{tabular}
\end{table}
Table 1: The parameter of simulation scenario.  
Figure 8: The acquisition process.  
frequency using 500 Hz intervals. Based on these parameters, the acquisition time when switching devices requires \(T_{acq\_total}=\frac{12.000\,\mathrm{Hz}\times 2}{500\,\mathrm{Hz}\,\mathrm{Z} \times 6\times T_{acq}=172.8\,\mathrm{ms}}\). The total switching time is \(T_{acq\_total}+T_{track\_lock}\), where \(T_{track\_lock}\) is the time of PLL lock time. However, the novel composite signal can ignore \(T_{acq\_total}\), which saves switching time. Furthermore, the \(T_{track\_lock}\) of the novel system is the same as that of the traditional system.  
Figure 9 shows the single acquisition success probability under different BOC and BPSK power ratio Monte Carlo simulations. When the ratio of \(\alpha\) and \(\beta\) is greater than 0.3:0.7, the main factor for the reduction of the acquisition probability is the reduction of the proportion of BOC signal power in the composite signal. When the ratio of \(\alpha\) and \(\beta\) is less than 0.3:0.7, the power of the BPSK signal will interfere with the acquisition of the BOC signal. Therefore, if the system is in a low carrier-to-noise (\(C/N_{0}\)) environment, it is reasonable to use \(\alpha:\beta=0.3:0.7\). However, when the \(C/N_{0}\) is higher than 70 dB-Hz, the power of the BOC signal can be reduced to improve communication performance.