# Integrated Communication and Measurement System with BOC-Assisted OFDM
## 4 Simulation Results and Performance Analysis
### Acquisition Performance  
The acquisition performance is mainly determined by three parameters: the success probability of a single acquisition, \(P_{success}\); the false alarm probability, \(P_{FA}\); and the false dismissal probability, \(P_{MA}\). These three parameters are obtained through repeated detection and statistics based on the Monte Carlo algorithm, as shown in Figures 11 and 12 (since the false alarm probability is approximately equal to zero, it is not shown in a figure). Figure 11 shows the success probability of single acquisition under different power ratios and different CNRs. As shown in Figure 11, the success probability of a single acquisition, \(P_{success}\), is not significantly different when \(\alpha\):\(\beta\) = 0.5:0.5 and \(\alpha\):\(\beta\) = 0.4:0.6 and when \(CNR=50\) dB-Hz, \(P_{success}\approx 50\%\); when the CNR increases to 53 dB-Hz, \(P_{success}\approx 100\%\). However, the performance gradually deteriorates as the power ratio further decreases. To achieve \(P_{success}\) = 100%, the requirements are as follows: when \(\alpha\):\(\beta\) = 0.3:0.7, \(CNR\geq 55\) dB-Hz; when \(\alpha\):\(\beta\) = 0.2:0.8, \(CNR\geq 57\) dB-Hz; and when \(\alpha\):\(\beta\) = 0.1:0.9, \(CNR\geq 62\) dB-Hz. In summary, as the power ratio decreases, the performance in terms of the success probability of single acquisition degrades.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values** \\ \hline Carrier frequency, \(f_{c}\) & 10.23 MHz \\ BOC subcarrier frequency, \(f_{sc}\) & 4.096 MHz \\ Number of OFDM subcarriers, \(N_{sc}\) & 16 \\ Sampling frequency, \(f_{s}\) & 80 MHz \\ Coding frequency, \(f_{code}\) & 1.023 MHz \\ Range of the Doppler frequency offset, \(f_{dappler}\) & \(-1\) kHz–\(1\) kHz \\ Pilot pattern & Comb-type pilots(with intervals of 3 subcarriers) \\ Channel model & Jakes \& AWGN \\ Bandwidth & 8.092 MHz \\ Cyclic-prefix length & 7.8 \(\mu\)s \\ Data rate & 0.628 Mbps \\ FL bandwidth & 20 Hz \\ PLL bandwidth & 10 Hz \\ SPLL bandwidth & 2 Hz \\ DLL bandwidth & 2 Hz \\ DLL correlator spacing & 0.5 chip \\ Loop update time & 1 ms \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
Figure 12 illustrates the false dismissal probability under different power ratios and different CNRs. As displayed in Figure 12, the false dismissal probability, \(P_{MA}\), is not considerably different when \(\alpha\):\(\beta\) = 0.5:0.5 and \(\alpha\):\(\beta\) = 0.4:0.6, and when \(CNR=50\) dB-Hz, \(P_{MA}\approx 50\%\). When the CNR increases to 54 dB-Hz, \(P_{MA}\approx 0\). However, the performance gradually deteriorates as the power ratio further decreases. To achieve \(P_{MA}=0\), the requirements are as follows: when \(\alpha\):\(\beta\) = 0.3:0.7, \(CNR\geq 55\) dB-Hz; when \(\alpha\):\(\beta\) = 0.2:0.8, \(CNR\geq 57\) dB-Hz; and when \(\alpha\):\(\beta\) = 0.1:0.9, \(CNR\geq 63\) dB-Hz. In summary, as the power ratio decreases, the performance in terms of the false dismissal probability degrades.  
As the power ratio decreases, the acquisition performance gradually deteriorates. The main factor influencing the degradation of the acquisition performance is the reduction in the proportion of the BOC signal in the composite signal. Moreover, the proportion of the OFDM signal may have an impact on the acquisition process, resulting in a decline in the acquisition performance. Therefore, when the CNR is below 55 dB-Hz, the use of \(\alpha\):\(\beta\) = 0.3:0.7 is reasonable. When the CNR exceeds 63 dB-Hz, the acquisition performance is no longer affected by the power ratio. Thus, a reduction in the proportion of the BOC signal can improve the communication performance and decrease the BER.  
Figure 11: Success probability of single acquisition under different conditions.  
Figure 12: False dismissal probability under different conditions.