## 4 Improvement Analysis of Downlink Signal Power Utilization Efficiency
If the power of the downlink ranging signal is unchanged and the power saved by detuning the DOR\({}_{1}\) beacon signal is allocated to the DOR\({}_{2}\) beacon signal, the power of the DOR\({}_{2}\) beacon signal will increase by more than \(100\%\) (one times better) as illustrated in Table 1.  
Table 1 provides a detailed analysis of the scenarios. Scenario 1 stands for the traditional modulation scheme, while Scenario 2 and 3 exemplify the proposed method, using Scenario 1 as a reference. When the DOR\({}_{1}\) beacon signal is not modulated in Scenario 2, that is, the modulation degree of the DOR\({}_{1}\) beacon signal is set to \(0\) rad, the power of the DOR\({}_{2}\) beacon signal is correspondingly larger by about \(0.55\) dB, which is about \(13\%\) (\(10^{0.055}\approx 1.135\)) higher than that in Scenario 1. In Scenario 3, the DOR\({}_{1}\) beacon signal is again not modulated and we enlarge the modulation degree of the DOR\({}_{2}\) beacon signal until the power of the ranging signal equals that in Scenario 1, then, it can be seen that the power of the DOR\({}_{2}\) beacon signal is correspondingly larger by about \(3.2\) dB, which is more than \(100\%\) higher compared with Scenario 1. Similarly, the power of the pseudo-code ranging signal in the S-band downlink can be expressed as follows:  
\[P_{\rm S,RG}=P_{\rm T}\cos^{2}(m_{\rm TM})f_{1}^{2}(m_{\rm RG}) \tag{13}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Scenario ID**} & \multirow{2}{*}{**Modulation Signal**} & \multirow{2}{*}{**Modulation Degree**} & \multicolumn{2}{c}{**Power of Downlink Signal**} \\  & & & **Relative to the Carrier** \\ \hline \multirow{4}{*}{1} & Telemetry signal & \(0.8\) rad & – \\  & Ranging signal & \(0.6\) rad & \(-15.09\) dB \\  & DOR1 beacon signal & \(0.5\) rad & \(-16.80\) dB \\  & DOR2 beacon signal & \(0.5\) rad & \(-16.80\) dB \\ \hline \multirow{4}{*}{2} & Telemetry signal & \(0.8\) rad & – \\  & Ranging signal & \(0.6\) rad & \(-14.54\) dB \\  & DOR1 beacon signal & \(0.0\) rad(detuned) & \(0\) dB \\  & DOR2 beacon signal & \(0.5\) rad & \(-16.25\) dB \\ \hline \multirow{4}{*}{3} & Telemetry signal & \(0.8\) rad & – \\  & Ranging signal & \(0.6\) rad & \(-15.09\) dB \\  & DOR1 beacon signal & \(0.0\) rad(detuned) & \(0\) dB \\  & DOR2 beacon signal & \(0.7\) rad & \(-13.60\) dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The relative power of the downlink signal with different modulation mode. Under the same condition of modulation as described in Equation (9), the power ratio of the pseudo-code ranging signal relative to the total power of the downlink signal is \(-14.54\) dB, which is also about 13% higher than that of the DOR\({}_{1}\) beacon signal modulated to the downlink carrier. Based on the analysis of Sections 2 and 4, the measurement accuracy or exploration distance improvement of the proposed method is shown in Table 2. The scenarios are consistent with that in Table 1. As can be seen, if the exploration distance keeps unchanged, the proposed method can improve the measuring accuracy by about 5.1% and 24.6% for Scenario 2 and 3, respectively. If the RSS keeps unchanged, the exploration distance can be increased by about 6.25% and 41.25% for Scenario 2 and 3, respectively.