## 5 Experimental Simulation Analysis  
### Energy Efficiency of the NR-ODBR-DCSK System  
For ease of reading and understanding, this section begins with a definition of the symbols that need to be applied, as shown in Table 3 below.  
In NR-ODBR-DCSK, the length of the reference signal in the current symbol period is \(\beta\), the length of the information signal is \(\beta\), and the specific equation for the bit energy transmitted in one codeword period is  
\[E_{b-NR-ODBR-DCSK}=E_{ref}+E_{data}=\sum_{k=1}^{\beta/P}x_{i,[ \frac{k}{P}]}^{2}+\sum_{k=1}^{\beta/P}\left(a_{k}x^{\prime}_{i,[\frac{k}{P}]- \beta}+b_{k}x^{\prime}_{i,[\frac{k}{P}]-\beta}\right)^{2} \tag{20}\]  
where \(E\) denotes the signal energy, \(E_{b-NR-ODBR-DCSK}\) is the NR-ODBR-DCSK signal energy, \(E_{data}\) is the NR-ODBR-DCSK information signal energy, and \(E_{ref}\) is the NR-ODBR-DCSK reference signal energy.  
The ratio of the transmitted data energy to the transmitted bit energy of NR-ODBR-DCSK within a frame, DBR, is given by Figure 2.  
\[DBR_{NR-ODBR-DCSK}=\frac{E_{data}}{E_{b-NR-ODBR-DCSK}}=1 \tag{21}\]  
The specific equation for the signal energy of DCSK in a frame is  
\[DBR_{DCSK}=\frac{E_{data-DCSK}}{E_{b-DCSK}}=\frac{1}{2} \tag{22}\]  
where \(DBR_{DCSK}\) is the ratio of transmitted data energy to transmitted bit energy, \(E_{data-DCSK}\) is the DCSK information signal energy, and \(E_{b-DCSK}\) is the DCSK signal energy.  
Table 4 below compares the NR-DCSK system proposed in reference [18], the SR-DCSK proposed in reference [6], the RSST-SR-DCSK system proposed in reference [26] and the HE-DCSK system proposed in reference [8]. Among them, the NR-DCSK system mainly improves the noise immunity performance, the SR-DCSK system improves the information transmission rate, the RSST-SR-DCSK system improves the information transmission security, and the HE-DCSK system provides the information transmission double-speed transmission performance.  
Comparing the DBR of the NR-ODBR-DCSK with that of other DCSK systems, it can be seen firstly that the energy efficiency of the NR-ODBR-DCSK is higher than that of  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Names of Different Modified DCSK Systems** & **DBR** \\ \hline NR-DCSK & \(1\) \\ SR-DCSK & \(\frac{\beta-R}{P+R}\) \\ RSST-SR-DCSK & \(\frac{P+1}{P+4}\) \\ HE-DCSK & \(\frac{1}{2}\) \\ NR-ODBR-DCSK & \(\frac{1}{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of DBR performance of different DCSK systems.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Mathematical Symbol** & **Connotation** \\ \hline \(E_{b-NR-ODBR-DCSK}\) & NR-ODBR-DCSK signal energy \\ \(E_{ref}\) & NR-ODBR-DCSK reference signal energy \\ \(E_{data}\) & NR-ODBR-DCSK information signal energy \\ \(DBR\) & Ratio of transmitted data energy to transmitted bit energy \\ \hline \hline \end{tabular}
\end{table}
Table 3: Several signal energy representations.  
the DCSK and NR-DCSK systems, secondly, that it is higher than that of the SR-DCSK system in certain cases, which is dependent on the length of the half-spreading factor of the SR-DCSK system, and lastly, that the NR-ODBR-DCSK system has the same DBR as the HE-DCSK system. This is due to the fact that HE-DCSK itself also provides a double-speed information transfer rate, but HE-DCSK has not been improved in any other way except for the increased information transfer rate.