# Lamb Wave-Based FDM-PPM Method Data Transmission Scheme in Plate Structures
## 3 Analysis of the Experimental Results for Lamb Wave FDM-PPM
### Analysis and Discussion of Bit Error Rate  
To demonstrate the superiority of the FDM-PPM method over other modulation techniques, this study conducted comparative tests on ASK and PPM signals with varying numbers of symbols (ranging from two to seven). The following discussion focuses on the example of ASK and PPM signals with seven symbols. The demodulation results of the ASK and PPM signals after compensation for Lamb wave echoes are shown in Figure 10 and Figure 11, respectively. Figures 10 and 11 show that the Lamb wave echo equalization algorithm effectively compensates for the echoes of continuously transmitted ASK and PPM signals. In Figure 11, the red line indicates the start and end positions of the PPM signal, respectively. After processing with this algorithm, the information transmitted by the ASK and PPM signals can be accurately demodulated. This study conducted multiple transmission and equalization experiments on ASK and PPM signals with varying numbers of symbols (ranging from two to seven). The results indicate that the demodulation performance of ASK and PPM signals is satisfactory after equalization. The detailed results are presented in Tables 2 and 3, respectively. Due to the different modulation principles of the ASK and PPM methods, the number of transmitted bits also varies. Specifically, the ASK method transmitted 421 bits of information, all correctly demodulated after equalization, achieving a demodulation accuracy of 100%. In contrast, the PPM method transmitted 512 bits of information, of which 498 bits were correctly demodulated, resulting in a demodulation accuracy of 97.2%. Following the experiment on single-frequency communication signals of Lamb waves, subsequent experiments were conducted on the continuous transmission of Lamb waves using FDM. The detailed experimental results are presented in Table 4.  
In summary, when continuously transmitting Lamb wave ASK data on the constructed plate, the Lamb wave echo equalization compensation algorithm is used to demodulate the data, ensuring correct demodulation with a system communication rate of 10 kbps. Using the PPM-based method for Lamb wave data transmission achieves an accuracy of 97.26%, with a system communication rate of 20 kbps. The FDM-based method for Lamb wave data transmission achieves an accuracy of 98.58%, with a system communication rate of 30 kbps. Employing the FDM-PPM modulation method for Lamb wave data transmission achieves \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of** & **Number of** & **Number of Correctly** & **Demodulation** \\
**Symbols** & **Transmitted Bits** & **Demodulated Bits** & **Accuracy** \\ \hline
2 & 12 & 12 & 100\% \\
3 & 18 & 18 & 100\% \\
4 & 36 & 36 & 100\% \\
5 & 75 & 75 & 100\% \\
6 & 132 & 132 & 100\% \\
7 & 148 & 148 & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The demodulation results of the Lamb wave ASK signals. Figure 11: (a–g) Intercepted Lamb wave PPM signals corresponding to excitation numbers 1 to 7, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of** & **Number of** & **Number of Correctly** & **Demodulation** \\
**Symbols** & **Transmitted Bits** & **Demodulated Bits** & **Accuracy** \\ \hline
2 & 36 & 36 & 100\% \\
3 & 72 & 72 & 100\% \\
4 & 80 & 80 & 100\% \\
5 & 90 & 90 & 100\% \\
6 & 108 & 101 & 93.5\% \\
7 & 126 & 119 & 94.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The demodulation results of the Lamb wave PPM signals. an accuracy of 90.7%, with a system communication rate of 50 kbps. The experimental results indicate that the ASK method has the lowest bit error rate but a relatively lower transmission rate. In contrast, the FDM-PPM method has the highest but relatively higher bit error rate. The experimental results show that the dispersion characteristics of Lamb waves cause distortion in the signal waveform, thereby significantly affecting the signal's phase discrimination.