# Demodulation of EM Telemetry Data Using Fuzzy Wavelet Neural Network with Logistic Response
## 4 Examples
### Comparison of the FWNN with BP Using Synthetic Data with Three Noise Variants
We further illustrate the performance of the proposed algorithms by comparing the output of the demodulated code with the result from the conventional BP technique in a system with an identical scenario and noise characteristics, as given in Table 1. The test for each noise variation is presented by a comparative figure and the information in the general table. The first is Figure 10, which depicts the BP and FWNN results when the transmitted signal noise is the combination of red and blue noise, with an SNR of 10 dB. The recovered codes were a good representation of the transmitted code. That is, high accuracy is attainable by both methods when the SNR is equal to or higher than 10 dB. Similarly, both methods recorded high accuracy with the pink and violet noise even at an SNR of 1 dB (Figure 11). However, for other noise characteristics, the accuracy of the BP technique was reduced to 97.5% and 95%, respectively, for the pink and blue noise and the AWGN noise, respectively (Table 1). Last is the performance of both techniques in the presence of AWGN noise. The results show a less accurate result for both methods with an SNR value of \(-15\) dB \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{5}{c}{**Time (s)**} & \multicolumn{5}{c}{**\% Accuracy**} \\ \cline{2-9}  & **Noise Characteristic** & **SNR-15** & **SNR 1** & **SNR-10** & **SNR-15** & **SNR-1** & **SNR-10** \\ \hline \multirow{3}{*}{FWNN} & AWGN & 0.45 & 0.38 & 0.34 & 93.1 & 100 & 100 \\ \cline{2-9}  & Red and blue & 0.42 & 0.42 & 0.44 & 100 & 100 & 100 \\ \cline{2-9}  & Pink and violet & 0.40 & 0.39 & 0.32 & 100 & 98 & 100 \\ \hline \multirow{3}{*}{BP} & AWGN & 0.12 & 0.19 & 0.15 & 87.5 & 95 & 100 \\ \cline{2-9}  & Red and blue & 0.21 & 0.21 & 0.23 & 98.8 & 97.5 & 100 \\ \cline{2-9}  & Pink and violet & 0.15 & 0.15 & 0.14 & 97.5 & 100 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of our FWNN with BP. The same number of unknown parameters (NUPs) was used for the training for each noise characteristic and SNR. Figure 10: Comparison of EM MWD response demodulation results when the signal is riddled with the combination of red and blue noise types. (**a**) The generated code, representing transmitted information; (**b**) the transmitted EM MWD signal; (**c**) transmitted signal with noise; (**d**) post-processed transmitted signal with reduced data samples; (**e**) recovered signal code using an FWNN with a logistic response; and (**f**) recovered signal code using a BPNN. SNR is 10 dB. (Figure 12) and the BP method having an accuracy of 87.5% and the FWNN an accuracy of 93.1% (Table 1). The displayed figures show the representative section of the obtained responses from the different techniques. Figure 11: Comparison of EM MWD response demodulation results when the signal is riddled with the combination of pink and violet noise types. (**a**) The generated code, representing transmitted information; (**b**) the transmitted EM MWD signal; (**c**) transmitted signal with noise; (**d**) post-processed transmitted signal with reduced data samples; (**e**) recovered signal code using an FWNN with a logistic response; and (**f**) recovered signal code using a BPNN. SNR is 1 dB. Figure 12: Comparison of EM MWD response demodulation results when the signal is riddled with AWGN noise types. (**a**) The generated code, representing transmitted information; (**b**) the transmitted EM MWD signal; (**c**) transmitted signal with noise; (**d**) post-processed transmitted signal with reduced data samples; (**e**) recovered signal code using an FWNN with a logistic response; and (**f**) recovered signal code using a BPNN. SNR is \(-\)15 dB. The effectiveness of the two techniques is established, as observed from the percentage accuracy in Table 1, which details the networks' performance under different signal-to-noise ratios. The two networks performed excellently, with a moderately low SNR value of 1.