# Demodulation of EM Telemetry Data Using Fuzzy Wavelet Neural Network with Logistic Response
## 5 Conclusions  
This paper presents the development of a fuzzy wavelet neural network model with a logistic response for EMT/EM MWD and validates its prediction on the pseudo-synthetic  
Figure 16: Description of a fuzzy wavelet neural network for EM MWD response demodulation with a logistic response. The generated signal signal-to-noise ratio is 8.3 \(\times\)\(10^{-4}\). (**a**) The generated code, representing transmitted information; (**b**) transmitted signal with noise; (**c**) Adaptively processed signal; (**d**) post-processed transmitted signal with reduced data samples; (**e**) recovered signal code using an FWNN with a logistic response.  
Figure 15: Description of a fuzzy wavelet neural network for EM MWD response demodulation with a logistic response. The generated signal signal-to-noise ratio is 8.3 \(\times\)\(10^{-3}\). (**a**) The generated code, representing transmitted information; (**b**) transmitted signal with noise; (**c**) Adaptively processed signal; (**d**) post-processed transmitted signal with reduced data samples; (**e**) recovered signal code using an FWNN with a logistic response.  
EMT data that was generated by means of combining binary phase shift key code modulation and actual field noise. In the implemented scheme, the frequency-time characteristics of the predicted signal are controlled by selecting an appropriate number of wavelet bases (\"N\") and the pre-selected range for \(p_{ij}^{3}\) to be used, prior to the training of the FWNN system. In addition, the problem of digital communication synchronization in the EM MWD environment using neural networks was addressed by adopting the cross-correlation technique. In order to reduce the computational cost and increase prediction accuracy, post-processing steps to reduce the data volume and obtain a more characterized attribute of the phase shift signal were introduced.  
The FWNN result was compared with that of the commonly used BPNN. Although both techniques performed well, with moderately low SNRs, sharing common response characteristics with expectation-maximization, the FWNN provided an advantage in terms of performance, with EMT/EM MWD signals with very low SNRs. It should be noted that the proposed structures differ from the usual time-series prediction models since they include a logistic layer for transmitted code prediction.  
The full EMT/EM MWD processing workflow results, including both adaptive processing and signal demodulation, show that the proposed FWNN prediction model provides an accurate return of the transmitted code for the pseudo-synthetic datasets. Further work could explore more methods of obtaining the start and stop times as well as the deduction of performance when the transmitter and receiver are out of synchronization. In future work, the present approach will be enhanced by adding a recurrent step in the algorithm's weather information, such as temperature. Additionally, the application of the above technique in various real field data will be pursued as the opportunity presents itself.  
Conceptualization, O.F.; methodology, O.F.; validation, O.F. and P.L.; formal analysis, O.F.; investigation, O.F. and Q.Z.; resources, Q.D.; data curation, O.F.; software, O.F.; writing--original draft preparation, O.F.; writing--review and editing, O.F., P.L. and Q.Z.; visualization, O.F.; project administration, O.F.; funding acquisition, Q.D. All authors have read and agreed to the published version of the manuscript.  
This research was supported, in part, by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA140501000).  
Not applicable, studies does not involve humans or animals.  
Not applicable, studies does not involve humans.  
Data availability Statement: Data are available by request from the corresponding author.  
The authors declare no conflict of interest.