Application of a New Combination Algorithm in ELF-EM Processing

: With regards to the electromagnetic measurement while drilling (EM-MWD), the extremely-low frequency electromagnetic wave signal (ELF-EM) below 20 Hz is usually used as the carrier of downhole measurement data due to the transmission characteristics of the electromagnetic wave (EM). However, inﬂuenced by the low frequency noise of drilling, the ELF-EM signal will be inevitably interfered by ﬁeld noise, which ultimately impedes decoding. The Fourier band-pass ﬁlter can e ﬀ ectively remove out-of-band noise but is incapable of handling in-band noise. Therefore, based on the traditional method, a hybrid algorithm of adaptive Wiener algorithm and correlation detection (AWCD) is designed, so as to enhance the in-band noise processing capability, and the e ﬀ ectiveness of such algorithm is well veriﬁed through coding and decoding simulation as well as experimental data. The proposed algorithm, as indicated by theoretical analysis and test data, can e ﬀ ectively solve actual engineering issues, providing methodological references to engineers and technicians.


Introduction
Currently, two transmission modes are mostly applied to the measurement while drilling (MWD) process, namely stand pipe for mud pulse detection [1] and electromagnetic (EM) wave transmission [2,3].As the latter is not dependent on drilling fluid, does not require the balanced pressure between downhole fluid and formation, and can send measured data in real-time, it is becoming the focus of MWD studies along with the development of such new technologies as under-balanced well and air drilling.Despite that, the signal processing capability of the system's surface receiver has posed a restriction upon its development.It is proven by theoretical studies that the signal strength will gradually decrease as the frequency of the MWD EM wave increases [3]; after taking engineering factors into consideration, ELF-EM below 20 Hz is commonly adopted as the carrier.As exploration deepens, the received EM signal of constant frequency is gradually weakened, interfered with by various noise from field operations and, therefore, affecting decoding accuracy.Effectively improving the processing capacity of the terminal receiver's algorithm can practically enlarge transmission depth, improve the signal to noise ratio (SNR), and reduce the error rate.Traditionally, designed filtering bandwidth is applied to smooth out-of-band noise [4], which is reliable and sound, and works well for the out-of-band noise, not the in-band noise.In addition, the Fourier transform-based denoising method is suitable for stationary signals, but it has a poor processing effect on non-stationary ELF-EM signals whose frequency changes with time.The key to extend transmission depth and lower decoding error rate is whether the in-band noise of ELF-EM signal can be filtered without affecting signal source.
extend transmission depth and lower decoding error rate is whether the in-band noise of ELF-EM signal can be filtered without affecting signal source.Researchers have proposed different solutions, such as the MWD system signal processing based on wavelet transform and pattern recognition [5] by Dong Xiani, which analyzed MWD channel attenuation features and noise characteristics, and established the signal filtering and recognition model to yield a combined method of wavelet transform, correlation filtering and pattern recognition.However, wavelet parameters need to be set on the basis of pre-analyzing signal features; and for signals with different SNR, the decomposition level of the best denoising effect shall be determined as well, all of which proves unfitting to the nonstationary and mostly real-time ELF-EM signal processing.In the harmonic interference elimination algorithm based on parameter estimation [6] by Long Ling et al., harmonic waves are estimated then reconstructed, with interference signals eliminated from received signals, iterating such processes until effective signals reach more than 50% of the effective signal, whereas this algorithm fails to filter out in-band noises and meet the real-time decoding requirement.Wang Hongliang et al. proposed a correlation adaptor-based EM-MWD signal detection algorithm [7] that carries out EM signal detection according to the initial signal strength and adaptive detection and correlation, but the designed algorithm requires high accuracy and real-time performance of the collected reference noise.The EM-MWD receiver of neural network algorithm proposed by Whitacre et al. [8] has adaptive learning ability, and performs better than correlation receivers, especially for non-white noise and ambient noise obtained from actual drilling sites.ELF-EM signal needs to be decoded in higher real-time efficiency, so the design of its learning algorithm is crucial.The multi-combinational adaptive tracking detection algorithm proposed by Li Fukai et al. [9] designed adaptive notches to obtain the reference noise and then used the adaptive cancellation algorithm to denoise it.This algorithm can eliminate in-band interference to some extent, but it is still difficult to remove in-band noise of large interference.In summary, some of the above methods have their own limits and others perform poorly with regard to in-band noise reduction, all of which is hard to meet the complex conditions of drilling projects.Therefore, to work out an effective method of removing the ELF-EM in-band noise has become a key to the transmission of EM-MWD.Figure 1 shows a typical schematic diagram of EM signal transmission in MWD.In order to study the denoising of ELF-EM signal in MWD, its coding methods and spectral characteristics must be explored first, and then the influencing factors to engineering applications.Furthermore, based on previous studies, this paper designs a combinational algorithm based on the adaptive Winner correlation detection algorithm (or AWCD) to further improve the in-band noise processing ability.By means of codec simulation and actual field data, the effectiveness of such algorithm is verified.Additionally, theoretical analysis and field data processing showed that the algorithm can solve practical engineering problems and provide reference to field technicians.

The Encoding and Influence Factors of ELF-EM Transmission in Strata
In terms of the transmission characteristics of ELF-EM in strata and the actual needs of MWD projects [10], the frequency of transmitted ELF-EM is usually set below 20 Hz.Pulse position modulation (PPM) uses the relative position of pulses for modulation, of which pulse amplitude and width remain unchanged, thus facilitating modulation and demodulation.In addition, it has higher power utilization rate with relatively low transmission power [11][12][13].As a result, the EM MWD system is more suitable for PPM modulation.The modulation and demodulation process is shown in Figure 2: Symmetry 2020, 12, 337 3 of 18

The Encoding and Influence Factors of ELF-EM Transmission in Strata
In terms of the transmission characteristics of ELF-EM in strata and the actual needs of MWD projects [10], the frequency of transmitted ELF-EM is usually set below 20 Hz.Pulse position modulation (PPM) uses the relative position of pulses for modulation, of which pulse amplitude and width remain unchanged, thus facilitating modulation and demodulation.In addition, it has higher power utilization rate with relatively low transmission power [11][12][13].As a result, the EM MWD system is more suitable for PPM modulation.The modulation and demodulation process is shown in Figure 2: A typical MWD ELF-EM modulated signal is shown in Figure 3 below, and its carrier frequency is 6.25 Hz.A typical MWD ELF-EM modulated signal is shown in Figure 3 below, and its carrier frequency is 6.25 Hz.

The Encoding and Influence Factors of ELF-EM Transmission in Strata
In terms of the transmission characteristics of ELF-EM in strata and the actual needs of MWD projects [10], the frequency of transmitted ELF-EM is usually set below 20 Hz.Pulse position modulation (PPM) uses the relative position of pulses for modulation, of which pulse amplitude and width remain unchanged, thus facilitating modulation and demodulation.In addition, it has higher power utilization rate with relatively low transmission power [11][12][13].As a result, the EM MWD system is more suitable for PPM modulation.The modulation and demodulation process is shown in Figure 2  A typical MWD ELF-EM modulated signal is shown in Figure 3 below, and its carrier frequency is 6.25 Hz.Symmetry 2020, 12, 337 3 of 18

The Encoding and Influence Factors of ELF-EM Transmission in Strata
In terms of the transmission characteristics of ELF-EM in strata and the actual needs of MWD projects [10], the frequency of transmitted ELF-EM is usually set below 20 Hz.Pulse position modulation (PPM) uses the relative position of pulses for modulation, of which pulse amplitude and width remain unchanged, thus facilitating modulation and demodulation.In addition, it has higher power utilization rate with relatively low transmission power [11][12][13].As a result, the EM MWD system is more suitable for PPM modulation.The modulation and demodulation process is shown in Figure 2  A typical MWD ELF-EM modulated signal is shown in Figure 3 below, and its carrier frequency is 6.25 Hz.The frequency domain analysis of Figure 4 is shown in Figure 5.It can be seen that the modulated signal frequency is distributed in relatively the lower frequency band below 20 Hz. and the main spectrum energy is concentrated in the 4~8 Hz frequency band.
Symmetry 2020, 12, 337 4 of 18 The frequency domain analysis of Figure 4 is shown in Figure 5.It can be seen that the modulated signal frequency is distributed in relatively the lower frequency band below 20 Hz. and the main spectrum energy is concentrated in the 4~8 Hz frequency band.According to the carrier modulation signal, the passband of the band-pass filter can be set to 4~8 Hz.However, this traditional filtering method cannot solve the problem caused by in-band noise interference that will affect or even stem decoding.The influence factors (interference sources) of the ELF-EM transmission process are analyzed here [14]: the ELF-EM signal is unavoidably subject to a large amount of low-frequency and high-frequency noise interference during transmission.Lowfrequency noise, ranging from 0 to 10 Hz, is mainly caused by mechanical vibrations, like pump stroke, compound rotation, drilling rig sliding, advancing, triplex drilling pump movement, etc. High-frequency noise, ranging from 10 to 100 Hz, is mainly generated by on-site electric operation, bit cone friction, turbo dynamo rotation, screw rotor rotation and the like [15,16].Additionally, the amplitude of interference noise varies irregularly, causing frequency spectrum aliasing between the signal and interference noise, which ultimately hinders back-end signal processing and decoding.
From the frequency domain analysis of PPM coded signal and the interference noise frequency analysis, there is a great deal of overlap between the frequency spectrum of interference signal and coded signal; so how to effectively remove the low-frequency interference in band has become an urgent issue to be solved in the current ELF-EM signal processing.

Filtering Algorithm Analysis
Traditional low-pass filter based on Fourier algorithm and FIR band-pass filter can effectively filter out-of-band noise but is incapable of handling in-band noise.Therefore, based on such traditional filters, a kind of correlation detection method combining adaptive algorithm with FIR Wiener algorithm is designed to further filter out in-band noise and improve the decoding SNR of the back end.

FIR Wiener Filtering Algorithm
If the received signal is denoted as  According to the carrier modulation signal, the passband of the band-pass filter can be set to 4~8 Hz.However, this traditional filtering method cannot solve the problem caused by in-band noise interference that will affect or even stem decoding.The influence factors (interference sources) of the ELF-EM transmission process are analyzed here [14]: the ELF-EM signal is unavoidably subject to a large amount of low-frequency and high-frequency noise interference during transmission.Low-frequency noise, ranging from 0 to 10 Hz, is mainly caused by mechanical vibrations, like pump stroke, compound rotation, drilling rig sliding, advancing, triplex drilling pump movement, etc. High-frequency noise, ranging from 10 to 100 Hz, is mainly generated by on-site electric operation, bit cone friction, turbo dynamo rotation, screw rotor rotation and the like [15,16].Additionally, the amplitude of interference noise varies irregularly, causing frequency spectrum aliasing between the signal and interference noise, which ultimately hinders back-end signal processing and decoding.
From the frequency domain analysis of PPM coded signal and the interference noise frequency analysis, there is a great deal of overlap between the frequency spectrum of interference signal and coded signal; so how to effectively remove the low-frequency interference in band has become an urgent issue to be solved in the current ELF-EM signal processing.

Filtering Algorithm Analysis
Traditional low-pass filter based on Fourier algorithm and FIR band-pass filter can effectively filter out-of-band noise but is incapable of handling in-band noise.Therefore, based on such traditional filters, a kind of correlation detection method combining adaptive algorithm with FIR Wiener algorithm is designed to further filter out in-band noise and improve the decoding SNR of the back end.

FIR Wiener Filtering Algorithm
If the received signal is denoted as x(n) = s(n) + w(n), where s(n) is the true signal and w(n) is the noise.Without loss of generality, we can assume x(n), s(n) and w(n) are stationary random signals of zero-mean, or even more simply, real signals.Now is to estimate s(n) from x(n).Let x(n) go through a linear shift invariance (LSI) system H(z) with the output as y(n).The aim of H(z) is to let y(n) approach a certain output d(n), as shown in Figure 6.
Symmetry 2020, 12, 337 5 of 18 ) (n x .Let ) (n x go through a linear shift invariance (LSI) system ) (z H with the output as ) (n y .

) (z H
is to let ) (n y approach a certain output ) (n d , as shown in Figure 6.

Select
) (n d as filtering requires [17,18]: , then signal smoothing is wrong; In the equation above,  represents a time segment and 0 , then above prediction is also called as onestep prediction.Filtering, prediction and smoothing can be defined as: Filtering is to estimate the data at t in the time segment t 0 ; prediction is to estimate the data at as the minimum.Since as the mean square value of ) (n d , and which is the target function.Define  as relative minimum to ) (k h , which is: Select d(n) as filtering requires [17,18]: , then signal smoothing is wrong; In the equation above, ∆ represents a time segment and , then above prediction is also called as one-step prediction.Filtering, prediction and smoothing can be defined as: Filtering is to estimate the data at t in the time segment 0 ∼ t; prediction is to estimate the data at t 1 in the time segment 0 ∼ t, where t 1 > t; and smoothing is opposite to prediction, which is, to estimate the signal at t 1 based on the data at time segment 0 ∼ t.
To make y(n) approach d(n) as much as possible, the mean-square error criterion is mostly applied to determine the approach.Define: as the minimum.Since Define: as the mean square value of d(n), and d(n) is mutually correlated to x(n).Thus, which is the target function.Define ε as relative minimum to h(k), which is: Symmetry 2020, 12, 337 6 of 18 and let Equation ( 6) equal to 0, to yield the best filter coefficient in terms of the minimum mean square error, and marked as h opt (k), which yields: and the mean square error as well: Equation ( 7) is the Wiener-Hoof Equation and the best filtering coefficient and Equation ( 7) can be transformed into: Define R x as the autocorrelation matrix (or Toeplitz Matrix) of M × M, h opt as the filtering coefficient matrix of M × 1, composed of h opt (0), h opt (1), • • • , h opt (M − 1), and r dx as the cross correlation matrix of M × 1, consisting of r dx (0), r dx (1), • • • , r dx (M − 1).Thus, Equation ( 9) can take the form of: Wiener filter coefficient can be obtained through matrix inversion, viz.: and the minimum mean square error is:

Adaptive Algorithm
Commonly applied adaptive algorithms include LMS, NLMS, RLS, etc.The adaptive linear spectrum enhancement algorithm (ALE) of NLMS is used here to further remove in-band noise.See [19,20] for the ALE description.
LMS is the most widely used algorithm, of which the derivation can be found in [19].However, the stability, speed, and the excess mean square error of its convergence are controlled by step size µ which is directly relevant to the power of input signal.Thus, a reasonable solution is dividing µ by signal power so that the stable convergence can be guaranteed while keeping µ independent from signal power and accelerating the convergence.Specific NLMS algorithm is as follows [18,21]: Expression of NLMS: Define the variable step size µ(n) as: where Px (n) is the estimated signal power at time n: As can be seen, Px (n) is time varying and can be obtained by recursion.To converge NLMS, α in Equation ( 14) shall be: To prevent µ(n) from approaching extremely large value when Px (n) is excessively small (e.g., the signal is too weak to be captured in certain time segment), Equation ( 14) can be modified as: where c is a small constant.

Correlative Filtering Detection Algorithm
Correlation algorithm works well for the detection of noise-interfered signal as it has noise suppression and processing ability, and can reduce error caused by noise when measuring signal amplitude.Define the two sine signals x(t) and y(t) respectively as [22]: and: of which the cross-correlation function is: Two signals x(t) and y(t) have the same frequency; if the amplitude of one signal is known, the other's amplitude can be measured.With correlation method and its noise suppression effect, the error incurred by noise when directly measuring signal amplitude can be well avoided.
The calculation formula of digital signal is: which can be represented by the matrix: Symmetry 2020, 12, 337 8 of 18 Correlation function can be worked out by recursive algorithm in which the previous function result would be updated when sampling the next (Nth) data, so as to acquire new correlation value.The recursive algorithm goes as follows: where the superscript N in R N xy (k) represents the estimated value of correlative function at time N, while N − 1 in R N−1 xy (k) stands for the previous value of correlative function.

The Framework of Adaptive Wiener Correlation Detection (AWCD)
Usually, the noise in MWD ELF-EM channel is time changing and unstable, not suitable for statistical analysis and processing.With a certain pass-band, the out-of-band signal can be removed, leaving in-band interference out of handling.To cope with that, based on FIR Wiener filtering and correlation detection, an AWCD algorithm is designed for adaptive denoising.Detailed process is shown in Figure 7 below: ( 1) (0) ) Correlation function can be worked out by recursive algorithm in which the previous function result would be updated when sampling the next ( N th) data, so as to acquire new correlation value.
The recursive algorithm goes as follows: where the superscript N in

The Framework of Adaptive Wiener Correlation Detection (AWCD)
Usually, the noise in MWD ELF-EM channel is time changing and unstable, not suitable for statistical analysis and processing.With a certain pass-band, the out-of-band signal can be removed, leaving in-band interference out of handling.To cope with that, based on FIR Wiener filtering and correlation detection, an AWCD algorithm is designed for adaptive denoising.Detailed process is shown in Figure 7 below:

Correlation detecting filter
Set up threshold and decode In Figure 7, ) ( X n is the surface acquisition signal of interference noise, of which, after band- pass filtering, out-of-band noise can be filtered out of main frequency to yield ) ( X 3 n is the detection signal of ) ( X 2 n after adaptive enhancement.With certain detection filtering, the signal ) ( X 4 n is obtained, which is followed by threshold decoding and then goes through adaptive judgment to output  In Figure 7, X(n) is the surface acquisition signal of interference noise, of which, after band-pass filtering, out-of-band noise can be filtered out of main frequency to yield X 1 (n); X 2 (n) is the result of X 1 (n) after FIR Wiener filtering; and X 3 (n) is the detection signal of X 2 (n) after adaptive enhancement.With certain detection filtering, the signal X 4 (n) is obtained, which is followed by threshold decoding and then goes through adaptive judgment to output Y(n).Such combinational algorithm takes advantages of different algorithms and filters out the ELF-EM out-of-band noise step by step.

Simulation Analysis
To testify the operability of AWCD, the MWD signal with various noise is simulated and then processed by AWCD and FIR filtering, respectively.Finally, AWCD detection result will be compared with that of FIR band-pass filtering.Analysis goes as follows: The comparison between FIR and AWCD results is as follows.Figure 8 shows the original time domain diagram of EM signal; the coding is S20223554320432 and the carrier main frequency is sine signal of 6.25 Hz.
To testify the operability of AWCD, the MWD signal with various noise is simulated and then processed by AWCD and FIR filtering, respectively.Finally, AWCD detection result will be compared with that of FIR band-pass filtering.Analysis goes as follows: The comparison between FIR and AWCD results is as follows.
Figure 8 shows the original time domain diagram of EM signal; the coding is S20223554320432 and the carrier main frequency is sine signal of 6.25 Hz.    Figure 10 shows the frequency domain diagrams of ELF-EM signal before and after AWCD filtering.When interference noise frequency reaches 3 Hz ，5 Hz, 7.5 Hz, 12.5 Hz, and 50 Hz, respectively, noise frequency drops correspondingly by 22.3 dB, 20.8 dB, 14.8 dB, 44.9 dB, and 58.5 dB after Wiener filtering (a 6.3 dB increase is seen at 6.25 Hz).With the above comparison between the data and time domain diagram of FIR band-pass filtering and of AWCD algorithm filtering, a conclusion can be drawn: (1) For interference at around main frequency points (5 Hz and 7.5 Hz), AWCD has obvious advantages over FIR (17.7 dB and 11.5 dB increase); (2) FIR performs better in terms of interference out of main frequency (5 Hz), as compared with data before and after 3 Hz, 12.5 Hz, and 50 Hz filtering; and (3) AWCD is closer to original signal than FIR; FIR filters out interference signal and the out-of-band spectrum of EM original signal at the same time.
Then compare AWCD with FIR band-pass correlation detection; the result is shown in Figure 12.It can be seen that the detection of AWCD is easier to decode than the traditional way.With the above comparison between the data and time domain diagram of FIR band-pass filtering and of AWCD algorithm filtering, a conclusion can be drawn: (1) For interference at around main frequency points (5 Hz and 7.5 Hz), AWCD has obvious advantages over FIR (17.7 dB and 11.5 dB increase); (2) FIR performs better in terms of interference out of main frequency (5 Hz), as compared with data before and after 3 Hz, 12.5 Hz, and 50 Hz filtering; and (3) AWCD is closer to original signal than FIR; FIR filters out interference signal and the out-of-band spectrum of EM original signal at the same time.
Then compare AWCD with FIR band-pass correlation detection; the result is shown in Figure 12.It can be seen that the detection of AWCD is easier to decode than the traditional way.Then coherent detection is used to decode and compare the results, as shown in Figures 13 and  14.AWCD result shows a more than 95% overlap ratio with EM waveform, and signal data can be well recovered after setting up certain threshold, with adaptive decision decoding being S20223554320432.In contrast, the overlap ratio between FIR and original EM waveforms is lower with error rate more than 50%, which is caused by the interference at main EM frequency points (5 Hz and 7.5 Hz).Then coherent detection is used to decode and compare the results, as shown in Figures 13 and 14.AWCD result shows a more than 95% overlap ratio with EM waveform, and signal data can be well recovered after setting up certain threshold, with adaptive decision decoding being S20223554320432.In contrast, the overlap ratio between FIR and original EM waveforms is lower with error rate more than 50%, which is caused by the interference at main EM frequency points (5 Hz and 7.5 Hz).
Symmetry 2020, 12, 337 12 of 18 With the above comparison between the data and time domain diagram of FIR band-pass filtering and of AWCD algorithm filtering, a conclusion can be drawn: (1) For interference at around main frequency points (5 Hz and 7.5 Hz), AWCD has obvious advantages over FIR (17.7 dB and 11.5 dB increase); (2) FIR performs better in terms of interference out of main frequency (5 Hz), as compared with data before and after 3 Hz, 12.5 Hz, and 50 Hz filtering; and (3) AWCD is closer to original signal than FIR; FIR filters out interference signal and the out-of-band spectrum of EM original signal at the same time.
Then compare AWCD with FIR band-pass correlation detection; the result is shown in Figure 12.It can be seen that the detection of AWCD is easier to decode than the traditional way.Then coherent detection is used to decode and compare the results, as shown in Figures 13 and  14.AWCD result shows a more than 95% overlap ratio with EM waveform, and signal data can be well recovered after setting up certain threshold, with adaptive decision decoding being S20223554320432.In contrast, the overlap ratio between FIR and original EM waveforms is lower with error rate more than 50%, which is caused by the interference at main EM frequency points (5 Hz and 7.5 Hz).

Analysis and Verification by Field Data
Now, the field EM signal with decoding difficulties (case 1) is used to verify the advantages of AWCD. Figure 15 is the time domain diagram collected on site, from which a strong low-frequency interference can be seen (the high-frequency part has already been filtered out by hardware lowpass).As shown in Figure 16, the interference frequency is within the frequency band of EM signal and overlaps with it, so traditional band-pass filter can exert limited filtering effect.

Analysis and Verification by Field Data
Now, the field EM signal with decoding difficulties (case 1) is used to verify the advantages of AWCD. Figure 15 is the time domain diagram collected on site, from which a strong low-frequency interference can be seen (the high-frequency part has already been filtered out by hardware low-pass).As shown in Figure 16, the interference frequency is within the frequency band of EM signal and overlaps with it, so traditional band-pass filter can exert limited filtering effect.

Analysis and Verification by Field Data
Now, the field EM signal with decoding difficulties (case 1) is used to verify the advantages of AWCD. Figure 15 is the time domain diagram collected on site, from which a strong low-frequency interference can be seen (the high-frequency part has already been filtered out by hardware lowpass).As shown in Figure 16, the interference frequency is within the frequency band of EM signal and overlaps with it, so traditional band-pass filter can exert limited filtering effect.

Analysis and Verification by Field Data
Now, the field EM signal with decoding difficulties (case 1) is used to verify the advantages of AWCD. Figure 15 is the time domain diagram collected on site, from which a strong low-frequency interference can be seen (the high-frequency part has already been filtered out by hardware lowpass).As shown in Figure 16, the interference frequency is within the frequency band of EM signal and overlaps with it, so traditional band-pass filter can exert limited filtering effect.The signal after the FIR band-pass filtering is shown in Figure 19 below, of which the SNR raised by 18 dB as compared with that before filtering.Additionally, in that case, when changed to AWCD, the SNR increased by 18 dB compared with traditional algorithm.Comparing the correlation detection of the two methods in Figure 20, the SNR strength of AWCD is around 17 dB higher than of the FIR.As a result, it has beenproven by field data that the new AWCD algorithm has better antiinterference ability and is easier to decode.The signal after the FIR band-pass filtering is shown in Figure 19 below, of which the SNR raised by 18 dB as compared with that before filtering.Additionally, in that case, when changed to AWCD, the SNR increased by 18 dB compared with traditional algorithm.Comparing the correlation detection of the two methods in Figure 20, the SNR strength of AWCD is around 17 dB higher than of the FIR.As a result, it has beenproven by field data that the new AWCD algorithm has better antiinterference ability and is easier to decode.The signal after the FIR band-pass filtering is shown in Figure 19 below, of which the SNR raised by 18 dB as compared with that before filtering.Additionally, in that case, when changed to AWCD, the SNR increased by 18 dB compared with traditional algorithm.Comparing the correlation detection of the two methods in Figure 20, the SNR strength of AWCD is around 17 dB higher than of the FIR.As a result, it has beenproven by field data that the new AWCD algorithm has better anti-interference ability and is easier to decode.
The signal after the FIR band-pass filtering is shown in Figure 19 below, of which the SNR raised by 18 dB as compared with that before filtering.Additionally, in that case, when changed to AWCD, the SNR increased by 18 dB compared with traditional algorithm.Comparing the correlation detection of the two methods in Figure 20, the SNR strength of AWCD is around 17 dB higher than of the FIR.As a result, it has beenproven by field data that the new AWCD algorithm has better antiinterference ability and is easier to decode.The next case uses the wavelet noise reduction processing algorithm introduced in [5], the bandpass filtering algorithm mentioned in [4], and the multi-combined adaptive tracking detection algorithm mentioned in [9] together with the AWCD combination algorithm proposed in this paper.In Figure 21 are shown the filtering results of each method in separate rows for comparison.From top to bottom are the original signal waveform, using AWCD combination algorithm filtering, FIR band-pass filtering, wavelet noise reduction filtering (the wavelet scale parameter is 7, the wavelet base is a sine wave), and adaptive tracking detection filtering.From the comparison of the filtering results, the AWCD combination algorithm proposed in this paper has the best filtering effect, followed by the adaptive tracking detection algorithm.Figure 22 shows the final detection results of the AWCD combination algorithm and other methods.The AWCD combination algorithm has obvious advantages over the FIR band-pass algorithm, wavelet noise reduction algorithm, and adaptive tracking detection algorithm.This case further validates the engineering practicability of the proposed algorithm.The next case uses the wavelet noise reduction processing algorithm introduced in [5], the band-pass filtering algorithm mentioned in [4], and the multi-combined adaptive tracking detection algorithm mentioned in [9] together with the AWCD combination algorithm proposed in this paper.In Figure 21 are shown the filtering results of each method in separate rows for comparison.From top to bottom are the original signal waveform, using AWCD combination algorithm filtering, FIR band-pass filtering, wavelet noise reduction filtering (the wavelet scale parameter is 7, the wavelet base is a sine wave), and adaptive tracking detection filtering.From the comparison of the filtering results, the AWCD combination algorithm proposed in this paper has the best filtering effect, followed by the adaptive tracking detection algorithm.Figure 22 shows the final detection results of the AWCD combination algorithm and other methods.The AWCD combination algorithm has obvious advantages over the FIR band-pass algorithm, wavelet noise reduction algorithm, and adaptive tracking detection algorithm.This case further validates the engineering practicability of the proposed algorithm.

Summary
Due to the complicated MWD engineering situation, the ELF-EM transmission channel are nonlinear and non-stationary, and the amplitude of signal and noise are both uncertain.The combination of band-pass filtering, adaptive filtering, Wiener filtering, and correlation detection can maximally filter out in-band noise in any cases, and can be applied to remove noises from received ELF-EM signal of different SNR.The combination is easy to apply, reliable in filtering, and of universality to the ELF-EM processing, which has been proven to be practical in enhancing the SNR of the received signal and reducing the bit error rate of the MWD communication.

Summary
Due to the complicated MWD engineering situation, the ELF-EM transmission channel are nonlinear and non-stationary, and the amplitude of signal and noise are both uncertain.The combination of band-pass filtering, adaptive filtering, Wiener filtering, and correlation detection can maximally filter out in-band noise in any cases, and can be applied to remove noises from received ELF-EM signal of different SNR.The combination is easy to apply, reliable in filtering, and of universality to the ELF-EM processing, which has been proven to be practical in enhancing the SNR of the received signal and reducing the bit error rate of the MWD communication.

Summary
Due to the complicated MWD engineering situation, the ELF-EM transmission channel are non-linear and non-stationary, and the amplitude of signal and noise are both uncertain.combination of band-pass filtering, adaptive filtering, Wiener filtering, and correlation detection can maximally filter out in-band noise in any cases, and can be applied to remove noises from received ELF-EM signal of different SNR.The combination is easy to apply, reliable in filtering, and of
previous value of correlative function.
advantages of different algorithms and filters out the ELF-EM out-ofband noise step by step.

Figure 8 .
Figure 8. Simulated EM signal time domain diagram.

Figure 9
Figure 9 shows the frequency domain diagram of EM signal before and after FIR band-pass filtering (the filter coefficients are wpl = 5.5, wpu = 7, wsl = 5, and wsu = 7.5, with orders of 128 and sampling rate fs = 200).Interference noise with the same power is added with frequency reaching 3 Hz, 5 Hz, 7.5 Hz, 12.5 Hz, and 50 Hz, together with white noise of equal power.Seen from the result in Figure 9, noise after FIR filtering drops by 31.4 dB, 3.1 dB, 3.3 dB, 54.2 dB, and 79.3 dB respectively.

Figure 8 .
Figure 8. Simulated EM signal time domain diagram.

Figure 9 18 Figure 9 .
Figure 9 shows the frequency domain diagram of EM signal before and after FIR band-pass filtering (the filter coefficients are wpl = 5.5, wpu = 7, wsl = 5, and wsu = 7.5, with orders of 128 and sampling rate fs = 200).Interference noise with the same power is added with frequency reaching 3 Hz, 5 Hz, 7.5 Hz, 12.5 Hz, and 50 Hz, together with white noise of equal power.Seen from the result in Figure 9, noise after FIR filtering drops by 31.4 dB, 3.1 dB, 3.3 dB, 54.2 dB, and 79.3 dB respectively.

Figure 9 .
Figure 9.Comparison between signal frequency domains before and after FIR filtering.

Figure 10
Figure10shows the frequency domain diagrams of ELF-EM signal before and after AWCD filtering.When interference noise frequency reaches 3 Hz, 5 Hz, 7.5 Hz, 12.5 Hz, and 50 Hz, respectively, noise frequency drops correspondingly by 22.3 dB, 20.8 dB, 14.8 dB, 44.9 dB, and 58.5 dB after Wiener filtering (a 6.3 dB increase is seen at 6.25 Hz).

Figure 10 .
Figure 10.Signal frequency domain diagrams before and after Wiener filtering.

Figure 11 Figure 11 .
Figure11gives the comparison between time domain diagrams of FIR and AWCD filtering effect.It is clearly shown that AWCD has better filtering performance than FIR, which means AWCD can remove the in-band interference signal with larger efficiency and has a lower influence on the original EM signal.

Figure 10 .
Figure 10.Signal frequency domain diagrams before and after Wiener filtering.

Figure 11 18 Figure 10 .
Figure 11 gives the comparison between time domain diagrams of FIR and AWCD filtering effect.It is clearly shown that AWCD has better filtering performance than FIR, which means AWCD can remove the in-band interference signal with larger efficiency and has a lower influence on the original EM signal.

Figure 11 Figure 11 .
Figure 11 gives the comparison between time domain diagrams of FIR and AWCD filtering effect.It is clearly shown that AWCD has better filtering performance than FIR, which means AWCD can remove the in-band interference signal with larger efficiency and has a lower influence on the original EM signal.

Figure 11 .
Figure 11.Filtering effect comparison in time domain diagram.Figure 11.Filtering effect comparison in time domain diagram.

Figure 15 .
Figure 15.Time domain diagram of field signal.

Figure 16 .
Figure 16.Frequency domain diagram of field signal.

Figure 15 .
Figure 15.Time domain diagram of field signal.

Figure 16 .
Figure 16.Frequency domain diagram of field signal.

Figure 15 .
Figure 15.Time domain diagram of field signal.

Figure 16 .
Figure 16.Frequency domain diagram of field signal.Figure 16.Frequency domain diagram of field signal.

Figures 17 and 18
Figures 17 and 18  are the time and frequency domain diagrams after AWCD processing, and a 35dB increase is seen in SNR.Figure17shows a good recovery of time-domain signal out of interfered signal source.

Figures 17 and 18 Figure 17 .
Figures 17 and 18  are the time and frequency domain diagrams after AWCD processing, and a 35dB increase is seen in SNR.Figure17shows a good recovery of time-domain signal out of interfered signal source.

Figures 17 and 18 Figure 17 .
Figures 17 and 18  are the time and frequency domain diagrams after AWCD processing, and a 35dB increase is seen in SNR.Figure17shows a good recovery of time-domain signal out of interfered signal source.