# Noise Cancellation Method for Mud Pulse Telemetry Based on Discrete Fourier Transform
###### Abstract
After undergoing processes such as de-noising, filtering, and signal identification, the ground system completes the restoration of underground measurement data. The mud pulse data transmission technology has reliable performance in a long communication distance. It is the earliest wireless drilling transmission mode used in practical engineering applications [6]. The system that uses mud pulse transmission technology does not need to make special changes to the drill string; therefore, the cost is relatively low. In addition, mud pulse transmission technology has good adaptability to the downhole environment because the mud channel is located inside the drill string and is minimally affected by geological factors [7]. So far, mud pulse transmission remains the most widely used wireless drilling transmission technology in practical engineering [8]. However, in the process of logging, noise interference is a significant factor affecting data recovery [9]. In the mud channel of the MWD system, the output of the pressure sensor for detecting mud pressure fluctuation not only contains useful signals from downhole but also large periodic pressure fluctuation caused by mud pump compression, pressure fluctuation caused by various mechanical actions, and other random noise. The amplitude of pump noise is much larger than that of a useful signal [10]. As drilling conditions change, the frequency of pump noise also changes gradually. The signal of downhole measurement data is transmitted to the ground through a mud channel, and its attenuation varies with the depth, mud compression coefficient, and pressure wave frequency. Therefore, determining how to effectively restore the true mud pulses' signal from strong noise is a major problem in signal processing in the MWD system [11]. Currently, many experts have come up with their own solutions. [PERSON] et al. [12] calibrated the mud pressure of the drilling fluid according to the piston position of the mud pump. During the transmission of MWD data, the position of the piston is tracked, and then calibration information is used to remove the mud pump noise. The de-noising method proposed by [PERSON] et al. [13] involves a spectrum analysis and the measurement of parameters related to pump operation in a drilling fluid system. The synthetic spectrum of the parameters comes from the number of pumps in the system and the number of harmonic frequencies in each pump. Therefore, the most closely matched spectrum can be used to remove the noise of the received signal on the ground. [PERSON] [14] realized de-noising by tracking the multi-harmonic characteristics of the noise components in the signal frequency band. The intra-band harmonic characteristics are considered as a noise reference. By combining the noise reference with the measured telemetry signal and applying an adaptive algorithm, the de-noised signal can be recovered. [PERSON] et al. [15] removed the noise through the first and second pressure pulses generated by drilling fluid. The first pressure pulse is transmitted and coded upward, and the first sensor detects the characteristics of the second pressure pulse in the mud wave. The ideal pulse generated by the downhole modulator is used to eliminate the noise of the second pressure pulse. [PERSON] et al. [16] proposed a mud pulse signal detection method based on continuous Fourier transform and continuous Morlet wavelet transform. In the laboratory tests, the hydraulic noise whose amplitude is greater than the pressure pulse is separated successfully, showing a better de-noising effect than the traditional method. [PERSON] et al. [17] studied the application of an adaptive cancellation algorithm. They set up a mud diversion channel between the main pressure sensor and the mud pump and used the mud pressure signal in the diversion channel as the reference input to reduce the signal-to-noise ratio of the reference input. At the same time, they proposed a nonlinear digital gain method and a mean filter method to reduce the influence of the signal components in the reference input.