# Noise Cancellation Method for Mud Pulse Telemetry Based on Discrete Fourier Transform
###### Abstract  
Mud pulse telemetry (MPT) systems are widely recognized for their effectiveness and are most commonly used to transmit downhole data to the surface in real time. These data facilitate the drilling process and make it more cost-efficient. In MPT, the mud channel presents a challenging communication environment, primarily due to various sources of noises, with pump noise being the most dominant. In this paper, a noise cancellation method based on discrete Fourier transform (DFT) is proposed for demodulation under a low signal-to-noise ratio, eliminating the pump noise generated by two pumps with a single sensor during drilling. The method employs DFT to estimate the noise spectrum, subtracts noises from the received signal, and performs an inverse transformation to reconstruct the original signal estimation. The effectiveness of the proposed method is evaluated through a simulation analysis and field experiments. The simulation results indicate that the major components of multiple pump noises could be successfully eliminated. The field experiment results demonstrate that the demodulation of the received data achieves advanced data rate communication and a low bit error rate (BER) in a 3000 m drilling system. m _Article_  
Academic Editor: [PERSON]  
Received: 27 November 2024  
Revised: 31 December 2024  
Accepted: 2 January 2025  
Published: 4 January 2025  
**Citation:** [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Noise Cancellation Method for Mud Pulse Telemetry Based on Discrete Fourier Transform. _[PERSON]. Sci. Eng._**2025**, _13_, 75. [[https://doi.org/10.3390/jmsc13010075](https://doi.org/10.3390/jmsc13010075)]([https://doi.org/10.3390/jmsc13010075](https://doi.org/10.3390/jmsc13010075))  
Copyright: 0 2025 by the authors. License MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/))). At present, the data transmission technology in the MWD system can be roughly divided into two types: wired telemetry and wireless telemetry. There are many ways to realize wired telemetry, including cable telemetry, optical fibre telemetry, and intelligent drill string telemetry, which are high in transmission speed but have a high cost and short service life [3]. Wireless telemetry mainly includes mud pulse telemetry, electromagnetictelemetry, and acoustic telemetry, with mud pulse telemetry being the most widely used [4]. The attenuation of an electromagnetic wave signal and weak anti-interference ability are still the main factors restricting the development of electromagnetic telemetry technology, which make an electromagnetic MWD system only suitable for short-distance transmission and impose strict requirements on formation resistivity [5]. Acoustic telemetry is difficult to use because an acoustic wave is a kind of mechanical wave with serious attenuation. Moreover, the drilling environment is complex, and the existence of noise makes it difficult to detect and identify the acoustic wave carrying information. Compared with other methods, mud pulse telemetry has a long transmission distance and good performance. However, its low data transmission speed remains the primary limitation hindering its development [3]. Mud pulse transmission technology uses circulating mud flow in drill string as a medium to realize communication between the ground and underground. The mud pulse transmission system is usually equipped with a mud pulse signal generator located downhole. Driven by the downhole control circuit, the generator operates periodically according to the data to be transmitted so as to change the cross-sectional area of the mud circulation channel. This process generates periodic pressure changes in the mud column and completes the conversion from electrical signals into mud pressure signals.