A Fractional Fourier Transform-Based Channel Estimation and Equalization Algorithm for Mud Pulse Telemetry

Abstract

Mud pulse telemetry (MPT) systems are a promising approach to transmitting downhole data to the ground. During transmission, the amplitudes of pressure waves decay exponentially with distance, and the channel is often frequency-selective due to reflection and multipath effect. To address these issues, this work proposes a fractional Fourier transform (FrFT)-based channel estimation and equalization method. Leveraging the energy aggregation of linear frequency-modulated signals in the fractional Fourier domain, the time delay and attenuation parameters of the multipath channel can be estimated accurately. Furthermore, a fractional Fourier domain equalizer is proposed to pre-filter the frequency-selective fading channel using fractionally spaced decision feedback equalization. The effectiveness of the proposed method is evaluated through a simulation analysis and field experiments. The simulation results demonstrate that this method can significantly reduce multipath effects, effectively control the impact of noise, and facilitate subsequent demodulation. The field experiment results indicate that the demodulation of real data achieves advanced data rate communication (over 12 bit/s) and a low bit error rate (below 0.5%), which meets engineering requirements in a 3000 m drilling system.

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