Proton precession magnetometer is a high-precision device for weak magnetostatic field measurement. The measurement accuracy depends on the frequency measurement of free induction decay (FID) signal, while the signal to noise ratio (SNR) is an important factor affecting the results. Many signal processing methods have been proposed to improve the SNR of FID signal. However, the theoretical analysis of different types of noises for FID signal has not be conducted yet. In addition, the relationship between the frequency measurement accuracy and SNR has not been explicitly established and quantified. This paper first proposes a background noise model based on the extracted features from the FID signal. With this model, background noises, such as white noise, narrow-band noise, and phase noise etc., can be calculated and estimated. Secondly, the relationship between the frequency measurement accuracy and SNR is identified. We also built a prototype proton magnetometer for field tests and validation purpose. Experiments were conducted to investigate this relation through simulation. Different values for frequency accuracy were obtained with different SNRs from the acquired FID signals from field tests. The consistence between the measurement and computational results is observed. When SNR is larger than 30 dB, the absolute frequency accuracy becomes constant which is about 0.04 Hz. With the stability taken into account, the accuracy can be better even when the SNR is higher than 30 dB. This study provides a reference to optimize the design of proton precession magnetometer and the frequency calculation for FID signal. K: Models and simulations; Instrumental noise; Data analysis; Detector control systems (detector and experiment monitoring and slow-control systems, architecture, hardware, algorithms, databases)1Corresponding author.

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In practical applications of electromagnetic measurement while drilling (EM-MWD) in the underground coal mine, the signal-to-noise ratio (SNR) of a receiver cannot always meet the requirements of reliable communication conditions due to the earth attenuation, interfering signal from the well site, and so on. Aimed to solve these problems, this paper presents a low error rate Bose-Chaudhuri-Hocquenghem (BCH)-based encoder-decoder technology for EM-MWD. First, this paper studies the relationship among the BCH encoding error performance and the decoding method, the source length, and other factors through simulation; then, we obtain an optimal length of BCH code for EM-MWD through analyzing the bit error performance of hard-decision decoding and soft-decision decoding with different lengths of BCH code. Finally, we compare the proposed algorithm with the conventional binary phase-shift keying (BPSK) approach in the actual environment. The results show that the proposed algorithm can reduce the bit error rate by about ten times at a lower SNR, achieving a reliable communication condition when the SNR of a received signal is reduced. It demonstrates the effectiveness of the proposed BCH encoder and the decoder algorithm based on BPSK for EM-MWD. INDEX TERMS EM-MWD system, BPSK, BCH coding, optimized coding techniques.

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