In phase-sensitive optical time-domain reflectometers (Ф?OTDRs), coherent and polarization fading caused by inherent destructive interference and polarization mismatch, affect phase restoration performance. Traditional signal fading suppression methods typically require additional hardware structures, which increases system complexity and cost. Moreover, vibration signals are non-stationary with complex frequency components, which further increases the fading suppression challenge. Therefore, it is of paramount significance to investigate a novel signal fading suppression method to achieve accurate phase reconstruction on the simplest structure in scientific research and engineering applications.

In this study, the random signal fading process in Ф-OTDR is analyzed, and it is confirmed that the fading point phase is a random noise value that follows uniform distribution. Using the empirical mode decomposition (EMD) algorithm, phase noise including phase accumulation noise and laser frequency drift is filtered out and phase information modulated by external vibration is extracted. The extracted phase data are subsequently organized into a two-dimensional space-time map, which are input into a generative adversarial network (GAN) to realize the repair of the fading data. The GAN training dataset, which is generated using software simulation, contains a total of 12000 images including the phase spectra of sinusoidal, square, and triangular wave vibration signals, Gaussian pulse vibration signal, and random vibration signal.

Experiments are designed as follows. The total length of the sensing fiber is 10.12 km, which is connected by three sections of single-mode fibers of 4.17, 1.92, and 3.95 km in length, respectively. A piezoelectric ceramic (PZT) is connected between each section of fiber and driven by the signal generator to produce the required vibration signal. Phase demodulation is performed at two vibration positions (4.186 km and 6.148 km), and a strong noise is observed in the raw space-time spectrum of phase [Figs. 8 (a)?(d)]. Subsequently, using the EMD algorithm, the phase noise (phase accumulation noise and laser frequency drift noise) is suppressed, however, the fading noise remains [Figs. 8 (e)?(h)]. Next, the processed space-time spectrum of phase is segmented and input into the GAN to repair the fading data. The phase information follows the modulation of external vibration signals, which indicates that the fading noise is suppressed after the GAN data repairing [Figs. 8 (m)?(p)]. Further, one-dimensional time and distance slices are performed on the phase space-time spectrum, respectively. It can be observed that, owing to signal fading, the phase correlation in the sensing area is disrupted, resulting in a fading peak appearing at certain positions on the sensing fiber [Figs. 9 (a)?(d)]. Thus, the phase value at the fading point overwhelms the phase information modulated by the external vibration signal, which causes phase distortion [Figs. 9 (e)?(h)]. Subsequently, after applying the EMD-GAN method, signal fading is clearly suppressed [Figs. 9 (i)?(l)] and the phase follows the external vibration signal modulation [Figs. 9 (m)?(p)]. Finally, repetitive tests are conducted on different types of vibration signals and the average probability of signal fading in the Ф?OTDR sensing system decreases from 2.61% to 0.27%. This further validates the effectiveness of the proposed EMD-GAN method.

This study proposes a novel signal fading suppression scheme based on EMD-GAN. By analyzing the random signal fading process in Ф-OTDR, it is proved that the fading point phase is a random noise value that follows uniform distribution. Using the EMD algorithm, phase noise is filtered from the original demodulated data, and the reconstructed space-time spectrum of phase is input into the GAN to repair fading data. Four different vibration signal types, including sinusoidal, square, triangular, and variable-frequency wave vibration signals are used for experimental verification. The experimental results demonstrate that the proposed method reduces the average probability of signal fading from 2.61% to 0.27% over a sensing fiber length of 10.12 km. Finally, this contribution presents a novel solution to address signal fading suppression and accurate phase restoration in Ф-OTDR sensing systems without increasing hardware structural complexity.