# A Fading Suppression Method for \(\Phi\)-OTDR Systems Based on Multi-Domain Multiplexing
## 1 Introduction  
Distributed fiber-optic sensing technology possesses both signal transmission and sensing capabilities, enabling the acquisition of tens of thousands of sensing points along a single fiber. It also features advantages such as electromagnetic interference immunity, high sensitivity, and wide detection range [1], making it a research hotspot. Phase-sensitive optical time domain reflectometry (\(\Phi\)-OTDR) has become an important branch of it, standing out for its high sensitivity and fast response speed [2] for monitoring various physical parameters. \(\Phi\)-OTDR is based on the Rayleigh backscattered signal (RBS),employing a highly coherent laser as the light source, which has been widely applied in various fields, including perimeter security monitoring [3; 4], marine monitoring [5; 6], and earthquake monitoring [7; 8]. However, \(\Phi\)-OTDR systems are often affected by fading noise, which has limited their application [9; 10; 11; 12]. Typically, fading noise includes interference fading noise and polarization fading noise. Interference fading noise is caused by the inhomogeneity of the refractive index of the fiber core and the use of a narrow linewidth laser as the light source in \(\Phi\)-OTDR systems. The presence of interference fading leads to random fluctuations in the amplitude of the RBS [9]. Polarization fading refers to the mismatch of polarization states between the local light and the RBS, which decreases the visibility of the intermediate frequency (IF) signal [10]. This fading may cause the amplitude of the IF signal to drop into a lower range, which leads to waveform distortion in the demodulated time-domain signal, a decrease in the signal-to-noise ratio (SNR), and, consequently, a reduction in the accuracy of monitoring. The fading mentioned above always leads to false alarms, which cause many inconveniences to the application of \(\Phi\)-OTDR systems in engineering. To suppress fading noise, researchers have explored many methods, such as spatial-domain multiplexing (SDM) [11; 12; 13; 14], polarization-domain multiplexing (PDM) [15; 16; 10], and frequency-domain multiplexing (FDM) [17; 18; 19]. All these methods achieve fading noise suppression by multiplexing independent and uncorrelated channels. SDM suppresses fading through the spatially independent distribution of the RBS. Three of the seven optical fiber cores were connected start-to-end in an S shape [11], and a strategy based on spectral similarity was used to process multiple independent signals. The distortion rate could be reduced from an average of 9.34% to less than 2% under 270 s of continuous operation. However, due to the series connection of multiple fiber cores, the frequency response and the dynamic range of the system were limited. Another way to implement SDM is to use a spatial weighting algorithm [12; 13; 14]. This is initially achieved through maximum amplitude selection [12] and direct averaging [13]. However, the phase consistency and the spatial resolution consistency of adjacent spatial regions are destroyed. Then, a spatial weighting algorithm based on the carrier-to-noise ratio (CNR) was proposed [14], reducing the probability of fading noise from 6.23% to 0.19%. However, when the weighting intervals increase, the spatial resolution inevitably decreases. Moreover, none of these methods can suppress the polarization fading noise. PDM suppresses fading through the polarization state-independent distribution of the IF signal. By optimizing complementary polarization state measurements, the fading was suppressed [10]. The statistical characteristics of location-related intensity distribution in \(\Phi\)-OTDR were studied [15], and the probability density functions in the cases of polarization mismatch and polarization match were given. When simultaneously detecting vibration signals of 500 Hz and 800 Hz, compared with the traditional coherent detection \(\Phi\)-OTDR, the SNR of the polarization diversity detection was increased by 10.9 dB and 8.65 dB, respectively.