# A Fading Suppression Method for \(\Phi\)-OTDR Systems Based on Multi-Domain Multiplexing
## 4 Experimental Results and Analysis
### PDM, FDM, and Spatial Weighting  
In this section, the contributions of PDM and FDM to the suppression of fading noise are compared, and we show this effect of fading suppression through waterfall charts and the root mean square of the demodulated phase of optical fiber. The length of the optical fiber connected is 4 km for FUT1 and 200 m for FUT2, the pulse repetition frequency is set to 20 kHz with a pulse width of 200 ns, and a sinusoidal signal of 30 Hz and 0.2 V is applied using PZT. As shown in Figures 6 and 7, the waterfall charts display the phase demodulation waterfall diagrams of the P state and S state at frequencies of 80 MHz, 100 MHz, 120 MHz, and 150 MHz. As shown in Figure 6, fading events of varying degrees are shown at the positions of the optical fiber where no disturbance is applied. As shown in Figure 7, the applied disturbance events are distorted due to the influence of fading, and the spatiotemporal continuity is disrupted. This means there may be false alarms and a decrease in the accuracy of disturbance event reconstruction, which is not conducive to the engineering application of the \(\Phi\)-OTDR system. Especially in Figure 6b, the influence of fading is particularly evident. We separately optimize the demodulated phases in Figure 7b using PDM with the P state and the S state, spatial weighting with a weighting interval of GL, FDM with 4 frequencies, and a combination of the first three methods. The results are shown in Figure 8.  
Figure 6: Waterfall charts of the optical fiber without disturbance: (**a**) 80 MHz, P state; (**b**) 80 MHz, S state; (**c**) 100 MHz, P state; (**d**) 100 MHz, S state; (**e**) 120 MHz, P state; (**f**) 120 MHz, S state; (**g**) 150 MHz, P state; and (**h**) 150 MHz, S state. As shown in Figure 8, when PDM is used alone, the fading noise is greatly suppressed, but obvious residues can still be observed near the disturbance event. To clearly demonstrate the effectiveness of these four methods in suppressing the fading noise, we focused  
Figure 8: Waterfall charts of the optical fiber: (**a**) PDM with the P state and the S state, (**b**) spatial weighting with a weighting interval of GL, (**c**) FDM with 4 frequencies, (**d**) a combination of the first three methods. Figure 7: Waterfall charts of the optical fiber with a disturbance event: (**a**) 80 MHz, P state; (**b**) 80 MHz, S state; (**c**) 100 MHz, P state; (**d**) 100 MHz, S state; (**e**) 120 MHz, P state; (**f**) 120 MHz, S state; (**g**) 150 MHz, P state; (**h**) 150 MHz, S state. on observing the area ca. 3600-3900 m around the disturbance event, which is shown in Figure 9.  
In Figure 9, near the disturbance event in Figure 9a-c, it is clearly observable that there are still a few residual noises, which lead to false events. However, in Figure 9d, this phenomenon is well-eliminated. This indicates that the fading noise can be more comprehensively suppressed by combining PDM, FDM, and spatial weighting. We use the RMS to quantitatively evaluate the fading suppression effects of these four methods on the spatial regions where no active disturbances have been applied. That is shown in Figure 10. When the four methods are used separately, the RMS value of PDM is the largest, indicating the worst suppression effect on fading noise. The RMS value of MDM is the smallest, dropping below 0.005, showing the best fading suppression effect. The above results and analyses indicate that it is difficult to comprehensively combat fading noise by using a single method. Therefore, MDM is essential for combating fading  
Figure 10: Distance distribution of the RMS: (**a**) the RMS distance distribution of the quiet area before the disturbance event; (**b**) the RMS distance distribution of the quiet area after the disturbance event. Figure 9: Waterfall charts of the optical fiber with a disturbance event: (**a**) PDM with the P state and the S state, (**b**) spatial weighting with a weighting interval of GL, (**c**) FDM with 4 frequencies, (**d**) a combination of the first three methods. noise.