# A Fading Suppression Method for \(\Phi\)-OTDR Systems Based on Multi-Domain Multiplexing
## 4 Experimental Results and Analysis
### PDM, FDM, and Spatial Weighting
However, the abovementioned MDM method is based on the performance limits of these methods. In practice, it is not always necessary to use exactly four frequencies, nor is it always necessary to set the weighting intervals to GL. We are eager to find a combination that minimizes costs and achieves the best fading suppression. To this end, we try our best to exhaust all combinations of the parameters of these methods in multi-domain multiplexing, including the number of polarization states in PDM, the number of frequencies in FDM, and the intervals of spatial weighting. To quantitatively evaluate fading resistance capabilities of these combinations, we present the fading resistance performance of these combinations in the form of three-dimensional bar charts. The specific situations are divided into a single P state, a single S state, and the combination of both P and S. The coordinate axes on the bottom surface of the figure represent the number of frequencies and the amount of spatial weighting intervals, respectively, and the \(z\)-axis represents the probability of fading occurrence. The number of frequencies is 1, 2, 3, and 4, respectively, and the spatial weighting intervals are 0, 0.25 GL, 0.5 GL, 0.75 GL, and GL, respectively. The RMS value for fading is defined as half of the value in previous studies [14]. The probabilities of fading occurrence for all combinations are shown in Figures 11-13. In Figures 11 and 12, to achieve a 1% fading probability, when the number of frequencies is 1, the intervals of spatial weighting should be at least GL, which means sacrificing a relatively large spatial resolution. When the number of frequencies is 2, the intervals of spatial weighting should be at least 0.25 GL. When the number of frequencies is greater than or equal to 3, a less than 1% fading probability can be achieved without spatial weighting. In Figure 13, after adding PDM in the P and S states, a 1% fading probability can be achieved using 2-frequency FDM without a decline in spatial resolution. Using FDM with more than 3 frequencies can achieve a 0.01% fading probability without a decline in spatial resolution. If the decline of spatial resolution can be accepted, a 0.01% fading probability can be achieved with only 2-frequency FDM and a spatial weighting interval of 0.25 GL. The above analysis results show that it is feasible to achieve a balance between the performance and hardware complexity of different application conditions through MDM. This provides a guiding solution for the anti-fading of \(\Phi\)-OTDR. In engineering applications, the optimized design for fading suppression can be flexibly carried out, which broadens the scope of engineering applications of \(\Phi\)-OTDR. In the future, further research can focus on the design strategies of \(\Phi\)-OTDR systems. It is necessary to reduce the system cost and complexity while ensuring the fading suppression effect to improve the overall performance of the system. There is no need to use a 4-frequency FDM as in this paper. Instead, according to the actual application requirements, the optimal combination of hardware and algorithms in terms of cost and performance should be selected.