## 4 Discussion  
It can be concluded from Figures 7-11 that the array length from cross-correlation coefficient computing has a great influence on the temperature/strain measurement accuracy. If the CRN remains stable, the minimum length of 11 frequency points can be adopted. In fact, the CRN is not stable, especially when the OTDR trace average number is small, for example, 1000 times or less. In other words, if an array with a short length is used for the temperature/strain demodulation, the OTDR trace average number must be large, e.g., 10,000 times. Therefore, system measurement efficiency becomes an important issue. For a sensing fiber with a length of 100 km, the time to obtain one OTDR trace in a single probe pulse period is 1 ms, so, for an average number of 10,000 times, it takes 10 s to obtain one averaged OTDR trace. To sweep 11 frequency points to obtain the array of 3D Rayleigh scattering spectra, the total time needed is 110 s. However, the anti-noise effect of the array with 11 frequency points is quite low, and it may be difficult to ensure measurement accuracy. Then, if the array with 101 frequency points is adopted and the OTDR trace average number is 1000 times, the time needed to get the 3D Rayleigh scattering spectra is 101 s. Although the OTDR fluctuation becomes drastic with a low average number, a longer array length can overcome the randomness of the CRN, as shown in Figure 11. However, the measurement dynamic range with an average number of 1000 times is 5 dB lower than that with an average number of 10,000 times [10]. As the system measurement time consists of signal acquisition time and processing time, the signal processing time should be considered. Figure 12 shows the signal processing time with different array lengths (frequency sweeping points). The time for signal processing to obtain the temperature/strain demodulation is from 78.2 s to 90.4 s. Generally, the shorter the array length, the less time is needed, but the differences are not very big and can even be omitted in practical engineering. Therefore, the key is to balance the signal acquisition time and measurement accuracy.  
Table 1 shows the comparison of the system measurement time with different array lengths (frequency sweeping points). As the anti-noise performance of the system depends on array length, the trace average number has to be increased to reduce the fading noise for a short array length to accurately demodulate the temperature/strain values. Therefore, the trace average number is selected as 1000 times for the array with a length of 101 since  
Figure 11: The maximal cross-correlation coefficients after adding the Gaussian noise to the initial signal: (a) amplitude of 0.8 times; (b) amplitude of 1.0 times.  
it has excellent anti-noise performance, and for the arrays with shorter lengths, the trace average number is selected as 10,000 times. Although the array with a length of 51 also has good performance, we think that it cannot absolutely guarantee measurement accuracy, because a small trace average number will inevitably lead to large fluctuations in the OTDR trace. So, Table 1 indicates that the trace average number is the key factor that decides the measurement time for ultra-long-distance fiber temperature/strain monitoring. The total time consumption for an array with a length of 11 is a little less than that with a length of 101, but by the anti-noise performance contrast in Figures 7 and 11, it can be inferred that the array with 101 frequency sweeping points and a trace average number of 1000 times is the best-suited to achieve excellent measurement efficiency for ultra-long OPGW/OPPC temperature/strain monitoring.