# Monitoring Vehicles on Highway by Dual-Channel \(\varphi\)-OTDR
## 4 Performance Tests of DC-\(\varphi\)-OTDR on a Campus Road
The details about how to determine the k\({}_{\rm max}\) in both approaches will not be described here, we will present a detailed justification in another work. When k is changed between [1, k\({}_{max}\)], a larger step leads to a greater SNR. The overall results by both methods are summarized in Table 1, implying that: (1) when k \(\leq\) 125, the CDM fails to position the vibration peak; (2) when k\(\leq\)[1, k\({}_{max}\)] the localization by the CDM&V is independent on the k value; and (3) the CDM&V can enhance the SNR of the detection signals over the CDM. Furthermore, based on Equations (2) and (4), we use the synthetic signals, obtained by combining the accumulated differential signals from _fiber_ 1# and _fiber_ 2# via the CDM (Figure 3b) and CDM&V (Figure 3d), respectively, to discover the vibration signal. In the figures, the amplitude of each curve is normalized to the maxima. For the CDM-based synthesized signals, no signal peak can be found for the vibration when k \(\leq\) 125; whereas the SNR is increased to \(\sim\)3 dB when k = 300. This indicates again the high dependence of the algorithm on the k  
Figure 3: Accumulated vibration signals at 242 m for different differential steps by (**a**) the CDM based on Equation (1) and (**c**) the CDM&V based on Equation (3) in _fiber_ 1# and _fiber_ 2#, respectively. Synthesized signals for different k values by (**b**) the CDM based on Equation (2) and (**d**) the CDM&V based on Equation (4). In the figure, 2500 consecutive Rayleigh traces are measured for each fiber. value. For the CDM&V, the SNR of the synthesized signal achieves up to 5.7 dB for k = 100 and 8.5 dB for k = 300, which is much greater than the counterparts obtained by the CDM. From the results, it can be reasonably concluded that relative to the CDM, the CDM&V-based dual-channel system increases the signal SNR and weakens the dependence of vibration positioning on the k value. It is also seen from Figure 3 that although signal fading results in no vibration peak being observed in the single channel of _fiber_ 2#, the synthesized signals by the CDM&V can clearly show the signal regardless of the differential step. Additionally, it is observed that the SNRs of the dual-channel system are much better than those of the single one. When the vehicle is driving over the campus road, the backscattered Rayleigh traces in both _fiber_ 1# and _fiber_ 2# are continually acquired in the lab and processed by Equation (2) of the CDM and by Equation (4) of the CDM&V, respectively, to extract the synthesized detection signals. Figure 4 shows the respective vibration signals when the vehicle reaches at z = 200 m, 218 m, 242 m, and 252 m. It is seen that the CDM cannot detect any vibration for k = 100 or lower at all these positions. On the contrary, the CDM&V shows a robust ability to determine the vibration peak with a greatly enhanced SNR. The SNR improvement is especially significant at z = 218 m where the vibration signal is less affected by the passing electric bicycles and pedestrians. Compared to the result obtained using the CDM (Figure 4b, SNR = 2.5 dB), the SNR of the vibration signal is improved by \(\sim\)5.0 dB for k = 300 when applying the CDM&V. From Figure 4d, it is seen that the CDM is unable to locate the vibration at 252 m due to the vehicle approaching the end of the road with a near-zero speed. Instead, the CDM&V detects the peak with an SNR of \(\sim\)0.4 dB for k = 1, \(\sim\)0.9 dB for k = 100, and \(\sim\)1.5 dB for k = 300. Overall, the results in Figures 3 and 4 show that the DC-\(\varphi\)-OTDR has the ability to locate the vibration with a decreased probability of wrong measurement and with a considerably improved SNR, and the CDM&V alleviates the differential step dependence in vibration detection.