# Monitoring Vehicles on Highway by Dual-Channel \(\varphi\)-OTDR
## 5 Vehicle Locating on a Highway
The results are given in Table 2. When the CDM&V is applied to locate the vehicle position, the vibration peak can be easily found for k being varied in [1, N/2], which also shows no dependence of the presented algorithm on the step values. If k = 5, the CDM&V provides a respective SNR improvement of 2.3 dB, 1.3 dB, and 4.8 dB for the accumulated signal in _fiber_ 1#, the accumulated signal in _fiber_ 2#, and the synthesized signal compared to the counterparts by the CDM, which could be seen in Figures 5a\({}_{2}\), 5b\({}_{2}\) and 5c\({}_{2}\). It is also important to note that for any k value within the concerned range, the SNRs of the synthesized signals are also much greater than those of the accumulated ones either obtained from _fiber_ 1# or 2#. The noise level could be further suppressed for k = 30 by the CDM&V as seen in the third column of Figure 5. These results demonstrate the powerful capability of the DC-\(\varphi\)-OTDR in terms of positioning the moving vehicles on the highway with a considerably improved SNR, which are in accordance with those concluded over the campus road. Figure 5: Vibration signals at 8.3 km for different differential steps (i.e., k). The first and second rows respective denote the accumulated differential signal in _fiber_ 1# and in _fiber_ 2#, and the third row is the synthesized signals combining _fiber_ 1# and _fiber_ 2#. The first column is computed by the CDM, and the second and third are by the CDM&V. In the experiment, 100 consecutive Rayleigh traces are measured for each sensing fiber (N = 100). We also try to figure out the vibrations by the synthesized signals of the DC-\(\varphi\)-OTDR when the vehicle is travelling on the highway from z=\(-8.3\) km to z=\(-8.6\) km. As an example, Figure 6 presents three positions located by the CDM (the first column) and by the CDM&V (the second and third columns), respectively. For effective comparison, the curves are normalized to their respective maxima. It is seen that the DC-\(\varphi\)-OTDR by the CDM lacks the ability to read the vehicle at z = 8.48 km and z = 8.57 km for a differentiating step of 5. With the same step, the DC-\(\varphi\)-OTDR by the CDM&V clearly distinguishes all the three vibration peaks with a SNR of 5.5 dB, 2.9 dB, and 2.1 dB, respectively. These SNRs meet the minimum detectable requirements of 2 dB given in [22]. When the k value is increased to 30, the CDM-processed synthesized signals can also locate all the vibration peaks but with a much larger noise level compared to those obtained by the CDM&V. The results are given in Table 3. The well-suppressed noise by the CDM&V can easily be seen in Figure 6(a\({}_{3}\), b\({}_{3}\), c\({}_{3}\)). The locations determined by the DC-\(\varphi\)-OTDR are confirmed by the camera videos. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SNR** & **k** & **Fiber 1\#** & **Fiber 2\#** & **(Fiber 1\#) \(\times\) (Fiber 2\#)** \\ \hline \multirow{4}{*}{CDM} & k = 1 & / & / & / \\  & k = 5 & / & 0.5 dB & 0.7 dB \\  & k = 30 & 1.5 dB & 0.8 dB & 3.9 dB \\  & k = N/2 = 50 & 1.8 dB & 1.5 dB & 5.5 dB \\ \hline \multirow{4}{*}{CDM\&V} & k = 1 & 1.8 dB & 1.7 dB & 2.3 dB \\  & k = 5 & 2.3 dB & 1.8 dB & 5.5 dB \\ \cline{1-1}  & k = 30 & 1.5 dB & 2.4 dB & 4.6 dB \\ \cline{1-1}  & k = N/2 =50 & 3.6 dB & 3.8 dB & 7.9 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Vibration signal comparison between the CDM and CDM&V. Figure 6: Synthesized signals of the vehicle by the CDM and CDM&V at different locations. (a\({}_{1}\), a\({}_{2}\), a\({}_{3}\)) z = 8.3 km; (b\({}_{1}\), b\({}_{2}\), b\({}_{3}\)) z = 8.48 m; (c\({}_{1}\), c\({}_{2}\), c\({}_{3}\)) z = 8.57 m. The first column is computed by the CDM based on Equation (3), and the second and third are calculated by the CDM&V based on Equation (4).