# Monitoring Vehicles on Highway by Dual-Channel \(\varphi\)-OTDR
## 4 Performance Tests of DC-\(\varphi\)-OTDR on a Campus Road  
Before applying the DC-\(\varphi\)-OTDR to locate the running vehicles on the highway, we firstly investigate its sensing performance over a short-distance campus road (as shown in Figure 1b). In the experiment, the driving speed of the testing vehicle is in the range of 20-40 km/h. Both sensing fibers forming the DC-\(\varphi\)-OTDR are \(\sim\)260 m, which is limited by the length of the straight section in the campus, and tightly tied together before buried in soil along the road. They originate from the same fiber spool, in order to reduce the impact of speed mismatch on the product of Equation (2) and Equation (4). It should be mentioned that only the last 130 m of fiber is used for vibration sensing, since the first 130 m functions to guide the probing optical pulses from the lab to the sensing road after passing through several 90-degree curved sections. That is, the testing vehicle is driving from z = 130 m to z = 260 m. Although the measurement path is relatively short, the undesirable vibrations caused by the passing electric bicycles and pedestrians adds a lot of extra noises to the system, which brings some difficulties to signal demodulation. The repetition rate of the probe pulses is set to be 200 kHz, guaranteeing that only one probing pulse is travelling within the fiber at any time. For each sensing fiber, an injected optical pulse would generate one raw trace of backscattered Rayleigh signal, and a total of 2500 consecutive traces were recorded in 12.5 ms by the data acquisition for the effective positioning of the vehicle. Over this time duration, the vehicle only drives forward about 14 cm, which is much less than the spatial resolution. The vibration point along each sensing fiber could be independently detected by measuring any abnormal change in the summed differential signal via both the CDM and CDM&V. Figure 3 shows the results when the vehicle was driving at 242 m; whereas Figure 3a,c are the accumulated vibration signals from single channel (i.e., _fiber_ 1# or _fiber_ 2#, which is equivalent to the SC-\(\varphi\)-OTDR), and Figure 3b,d are the synthesized ones obtained by combining both sensing fibers (the DC-\(\varphi\)-OTDR). In Figure 3a, both the raw traces measured in _fiber_ 1# and _fiber_ 2# are processed by the CDM. The signal fading phenomenon can be apparently observed in _fiber_ 2#, meaning that the vibration location cannot be correctly identified if that channel alone is used for probing. In _fiber_ 1#, the vibration signal is buried in noise for k = 100 (i.e., every two Rayleigh traces used for subtraction are separated by 100). When k is increased to 300, the SNR enhancement is significant (2.6 dB) and the vibration signal of the vehicle is quite clear. To reach an SNR of 0.5 dB in _fiber_ 1#, the two Rayleigh traces used for differentiation in Equation (1) has to be spaced apart by larger than 125. The result indicates that the CDM demodulation is highly k dependent. Here, the SNR is defined as a ratio between the peak power at the vibration position and that at the strongest side-peak not belonging to the main lobe. In Figure 3c, the proposed CDM&V is employed to deal with the Rayleigh traces. As expected, no remarkable SNR improvement is observed in _fiber_ 2# due to fading effect. Whether k = 100 or 300, the CDM&V shows the ability of locating the signal peak in _fiber_ 1#, with respective resulting SNRs of 3.3 dB and 5.5 dB. It is interesting to notice that the CDM&V provides 2.9 dB SNR improvement when k = 300 in _fiber_ 1# relative to the CDM. Our additional calculation shows that the CDM&V is able to seek the vibration peak with an SNR of 2.4 dB even with a minimum differential step of k\({}_{\rm min}=1\). For the upper limit of the differencing space, k\({}_{\rm max}\) is safely set to be half of the total Rayleigh traces. In the case, k\({}_{\rm max}\) = N/2 = 2500/2 = 1250.