# Monitoring Vehicles on Highway by Dual-Channel \(\varphi\)-OTDR
## 3 Methods of Vibration Positioning  
In the DC-\(\varphi\)-OTDR system, two processing techniques are employed for signal demodulation. One is the most widely used--the CDM [20; 21]. To improve some shortcomings in the CDM, we present a modified signal processing algorithm. Meanwhile, the measurement results between two methods are compared. Figure 1: (**a**) Experimental set-up of the DC-\(\varphi\)-OTDR, (**b**) Testing on a campus road, and (**c**) Testing on a highway. The red lines in (**b**) and (**c**) respective indicate the approximate positions of the sensing cable experimented in the campus and paved along the highway. The inset in (**c**) is the optical cable buried in the soil over the measured zone. The CDM is generally adopted to measure the location of external vibrations in \(\varphi\)-OTDR system. In the method, several tens of or hundreds of consecutive Rayleigh scattering traces are detected within a given time interval and then every two Rayleigh traces spaced apart by k (which will be named as differential step in the following) are subtracted in the subsequent data processing. In order to locate the vibration, the results of each subtraction are summed together to create the detection signal. Specifically, let \(D[j]\) be the \(j\)-th of the N scattering traces from one of the two sensing fibers, the vibration point could be positioned based on the accumulated differential signal \(\mu\), which can be written by:  
\[\mu_{m}=\sum_{j=k+1}^{N}\left|D[j]-D[j-k]\right|_{m^{\prime}}(m=1,2), \tag{1}\]  
where \(D\) is raw traces without any average denoising; \(m\) represents the number of the sensing fibers: m = 1 means the first fiber (_fiber_ 1#) and m = 2 the second fiber (_fiber_ 2#). For reducing the probability of false measurement caused by signal fading and noise interference as in the SC-\(\varphi\)-OTDR, the final vibration location in the DC-\(\varphi\)-OTDR will be determined jointly by the results from two sensing channels. The reason is that the possibility of wrong results occurring at the same time in the same position on each sensing fiber would be very small. Thus, in the dual-channel sensing system as shown in Figure 1, we accordingly extend Equation (1) to the following expression to obtain the synthesized detection signal. \[\mu=\mu_{1}\times\mu_{2}, \tag{2}\]  
where \(\mu_{1}\) and \(\mu_{2}\) are the accumulated differential signals in _fiber_ 1# and _fiber_ 2#, respectively, and can be independently calculated by Equation (1). In Equation (2), the differential intervals of \(\mu_{1}\) and \(\mu_{2}\) are supposed to be the same. Moreover, it has to be noted that the two elements from \(\mu_{1}\) and \(\mu_{2}\) with identical indices should correspond to the same sensing position in order to avoid spatial mismatching in the multiplication of Equation (2); namely, both the \(j\)th elements of \(\mu_{1}\) and \(\mu_{2}\) should represent the signal amplitude returned from position \(\mathrm{z}_{j}\). Hence, position matching between \(\mu_{1}\) and \(\mu_{2}\) is important to ensure no double signal peaks or zero peaks are produced in the synthesized signal, \(\mu\), for a single vibration event at a certain point. In the paper, we propose a method to the realize position alignment between \(\mu_{1}\) and \(\mu_{2}\) by digitizing the two raw traces from _fiber_ 1# and _fiber_ 2# with equal spatial distance. In our case, the distance separation between any two adjacent sampling points is set to be one meter. That is, the sampling period of the raw traces is given by: \(T_{\mathrm{m}}=n_{\mathrm{m}}/c\) (m = 1, 2); here \(c\) is the light speed and \(n_{\mathrm{m}}\) denotes the effective refractive index of fiber m (\(n_{1}\) and \(n_{2}\) are estimated to be 1.4498 and 1.4468, respectively). Thus, it is easy to compute the sampling frequencies for the two sensing channels.