# An Accurate Probabilistic Model for TVWS Identification
## 5 Experimental Results and Discussion
### Data Characteristics  
As previously mentioned, the value of \(P_{fa}\) was selected as 3% for processing the collected data. The obtained results are shown and discussed next. The M-SSS is mounted on a vehicle to collect the samples. The maximum speed limit (\(v\)) in the city at the expressway is 120 Km/h, considering that the RFE takes a sample every 0.340 s (\(t_{s}\)), the maximum distance (\(d\)) between two successive samples taken, is given by  
\[d=v*t_{s} \tag{17}\]  
and according to this, \(d\) is 11.33 m. When the vehicle is travelling faster, this value can decrease according to the speed variations. This maximum distance of the taken samples is small enough to plot the spectrum with an accurate level that represents how the spectrum is being used in the sampled area. For a particular reading, Figure 11 illustrates: (**a**) The plot of the spectrum vs power; (**b**) The pdf of the composed signal combined with the pdf of the noise; And (**c**) the ROC curve of the \(P_{fa}\) vs \(P_{d}\). This information is used to identify the presence of PU in a sensed band as well as the level of the noise, and it also permits calculation of the adaptive \(T\) for each case. This adaptive \(T\) is also shown on Figure 11a. In the horizontal axis, channels from 19 to 51 are represented, and vertical the axis corresponds to the absolute power of the signal measured in dBm. Figure 10: Composite signal and noise sensed in point P11: (**a**) pdf of the sensed signals; (**b**) visual representation of a \(T\) that observes a \(P_{fa}=3\%\); (**c**) Detailed Receiver Operating Characteristics (ROC) curve; (**d**) Re-calculated \(P_{d}\). Using the same concept of the previously explained figure, Figures 12-14 show the spectrum diagram, pdf of noise and composite signal, and ROC curve, respectively for ten different locations. In Figure 12a, for channel 21 and channels 39-45, we observe that the signal energy is above \(T\). We also observe that some noise peaks are also above \(T\). This reading was taken in a location which is on the eastern end of the city. The subsequent readings were taken in a trajectory that approaches to the central part of the city. In Figure 12b, it is observed that signal energy is detected in channels 31 and 32 in addition to the channels mentioned in Figure 12a. From Figure 12c, it appears that there are energy peaks in channel 50 along with channels 31 and 32, but energy of channel 21 decreases to a level below \(T\). In Figure 12d, the energy of the detected channels maintains its values in relation to the previous figure. In Figure 12e there are well-defined peaks of energy in channels 20-21, 26, 31-32, 38 to 46, and 50. In Figure 12f, the profile is maintained, the general levels of energy decreases, but the same channels are detected. For Panels (g), (h), (i), and (j), the detected energy does not present any significant variation and it is the usual energy profile of the channels detected in the central area of the city. The channels detected are 20-21, 25-26, 31-32, 38 to 46, and 50. Figure 11: For a specific point sensed: (**a**) Spectrum diagram; (**b**) pdf noise and composite signal; and (**c**) ROC curve with the \(P_{fa}\) vs \(P_{d}\). For the next block of plots in Figure 13, the pdf of the noise \(W(f)\) and the composite signal \(X(f)\) are shown. Their relative amplitudes and positions vary depending on the presence of energy and noise detected. These small variations mark the difference that determined to set adaptive \(T\) for each case. Figure 12: \(W(f)\) and \(X(f)\) represented in the frequency domain. Panels (**a–j**) spectrum vs power sensed in Points 1–10, there are variations on the energy detected due to the different location in which the samples were taken. In Figure 14, the ROC curves from each of the ten locations are plotted. These curves represent the relation between \(P_{fa}\) and \(P_{d}\) in each case. The different values respond to the variations previously registered in the sensed locations.