# Rapid Estimation of TVWS: A Probabilistic Approach Based on Sensed Signal Parameters
## 3 Analysis of the Collected Data  
With the MSSS mounted on a vehicle, the TV-UHF spectrum was sensed across a wide area. As mentioned before, it collected one reading every 340 ms and each reading was composed of 112 samples of \(W(p)\), 112 samples of \(Xo(p)\), their respective time stamp, and the latitude-longitude information. This procedure allowed us to create a spatiotemporal map of the sensed TV-UHF spectrum, as illustrated in Figure 4. To conduct this research, more than eight million samples were collected in the city of Windsor, Ontario, Canada. By scrutinizing the figure, we realize that there are different spectrum occupation rates according to the geolocation of the readings. The images framed in blue show the TV-UHF spectrum sensed, and we can observe therein peaks of energy that may correspond to PU signals distributed along different frequencies, so that those energy peaks identify the channels as being used. This irregular spectrum occupancy can be used for DSA to improve wireless communications services that require the electromagnetic spectrum. The first action needed is to find used channels, and then, we need to identify their frequency and to get the geographical location. To do this, we must find an optimal threshold, denoted as \(T\), to be used as a reference to decide the occupancy of a channel. At the same time, we can characterize the spectrum behaviour based on the taken samples. To calculate the best value for \(T\), we have to consider that a higher value of \(T\) will reduce \(P_{fa}\) but that it also will increase \(P_{m}\), which will  
Figure 4: Spatiotemporal map of the spectrum sensed in our area of interest. Figure 3: Example measurements: (**a**) noise of the system, \(W(p)\); (**b**) composite signal sensed, \(X_{o}(p)\); and (**c**) the presence of the PU clearly observed when ten sampled points overlapped in order to illustrate the behaviour of the UHF TV spectrum in the sensed area. result in missed detection of real PU signals with low energy and will introduce errors in the results, as observed in Figure 5 with \(T_{high}\). On the other hand, a lower value for \(T\) reduces \(P_{m}\), which increases \(P_{fa}\). This provokes noise peaks with high energy, which may be considered PU signals, again producing errors in the results, as is observed in Figure 5 with \(T_{low}\). It is a fact that the spectrum occupancy could be significantly changed when the threshold varies [18]. Here resides the importance to find an adequate value for \(T\). Based on this, a good option to estimate \(T\) is explained in [6]. Now, let us consider that, for each reading, in which we measure \(W(p)\), its mean value \(\overline{\text{W}}\) represents the noise floor that we will use as a reference to calculate our \(T\) explained:  
\[T=\overline{\text{W}}+M \tag{1}\]  
with \(M\) as the margin that is obtained by using  
\[M=\sigma_{W}*Z_{W} \tag{2}\]  
where \(\sigma_{W}\) is the standard deviation of \(W(p)\) and \(z_{W}\) is the Z-score that defines a \(P_{fa}\) equal to 3%. The obtained \(T\) is represented in Figure 5.  
Once the procedure to calculate \(T\) is defined, we wrote a script that compared each point read by the MSSS with \(T\) and its corresponding frequency in MHz. The sensed band ran from 500 MHz to 698 MHz, and each TV channel had a bandwidth of 6 MHz [1]. The script identified the points located above \(T\) and marked them as used channels; the points below \(T\) were considered TVWS. The output of the script is observed in Figure 6, where we visualize it with colours: in gray are the occupied channels, in white are the TVWS, and in yellow is channel 37 (608 MHz to 614 MHz), which is assigned to radio astronomy services. By comparing panels (a)-(c), we observe the changes from one to another location, where some channels are detected according to its geographical position.