# Rapid Estimation of TVWS: A Probabilistic Approach Based on Sensed Signal Parameters
## 4 Proposed Rapid Estimation Method
### REM Block  
The REM block has been designed to find possible relationships with the obtained parameters to estimate TVWS in the TV-UHF spectrum of a specific geographical area. Its input consists of the data provided by the information collecting block and by the signal analysis block, as shown in Figure 1. To find E-TVWS, the measured parameters are taken from the information collecting block, and the calculated parameters are obtained form the signal analysis block. The REM block uses the sensed parameters and the calculated parameters to obtain the auxiliary parameters, as represented in Figure 13.  
To find a REM, we needed to use auxiliary parameters that allow us to understand the behaviour of the sensed signals and to obtain a numeric value to identify a possible relation among the sensed signal. These auxiliary parameters are described next:  
* Parameter \(I\) is the first auxiliary parameter obtained, and it represents the projection line of the intersection point between \(W(p)\) and \(X(p)\), as shown in Figure 7b. Parameter \(I\) marks the limit that separates the noise of the signal components of the composite signal \(X(p)\), and it can be calculated using \[I=W(p)\cap X(p)\] (10)
* Parameter \(Z_{1}X\) is represented by a line plotted in the upper limit of \(X(p)\). To calculate its coordinates, we have to consider a \(Z\)-score that delimits 99% vs. 1% of the AUC in the right side of normal curve \(X(p)\). This reference parameter will be very helpful to find the peak values of \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline _Point_ & _PU_ & \(P_{d}\) & \(\overline{W}\) & \(\sigma_{W}\) & \(\overline{X}\) & \(\sigma_{X}\) & \(Z_{X}\) & \(I\) & \(T\) & \(Z_{1}X\) \\ \hline P1 & 10 & 37.15 & \(-\)109.05 & 1.8764 & \(-\)106.36 & 4.8409 & \(-\)0.3280 & \(-\)106.46 & \(-\)105.53 & \(-\)95.827 \\ P2 & 9 & 42.42 & \(-\)109.26 & 2.1576 & \(-\)106.35 & 5.9925 & \(-\)0.1913 & \(-\)106.18 & \(-\)105.20 & \(-\)92.401 \\ P3 & 12 & 47.17 & \(-\)109.28 & 2.1431 & \(-\)105.74 & 6.8842 & \(-\)0.0710 & \(-\)106.00 & \(-\)105.25 & \(-\)89.702 \\ P4 & 12 & 41.22 & \(-\)108.08 & 2.0791 & \(-\)105.79 & 7.2981 & \(-\)0.2218 & \(-\)104.77 & \(-\)104.17 & \(-\)88.784 \\ P5 & 14 & 49.37 & \(-\)109.29 & 2.0040 & \(-\)105.63 & 6.8174 & \(-\)0.0158 & \(-\)106.15 & \(-\)105.52 & \(-\)89.743 \\ P6 & 15 & 56.17 & \(-\)109.25 & 1.7163 & \(-\)104.78 & 8.0119 & 0.1552 & \(-\)106.22 & \(-\)106.02 & \(-\)86.112 \\ P7 & 15 & 42.38 & \(-\)109.47 & 2.0123 & \(-\)106.57 & 4.5941 & \(-\)0.1922 & \(-\)106.88 & \(-\)105.68 & \(-\)95.869 \\ P8 & 16 & 50.82 & \(-\)109.37 & 2.1551 & \(-\)105.16 & 7.7402 & 0.0205 & \(-\)105.92 & \(-\)105.32 & \(-\)87.124 \\ P9 & 12 & 50.16 & \(-\)109.42 & 2.0332 & \(-\)105.57 & 7.0974 & 0.0039 & \(-\)106.20 & \(-\)105.60 & \(-\)89.030 \\ P10 & 12 & 45.85 & \(-\)109.12 & 2.1267 & \(-\)105.83 & 6.8013 & \(-\)10.041 & \(-\)105.88 & \(-\)105.12 & \(-\)89.987 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Tabulated results obtained from the ED, SA, and RA blocks. Figure 13: REM parameters were used to find the estimation of the TVWS (E-TVWS), where sensed parameters are obtained by the MSSS, whereas calculated and auxiliary parameters are obtained by the signal analysis block. the composite signal \(X(p)\), which usually are the PU signals. To determine the value of \(Z_{1}X\) we can use  
\[Z_{1}X_{i}=\overline{X}(p_{i})+\sigma_{Xi}*2.33 \tag{11}\]  
where \(Z_{X}=2.33\) corresponds to the Z-score that defines an AUC of 1% versus 99% from right to left on the composite signal \(X(p)\). We have defined parameters named \(\left(\tau\right)\) to identify the distance from \(Z_{1}X\) to other parameter, as is explained in Table 3.
* Parameter \(\tau_{\overline{W}}\) refers to the distance measured from the \(\overline{W}\) and \(Z_{1}X\). It provides an idea of how spread out the composite signal \(X(p)\) in reference to noise signal \(W(p)\) is. If \(\tau_{\overline{W}}\) is bigger, this means that more _PU_s were detected in the \(X(p)\) signal.