## 4 Channel Characterization Metrics
A simple way to calculate the quantile is to sort the RSSI values and find the entry with the index corresponding to the \(x\%\) of the vector length. The lower this value, the less peaks occur in the RSSI signal and the lower interference from other radio systems is expected. * Number of samples over threshold (soft): It is the number of RSSI samples over a specified power level threshold. The lower this value, the less peaks occur in the RSSI signal. All mentioned properties have in common that lower values indicate less interference and thus better channels. These properties must be transformed into a channel gain metric, \(H\), that is directly proportional to the channel quality, so that it can be directly introduced in the equations presented in Section 5. To do this, a simple linear adjustment is performed:  
\[H=\alpha\cdot x+\beta \tag{3}\]  
where \(x\) is an arbitrary statistical property of the RSSI signal and \(\alpha\) and \(\beta\) are parameters to be adjusted. Furthermore, the \(H\) metric is normalized between \([0,1]\), so that the \(\alpha\) and \(\beta\) parameters are derived in the following way:  
\[ \begin{array}{c}[\min(x),\max(x)]\rightarrow[1,\ 0]\\ 1=\alpha\cdot\min(x)+\beta\\ 0=\alpha\cdot\max(x)+\beta\end{array} \right\}\rightarrow\left\{ \begin{array} []{c}\alpha=\frac{1}{\min(x)-\max(x)}\\ \beta=-\frac{\max(x)}{\min(x)-max(x)}\end{array} \right. \tag{4}\]  
Figure 3 shows an illustrative example of this linear projection from the mean value of the RSSI signal (that ranges from \(-120\) dBm to \(0\) dBm) to a normalized quality metric. The power metric presented in Equation (5), \(Q=1H\,|\,^{2}\), is also represented. For the RSSI values in Figure 2, the calculated statistical properties are represented in Figure 4. The derived channel gains are represented in Figure 5.  
Figure 4: Different statistical properties obtained from the RSSI values in Figure 2: (**a**) Mean value; (**b**) Standard deviation; (**c**) Skewness; (**d**) 50% quantile; (**e**) SOTH with \(-70\) dBm threshold. Figure 3: Example of linear projection from the mean value of the RSSI signal (blue) to a normalized channel gain, \(H\) (red). The dashed red line represents the power metric, \(Q\), derived from the channel gain. It can be observed that most of the statistical properties result in similar channel gains for the considered RSSI signal. This does not stand for the skewness metric, which suggests that channels 2, 6, 10 and 14 are worse than channels 4, 8 and 12, for instance. Even if channels 2, 6, 10 and 14 have higher interfering power peaks, they also have more continued traffic, resulting in a more symmetric skewness function and, thus, lower skew values. Therefore, the skewness metric would be a better indicator of channel quality when dealing with dynamic interferences that vary a lot in time, while the others would be better when dealing with static interferences that hold in time. So, one of the open questions will be to find the most appropriate metric for a reliable channel quality indicator. Even more, for some metrics, some parameters will have to be adapted for each specific application (the cut value and the power threshold for the x% quantile and SOTH respectively). One of the main objectives of the proposed method is to automatically decide the best RSSI property for each specific scenario.