# Spectrum Awareness for Cognitive Radios Supported by Radio Environment Maps: Zonal Approach +
## 5 Analysis of the Results  
In this chapter, the results of the tests are discussed. In the literature on the topic, the RMSE metric is the most commonly applied one to assess the fidelity of maps. In this paper, the RMSE is used to evaluate the quality of the signal strength representation for the global analyzed area and also separately for the four zones that were created with the aim to reflect the idea of the spectrum sharing among PUs and various SUs (Figure 1). The division of the area into zones may be treated as clustering of sensors or SUs with respect to their location and distance to the PU transmitter. Figure 3: Exemplary maps constructed for selected interpolation techniques and various number of sensors (signal level in dBm): (**a**) 26 sensors—Nearest Neighbor (NN); (**b**) 20 sensors—Inverse Distance Weighting (IDW) p3; (**c**) 13 sensors—Kriging. In the paper, the analysis of the RMSE metric was conducted from two perspectives:
* Globally, for the \"lowest RMSE\" test case for each scenario with 13, 20, and 26 sensors, i.e., for selected tests with the lowest RMSE value. * Separately, for each of the zones presented in Figure 2.  
In the next step, the analysis of the correctness of the signal level estimation was made separately for each control sensor for the \"lowest RMSE\" test case. This analysis was carried out with respect to selected interpolation techniques. The RMSE was calculated according to the formula given below:  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}\left(X_{i}-\overline{X}\right)^{2}}{n}}, \tag{4}\]  
\[X_{i}=S_{ri}-S_{oi}, \tag{5}\]  
where:  
\(n\) is the number of control sensors,  
\(S_{ri}\) is the signal level [dBm] measured by \(i\)-th control sensor,  
\(S_{oi}\) is the signal level [dBm] interpolated for \(i\)-th control sensor,  
\(X_{i}\) is the difference between measured and interpolated signal level [dB] for \(i\)-th control sensor,  
\(\overline{X}\) is the average value of \(X_{i}\). The analysis of the dependency between the quality of maps and the density of the sensor network was provided in [45]. The general conclusion of this study was that the RMSE dropped as the number of sensors increased. This statement was valid for all interpolation techniques that were taken into account (NN, IDW, and Kriging). Analyzing our results, we also confirmed that the lowest ARMSE for each scenario was offered by Kriging and IDW with the power of 3 or 4. The differences between the RMSE values obtained in individual tests for a given scenario were significant (up to 4.6 dB for the scenario with 26 sensors). A more thorough analysis revealed that this was due to unfavorable locations of some sensors, mainly terrain obstacles on the propagation path between the TX antenna and the sensors. Therefore, to minimize the impact of the arrangement of sensors on the results, for further analysis we selected the best test for each scenario. The best test is understood as this one of the three tests which has the lowest RMSE value calculated for all interpolation methods in a specific scenario prior to the division of sensors into four zones. In Table 2, we present the results of RMSE for all the tests with respect to the interpolation techniques. Note that the name of the test contains the number of sensors providing measurement data for the interpolation process. The tests with the lowest RMSE values are marked in bold in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\ \begin{tabular}{c} **Test** \\ **ID** \\ \end{tabular}  } & \multicolumn{6}{c}{**RMSE for Various Interpolation Methods**} & \multirow{2}{*}{ \begin{tabular}{c} **Avg.** \\ **RMSE** \\ \end{tabular}