# Spectrum Awareness for Cognitive Radios Supported by Radio Environment Maps: Zonal Approach +
## 5 Analysis of the Results
 } \\ \cline{2-2} \cline{6-10}  & \(\mathbf{IDWp1}\) & \(\mathbf{IDWp2}\) & \(\mathbf{IDWp3}\) & \(\mathbf{IDWp4}\) & \(\mathbf{IDWp5}\) & \(\mathbf{IDWp6}\) & \(\mathbf{Kriging}\) & \(\mathbf{\mathrm{NN}}\) & \(\mathbf{\mathrm{RMSE}}\) \\ \hline
**Test\_13a** & **9  
Below we present the list of the lowest RMSE tests for each scenario:  
* Test_13a for the scenario with 13 sensors,
* Test_20c for the scenario with 20 sensors,
* Test_26a for the scenario with 26 sensors. Figure 4 presents the results for selected tests with the lowest RMSE value. The RMSE is presented with respect to the eight interpolation techniques. These results generally confirm the statement given above since the lowest RMSE occurred for:  
* Kriging in Test_13a (6.3 dB),
* IDW p4 in Test_20c (5.0 dB),
* IDW p4 in Test_26a (6.3 dB), and was comparable with the result for IDW p3 (6.4 dB) and for Kriging (6.5 dB). It should be emphasized that, surprisingly, the lowest RMSE for Scenario 20 was lower than for other scenarios, especially for Scenario 26 with more sensors in the network. This effect may be explained in the following way: Although the number of sensors plays an important role in REM quality, another essential factor is the deployment of sensors. Therefore, in the case of a small number of sensors, the RMSE may be low when sensors were arranged properly. The analysis of this effect was presented in [46]. It is also worth noting that, independently of the scenario, the IDW p1 and NN interpolation techniques offered the worst REM quality when only the RMSE value was taken into account. For this reason it seems that, considering only the RMSE value, these methods should not be recommended for REM construction. On the other hand, irrespective of the scenario, the RMSE for Kriging oscillated at a low level (around 6 dB). This method of interpolation was the most stable, regardless of the number of sensors. An in-depth analysis of RMSE values with respect to the four zones shown in Figure 2 and for tests with the lowest RMSE values is presented below:  
* Figure 5--Test_13a, scenario with 13 measurement sensors,
* Figure 6--Test_20c, scenario with 20 measurement sensors,
* Figure 7--Test_26a, scenario with 26 measurement sensors. Figure 4: RMSE (value in dB) for tests with 13, 20, and 26 sensors—lowest RMSE test case. Figure 5: RMSE in zones (value in dB) for Test_13a. Figure 6: RMSE in zones (value in dB) for Test_20c. Figure 7: RMSE in zones (value in dB) for Test_26a. The analysis of the results presented in Figure 5 revealed that the lowest RMSE occurred for Zone 1 (7.15 dB), Zone 2 (5.9 dB), and Zone 4 (2.3 dB) for Kriging. Surprisingly, in Zone 3, NN method (RMSE approx. 3 dB) outperformed other interpolation techniques. Moreover, it is clearly visible that the application of IDW method with the power \(p\) from 1 to 3 resulted in the highest RMSE for Zone 4. In contrast, when IDW method with the power \(p\) from 4 to 6 was applied, the highest RMSE appeared for Zone 1. However, for Zone 1, the highest RMSE in this test occurred for NN method (12.4 dB). Figure 6 shows that for most interpolation methods, the RMSE value did not exceed 6 dB in any of the zones. The specificity of this test case is that Kriging and IDW interpolation method with the power \(p\) ranging from 4 to 6 gave the smallest values of RMSE and similar trends of changes in RMSE values for individual zones. It is difficult to indicate here one interpolation method that would be the best for all the zones, because the lowest RMSE occurred for:  
* IDW p3 method in Zone 1 (RMSE approx. 5.3 dB),
* IDW p4 method in Zone 2 (RMSE approx. 4.7 dB),
* NN method in Zone 3 (RMSE approx. 3.7 dB),
* Kriging method in Zone 4 (RMSE approx. 0.65 dB). Nevertheless, the differences between the lowest RMSE values were quite insignificant and amounted to not more than 1.6 dB for almost all the zones except Zone 4, where Kriging outperformed the other interpolation techniques.