# Spectrum Awareness for Cognitive Radios Supported by Radio Environment Maps: Zonal Approach +
## 5 Analysis of the Results
For IDW methods with the power p3 and p4, which were assessed as promising on the basis of the RMSE comparison, the maximum values of these differences were quite significant and amounted to:  
* 13.2 dB for Test_13a, see Table 1,
* 6.3 dB for Test_20c, see Table 2,
* 8.4 dB for Test_26a, see Figure 5:0  
One of the solutions to the above problem could be constant correction of the interpolated level for distant zones. When Kriging was applied, the results of interpolation for Zone 4 reflected the results of measurements well, as there were four CEPs and one OEP with the overestimation that amounted to 3.5 dB only. Figure 8 shows the comparison of CEPs expressed as a percentage of the total number of control points. These results are presented with respect to different numbers of measurement sensors and interpolation techniques, see Tables 3-5. The following notation was applied: CEP_xx, where xx denotes the number of measurement sensors providing data for the interpolation process. It can be easily noticed that in most cases, the highest correct estimation ratio appeared for Kriging and NN, while the lowest ratio was observed for IDW p1 and IDW p2. The  
Figure 5:1 Correct estimation ratio for selected interpolation techniques for lowest RMSE tests. highest correct estimation ratio (approx. 62%) occurred for the scenario with 26 points applied for the interpolation process. Table 6 presents the comparison of the ratio of CEPs, OEPs, and UEPs for selected interpolation techniques and lowest RMSE tests. It can be easily noticed that for the scenario with the lowest number of measurement sensors providing data for the interpolation process (Test_13a), OEPs prevailed. It means that for a small number of measurement sensors, the signal level was overestimated for nearly all the interpolation techniques, except for NN. In fact, NN estimated quite well for a small and medium number of sensors used for interpolation. Surprisingly, for the highest number of measurement sensors, NN performed worse. In general, OEPs outnumbered UEPs for each scenario and for all the interpolation techniques. It is worth noting that when two factors were taken into account together, namely the number of CEPs and the trend of CEPs with the increased number of sensors, Kriging outperformed the other interpolation methods. The number of CEPs increased from 39% for Test_13a to 62% for Test_26a. Table 7 presents the comparison of the ratio of CEPs in zones for selected interpolation techniques and lowest RMSE tests. Unlike Table 6, the results shown in Table 7 are generalized for three scenarios. For Zone 1, IDW p1 and Kriging outperform other interpolation techniques. For Zone 2, there are no dominating interpolation techniques. The highest number of CEPs reaches 31% for three methods: IDW p1, IDW p2, and IDW p3. The reason for this poor performance could be the multi-path effect in urbanized Zone 2. For Zone 3, the highest number of CEPs occur for Kriging and NN (59%), and for IDW p3 (53%). For Zone 4, Kriging and NN outperform other interpolation methods. In this zone, the number of CEPs is the highest and amounts to 80%. A general conclusion from this analysis is that Kriging is the most accurate interpolation method for REM construction. Kriging offers the best performance in terms of the number of CEPs in three out of the four zones examined.