# Spectrum Awareness for Cognitive Radios Supported by Radio Environment Maps: Zonal Approach +
## 5 Analysis of the Results
It is worth noting that the RMSE values were considerably above 6 dB for NN method in Zone 1, for IDW p2 method in Zone 4, and for IDW p1 method for all the zones. NN method performed not very well when interpolating radio signals in a close proximity to the transmitter, because in such conditions there were significant variations in the received signal levels, particularly in urban areas. The RMSE value reached 10.8 dB for NN method in Zone 1. On the other hand, NN method offered quite small RMSE values when applied for the interpolation of radio signal for distant areas, where the variance of the received signal level was low. The RMSE value amounted to 0.8 dB for NN method in Zone 4. In Zone 4 (see Figure 7), Kriging offered the most accurate estimation of the signal strength (RMSE amounted to 2.1 dB). Moreover, in this zone we noticed a drop in the RMSE with the increase in the power \(p\) for IDW method, i.e., the highest RMSE occurred for IDW p1 (10.47 dB), while the lowest for IDW p6 (3.47 dB). In Zone 4, regardless of the number of sensors used for the interpolation, the highest RMSE values were obtained for IDW interpolation method with power \(p\) from 1 to 2 (approx. 10 dB). These methods do not seem to be suitable for REM maps for open areas located far away from the transmitter. In Zone 2 and Zone 3, quite similar and low RMSE values were noticed for Kriging and for IDW interpolation methods with the power \(p\) from 1 to 5. The lowest RMSE values in these zones were as follows:  
* Around 5.0 dB for IDW p5 and 5.1 dB for Kriging in Zone 2,
* approximately 3.4 dB for IDW p3 in Zone 3. It is worth noting that the highest RMSE values for these two zones were obtained for IDW p1 method. The analysis of the results revealed that for Test_26a, the highest RMSE values occurred for Zone 1, i.e., approximately 11.6 dB for IDW p1 and NN interpolation methods. The minimum RMSE value in Zone 1 amounted to 7.7 dB for IDW p3. A more thorough analysis of the RMSE values in Zone 1 showed that even for Kriging, the RMSE is reasonably high (8.2 dB). Moreover, the RMSE in Zone 1 with a smaller number of sensors (see the results for the Test_13a) was lower (7.2 dB). This comparison showed that even when the number of sensors was doubled, the RMSE in Zone 1 remained high. This observation may be explained in the following way. Firstly, effects like fading and shadowing, which are typical for radio transmission, make the received signal level change substantially. Unfortunately, these effects are not reflected in the interpolation methods. Secondly, although the number of sensors impacts the quality of the interpolation, the arrangement of sensors also playsan important role. An example of such a situation can be Test_20c, where the RMSE value in Zone 1 for Kriging method amounted to 6 dB, which is much lower than for Test_26a (8.2 dB). Thirdly, a characteristic feature of the interpolation methods under analysis is their inability to extrapolate the level of the radio signal, i.e., to estimate the level in the area closer to the transmitter if there were no measurement sensors located in the vicinity of the transmitter. To overcome the drawback of RMSE, as the next step of the REM quality analysis, the differences between interpolated and true values were calculated. The results from the best tests (the lowest RMSE test cases) were selected for this study. These results are given in the tables below for various numbers of control points: Table 3 (scenario with 26 control points), Table 4 (scenario with 19 control points), and Table 5 (scenario with 13 control points). It should be noted that for the test with 26 control sensors, there were 13 measurement sensors providing data for the interpolation process, because there were 39 sensors in total. The same rule applies to the rest of the tests analyzed below.