## 5 Measurements Processing & Results
\begin{bmatrix}\gamma(\|\mathbf{x}_{1}-\mathbf{x}_{1}\|)&\gamma(\|\mathbf{x}_{ 1}-\mathbf{x}_{2}\|)&\gamma(\|\mathbf{x}_{1}-\mathbf{x}_{3}\|)&\ldots&1\\ \gamma(\|\mathbf{x}_{2}-\mathbf{x}_{1}\|)&\gamma(\|\mathbf{x}_{2}-\mathbf{x}_ {2}\|)&\gamma(\|\mathbf{x}_{2}-\mathbf{x}_{3}\|)&\ldots&1\\ \ldots&\ldots&\ldots&\ldots&\ldots\\ 1&1&1&\ldots&0\end{bmatrix}\begin{bmatrix}\lambda_{1}\\ \lambda_{2}\\ \ldots\\ \mu\end{bmatrix} = \begin{bmatrix}\gamma(\|\mathbf{x}_{1}-\mathbf{x}_{0}\|)\\ \gamma(\|\mathbf{x}_{2}-\mathbf{x}_{0}\|)\\ \ldots\\ 1\end{bmatrix}  \tag{5}\]  
Ordinary Kriging assumes that the random spatial field is stationary in the wide sense, and consequently, it should have a constant mean value. In our case, this is not true because there is well-known dependence of the received power with the logarithm of the distance from the Access Point. To this end, the measurements are detrended by removing the value calculated by the following relationship:  
\[R=\alpha+\beta\cdot log(x) \tag{6}\]  
where \(x\) is the distance from AP and \(R\) is the received power in dBm. Constants \(\alpha\) and \(\beta\) are calculated by fitting the above equation to the data using Least Squares. The same formula can be applied for the transmission speed due to its linear dependence on the received signal strength for most of its range. [40; 41; 42]. In Figure 7, the measurements for the 802.11 ac 5 GHz case can be seen before and after detrending has been applied. By applying the methodology described previously, we perform spatial interpolation for the four measurement cases and use the resulting functions to extract statistics for the coverage area and the achieved transmission speed. Figures 8 and 9 depict heat maps of the RSSI and the download speed over a satellite image of the measurement area. The green dots represent the sample points. Samples were taken as far as possible in every direction while maintaining the minimum communication bandwidth required to exchange the SNMP queries with the AP and as a result, they can serve on their own to define the maximum communication range in each case. Figure 8: RSSI and download speed heat maps for the 2.4 GHz band of 802.11 ax & 802.11 n technologies overlaid on top of the satellite image of Figure 6.  
Figure 7: Scatter plot of the RSSI measurements for the 802.11 ac 5 GHz measurement case. On the left are the original data, and on the right are the data after the value calculated by Equation 6 has been subtracted. Coefficients \(\alpha\) and \(\beta\) are \(-23.8\) and \(-24.68\), respectively. It is evident that the surrounding environment has a strong effect on the overall coverage due to the absorption of RF energy by the various obstacles, which is more severe for the 5 GHz band, in agreement with the theory. The 2.4 GHz band is able to extend further into the openings of the surroundings, but the overall effect of containing the radiation in the open area around the AP is not significantly overcome. Tables 2 and 3 include metrics for a quantitative comparison between 802.11 ax WiFi and the previous generation standards. We have selected the RSSI and download data rate as indicators of the area coverage and quality of service that can be offered by each setup. 802.11 ax appears to achieve 10% greater coverage than its predecessors. More importantly, due to the addition of higher coding and modulation schemes (1024-QAM), WiFi 6 is able to deliver speeds in excess of 200 Mbps close to the AP. The 5 GHz band performs inferior to the 2.4 GHz band but has the potential to benefit from less spectrum congestion, owing to the greater number of channels, making the use of higher bandwidths (40 MHz or 80 MHz channel width) realizable in practice.