# Automatic Clustering for Improved Radio Environment Maps in Distributed Applications
## 6 Numerical Results  
In this study, our dataset is generated through simulation and consists of simulated RSRPs, having the network parameters summarized in Table 4. The collected RSRPs are used as the ground-truth for the coverage in the area of interest since they can be considered realistic field measurements. In fact, they represent the received pilot power, as defined by the LTE standard, in the two different environments (i.e., urban and rural), as shown in Figure 4. These measurements are calculated over a uniform grid of size \(1\) km \(\times\) \(1\) km. \begin{table}
\begin{tabular}{c c} \hline \hline
**BS Parameters** & \\ \hline Number & \(1\) \\ \hline Transmit power & \(46\) dBm \\ \hline Bandwidth & \(20\) MHz \\ \hline
**Channel Characteristics** & \\ \hline Thermal noise per Hertz & \(-174\) dBm/Hz \\ \hline Path Loss for urban area (\(d\) in km) & \(128.1+37.6\log_{10}(d)\)dB \\ \hline Path Loss for rural area (\(d\) in km) & \(100.54+34.1\log_{10}(d)\)dB \\ \hline Shadowing Log-normal & \(6\) dB \\ \hline Decorrelation distance & \(20\) m \\ \hline \hline \end{tabular}
\end{table} 
Table 4: BS parameters and channel characteristics. \begin{table}
\begin{tabular}{c c} \hline \hline
**inputs** & **:Number of clusters: \(U\)** \\  & **Dataset:**\(\mathcal{D}=\{\mathbf{o}_{n}\mid n=1,\ldots,N\}\) \\
**outputs** & **:Clusters:**\(\mathbf{c}_{u},u=1,\ldots,U\) \\
**1 init:** Randomly select \(U\) observations from \(\mathcal{D}\), and consider them to be the \(U\) initial set of centroids, denoted by \(\mathbf{c}_{u},u=1,\ldots,U\). \\
2 Calculate the distance between each observation \(\mathbf{o}_{n}\) and the cluster centroids using (9). \\
3 Assign each observation \(\mathbf{o}_{n}\) to the cluster whose centroid is the closest to it. \\
4 Determine the new centroids \(\mathbf{c}_{u},k=1,\ldots,U\) of all the \(U\) clusters. \\
5 Repeat steps 2–4 until the positions of the centroids remain unchanged.  
\end{table} 
Table 3: Time complexity of our framework. Here, we consider that the antenna is omnidirectional for this area. Given a resolution of \(5\) m \(\times\)\(5\) m, we have a total of 40,000 RSRP samples. In Figure 4, we present the RSRP map corresponding to the values computed based on (3). As shown on the map, a remarkable difference in the RSRP values can be clearly observed in two different areas of the map. This can be explained by the presence of two different environments in the simulated area. To measure the accuracy of the proposed approach, we examined its ability to distinguish between different clusters based on their environments. The differences represent different attributes for each cluster. For example, clusters may be different in terms of geographical area or behavior of wireless channels. Regardless of the type of differences, a key testing element is to measure the ability of the model to differentiate designated clusters. Therefore, we assigned 'Cluster 1' to the area with buildings and 'Cluster 2' to the open area with gardens and parks. We applied the KMC method to split the dataset into two parts based on these defined clusters. At this stage of the test, the target was to clearly define the two different rural and urban environments. Figure 5 illustrates the performance of the model based on KMC. It is seen that the model correctly and clearly distinguished between the two different environments. To assess the benefit of the clustering, we performed multiple steps. We first evaluated the performance of the Kriging prediction with the target dataset. Then, we modeled the measurement error using Gaussian noise with a zero mean and 3 dB variance. The generated noise was added to the RSRP measurements. Furthermore, we split the resulting RSRP dataset into learning and testing sets. Here, we used the learning set to estimate the predictor parameters, and the testing set to evaluate the performance of the predictor. It is worth mentioning that the learning set consisted of 10% of the whole dataset, wherein the points were uniformly selected over the area.