## 3 Experiment, Results, and Discussion
### Implementation Results and Discussion  
After some initial simple assessment tests, the model was applied to our evaluation scenario. Initially, we tested the planning of the site with three cells. We generated with the \(C/I\) of each pixel covered by that site: one with the original operator frequency planning, before optimization (Figure 13(a)) and after the CPSP planning (Figure 13(b)). The implementation in Metric was also used to assess the results of the proposed methodology. It runs in a physical machine while the proposed CPSP is cloud-based. Additionally, in terms of propagation, it uses the Okumura-Hata model to estimate receive power levels, requiring larger computation resources, as will be shown. It splits the \"world\" using angles and distances, creating a non-uniform grid. A strong limitation of the Metric algorithm is that its constraints only apply when planning cells from the same site. In this sense, planning a network with multiple sites can only be done sequentially, resulting in a non-optimal global solution.  
An empirical cumulative distribution function is generated, as represented in Figure 15, in order to compare network quality. Keep in mind that this distribution does not take in account pixels where the power of the most potent cell is not enough to enable connectivity, as the quality of the planning of the frequencies is not affected by it. Both CPSP and Metric plannings, even though they had different frequencies allocated, achieved similar network quality, as can be verified in Figure 15, and in an identical heatmap, Figure 13(b). Before optimization, the manual planning depicted in Figure 13(a) achieved 83.7% of the coverage area and below \((C/I)_{min}\) (9 dB). The bad quality of the area is visible by the average \(C/I\) of 7 dB. After planning, we can observe in Figure 15 that 99.9% of the coverage area is above 15 dB (6 dB higher than \((C/I)_{min}\)), enabling communication with excellent quality.  
Figure 14: Carrier to interference ratio within the coverage area of the planned site.  
Figure 15: Cumulative distribution function of the C/I within the coverage area of the planned site.  
For the scenario in under analysis, the proposed CPSP planning algorithm is compared to the one of the Metric tool. Even though both achieve similar results, as is visible in Figure 15, their performances are different, in terms of execution time and memory usage efficiency, as depicted in Figure 16. For planning three cells, the proposed algorithm used up 985 MB of memory, taking 27.7 s to execute, an improvement compared to the 4096 MBs used and 329.2 s from the already implemented one. The proposed algorithm is almost 12 times faster and four times less memory consuming. These results exclude the time and memory used to calculate the pre-processed propagation grids, which are pre-processed and available by Metric SaaS. Both the memory and time reduction can be explained by the more uniform world division and by the fact that the world map is generated once instead of in multiple individual generations for each cell.  
We then applied the algorithm to the whole scenario of 70 cells, in order to check how the pattern would behave when planning multiple sites, taking 161.6 s and using 1439 MB of memory (Figure 17. We cannot compare it to metric since it can only plan a site at the time, but it could plan each site individually, one by one, taking 70 times 329 s (23,044 s). This approach has another major problem. The obtained solution might not be the best one because of the planning order.  
The proposed procedure is composed of searches in the world map, a hashtable and linear optimization. For the next results, \"World map\" covers everything from reading the required files for  
Figure 16: Performance comparison between the proposed CPSP planning algorithm and the one of Metric tool, in terms of execution time and memory usage.  
Figure 17: Carrier to interference ratio in the city after optimization.