## 4 Results and Discussion
### Performance Evaluation
This, once again, was explained by the ability of NEAT to learn general solutions and not relying on the interpolation of known positions. To expand our results, Figure 5 shows the heat maps of the received power expressed in dBm for the isotropic antenna (top left) and beamforming with MSCPSO (top right), the GA (bottom left), and NEAT (bottom right). The heat-maps visually demonstrate that NEAT had the highest average power reaching the roads, which was reflected in a brighter color in its respective heat map, while the isotropic antenna had the lowest power. The isotropic antenna especially seemed to struggle at the road perpendicular to the car position, which was expected since there was no LOS component and the power was equally distributed in all directions. In comparison with the isometric antenna, both the GA and NEAT improved the power that reached this road by learning to generate beam shapes that focused the power in this specific direction. Meanwhile, MSCPSO depicted significant improvements over the isotropic antenna; however, its results were worse than the GA and NEAT, which was reflected in a darker shade in all four roads overall. As mentioned, the main focus of the work was for safety applications. Because of this, one very important result was the amount of time between a vehicle receiving a packet and a possible collision. This was measured by generating \(10^{4}\) positions for the car transmitting the packet, by calculating the maximum distance from the intersection where a car moving perpendicular to the transmitting car would receive the packet, and by dividing this distance by the velocity of the car was moving. This relationship is denoted as maximum response time. Figure 6 shows the curves obtained by the procedure that was previously described. In Figure 6, solid lines represent the mean for the maximum response time calculated for all the positions. The dotted lines represent the value for the worst case scenario. Curves and the respective minimum values for the isotropic antenna and beamforming antenna array optimized with NEAT, the GA, and MSCPSO are presented. It can be seen in Figure 6 that the average maximum response time was largest for NEAT, followed by GA, MSCPSO, and finally, by the isotropic antenna. This shows that, on average, the performance of NEAT was the best, whilst the result for the isotropic antenna was the worst. This is coherent with the results in Tables 4 and 5, where a similar trend can be appreciated. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Antenna** & **P1 (\%)** & **P2 (\%)** & **P3 (\%)** & **P4 (\%)** \\ \hline Beamforming with MSCPSO & 72.80 & 69.29 & 95.25 & 81.11 \\ Beamforming with GA & 99.51 & 99.48 & 98.34 & 96.09 \\ Beamforming with NEAT & 100 & 100 & 100 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Percentage of scenarios where the antenna array outperforms the isotropic antenna for different algorithms. It is interesting to note that even though the average value was greater for the GA than for MSCPSO, the GA had a much larger standard deviation, which resulted in a lower minimum value than MSCPSO. It is important to take this into consideration, since for safety applications, this type of border scenario may result in an accident, which was exactly what the work was looking to tackle. MSCPSO had the highest minimum value for the maximum response time, followed closely by NEAT. This was because MSCPSO had by far the lowest standard deviation for the response time in every position. This means that the algorithm managed to reach long distances at any position in the road, which is important in safety applications. However, NEAT achieved similar minimum values with a slightly larger average value, which indicates that NEAT performed better in most scenarios. Furthermore, both beamforming with NEAT and MSCPSO achieved a minimum performance similar to the average performance of the isotropic antenna. This shows that, even in the worse possible scenario, both algorithms performed similarly to an isotropic antenna on average.