# Discrete Environment-Driven GPU-Based Ray Launching: Validation and Applications
## 3 Validation
### Validation of the DED-RL Algorithm
#### 3.2.1 Comparison between DED-RL and RT  
In Figure 5, the performance of DED-RL is compared to RT for the same 18 San Francisco's cell sites considered in [6]: the standard deviation of the error w.r.t. measurements (\(\sigma_{E}\)) is reported for RT and DED-RL with x and y coordinates, respectively, while the red dashed line bisecting the xy-quadrant represents perfect correlation between the two models. Overall, the correlation between DED-RL and RT is evident, despite the fact that the two algorithms are different. Looking at the results of DED-RL simulations, for the majority of sites, \(\sigma_{E}\) is below 10 dB, and for a few sites, \(\sigma_{E}\) has values between 7 and 8 dB. The latter one can be considered a very good result as San Francisco is a really challenging scenario due to the variety of the urban layout (alternation of residential areas, vegetated areas, dense urban areas with high-rise buildings) and the presence of hilly terrain [6]. Figure 4: Performance of the DED-RL in the San Francisco scenario (mean error and mean standard deviation of error w.r.t. measurements) for different tile sizes. One site with ID A00002E5 shows bad performance for both DED-RL and RT: this fact is probably due to recently constructed buildings close to the base station site that were not present in the building database. Other sites that show poor performance in DED-RL, namely A00013B7, A0001623, A000127C, A000F8D, are all microcellular sites installed on buildings close to a street corner: in this case, small errors in base station location can yield large errors in the RF map, and probably DED-RL is more sensitive than RT to those errors due to environment discretization. On the other hand, some other sites (A0001632, A0001139, A00005 BA, A0001983, A00034F4) have better performance in DED-RL than in RT, while the performance of DED-RL and RT is very similar for all the remaining sites. Some of the optimizations suggested in [8] have been applied also in DED-RL, in order to achieve a better performance. For example, for some sites located in hilly regions, the combination of ORT diffraction with scattering and reflection is very important to increase coverage in strongly-NLOS locations: this is the case of site A0002 FFC, well described in [6]. After inserting the combination of scattering/reflection with ORT in the DED-RL simulation of site A0002 FFC, the mean error (\(\mu_{E}\)) reduced from \(-11.5\) to \(-6\) dB and the error standard deviation (\(\sigma_{E}\)) improved from \(9.9\) to \(7.8\) dB, thus confirming the findings already presented in [6]. Other sites are located in residential areas surrounded by vegetation, and in such cases, the results improve if vegetation polygons are properly modelled in the input database. This is the case of site A0000A49: after modelling vegetation, and assuming an attenuation of \(0.04\) dB/m (see Table 1) for the rays falling inside vegetation polygons, \(\mu_{\rm E}\) reduced from \(6.5\) to \(0.3\) dB, while \(\sigma_{E}\) improved from \(8.8\) to \(8.4\) dB. Finally, for some sites near street corners, a better performance is obtained by enabling transmission through the building closest to the transmitting antenna: in this case, in fact, transmission through the corner is as important as diffraction for the signal to propagate in the side streets. Global statistics in terms of mean error and error standard deviation for all 18 BS in San Francisco are shown in Table 2. On the average, the performance of the DED-RL is slightly better than RT, despite the discretization error, which is not present in image ray  
Figure 5: Performance Comparison of DED-RL with image RT, in terms of error standard deviation (\(\sigma_{E}\)) for the 18 BS analyzed in [6]. \(5\times 5\) m\({}^{2}\) tiles are considered in DED-RL simulations. tracing algorithms.