# Discrete Environment-Driven GPU-Based Ray Launching: Validation and Applications
## 3 Validation
### Validation of the DED-RL Algorithm
#### 3.2.4 Wideband Results  
The ray launcher's temporal accuracy was verified using Timing Advance (TA) ranging measurements collected from 4G LTE testing devices in the San Jose scenario.  
In LTE and 5G NR, TA is proportional to the roundtrip time between a base station (e.g., eNB, gNB) and user equipment (e.g., smartphones, IoT devices). A TA measurement can be converted to a ranging or Time of Arrival (ToA) measurement by removing timing offsets due to hardware components (e.g., wires) and digital components (e.g., filters), and dividing the remainder by two. In LTE, the ranging resolution is equal to 8 TS or 78.1 m, where TS is the basic timing unit [33]. Note that regular off the shelf handsets (e.g., Nexus 5X) will have the 8 TS ranging resolution. Though, special testing handsets (e.g., Samsung S5) can measure TA-based range at a finer resolution of 1 TS.  
LTE TA measurements were collected using a Google Nexus 5X phone and a Samsung S5 phone. For a particular pair of base station and handset measurement location, TA  
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{**Metric**} & \multicolumn{2}{c}{**SCENARIO**} & \\ \cline{2-3}  & **San José** & **North Atlanta** & **South Atlanta** \\ \hline Frequency & 850 and 1900 MHz & & \\ N. of cell sites (4G) & 79 & 63 & 331 \\ Mean \(\mu_{E}\) [dB] (before unbiasing) & 8.4 & 6.8 & 11.7 \\ Std. dev. of \(\mu_{E}\) [dB] (before unbiasing) & 8.3 & 8.2 & 7.4 \\ Mean \(\sigma_{E}\) [dB] & 6.9 & 8.1 & 8.4 \\ Std. dev. of \(\sigma_{E}\) [dB] & 2.2 & 1.8 & 2.3 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Global statistics for the RL simulations vs. Measurements in The San José and Atlanta scenarios.  
Figure 6: Comparison of (**a**) measurements and (**b**) RL simulations for measurement site n. 40 in San José: in this case \(\sigma_{E}=6.5\) dB.  
measurements were collected and aggregated together temporally and spatially within a small radius around the central location. The variability in the aggregated TA and the corresponding ranging measurements is dependent on the multipath characteristics, which was then compared to ray launching predictions. Note that the TA of the first arrival, TA1, was used to remove the timing offsets in the aforementioned TA estimates by subtracting the following quantity from them:  
\[\Delta\text{TA}=\text{TA}_{1}-\text{TA}_{\text{R}} \tag{6}\]  
where \(\text{TA}_{\text{R}}\) is the TA of the shortest possible path, that was the LOS or quasi-LOS path in the considered cases.  
The resulting TA estimates divided by two are compared with DED-RL-predicted channel impulse responses, plotted with red impulses in Figure 7, where bars are used to indicate the ToA estimates (blue) and the corrected ToA values (green), where the bar width indicates the ranging resolution. Note that, for each measurement, there are two estimates, corresponding to the first and to the second arrival. The match between ray launching impulses and the corrected TA ranges is generally good, with a good matching between the first- and second-arrival ray clusters and the corresponding green bars.