## 3 Materials and Methods
### 4.1. RSRP Measurements  
The results of the RSRP measurements as a function of the distance are visualized in Figure 6. The plots (a), (b), and (c) show the results for provider A, with data taken at different times and for both directions. In plots (d) and (e) the RSRP has been logged for two independent test drives covering both directions for provider B. Each of these measurements has been spatially correlated with all others to check consistency for a single provider and prove sufficient differentiation between different providers. The result of this analysis is presented in Table 5. While repeated measurements under various conditions including speed, direction, and time of day indicate a spatial correlation \(0.8<sc<0.9\), a value of \(sc\leq 0.8\) is found when correlating measurements for different providers.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Assessment** & **RSRP** & **RSRQ** & **RSSI** \\ \hline excellent & \(>=-10\) dBmW & \(>=-10\) dB & \(>-15\) dBmW \\ \hline good & \(-10\) dBmW \(\ldots\)\(-10\) dBmW & \(-10\) dB \(\ldots\)\(-15\) dB & \(-15\) dBmW \(\ldots\)\(-15\) dBmW \\ \hline fair & & & \(-15\) dBmW \(\ldots\)\(-15\) dBmW \\ \hline poor & \(-10\) dBmW \(\ldots\)\(-100\) dBmW & \(-15\) dB \(\ldots\)\(-10\) dB & \(-15\) dBmW \\ \hline \multicolumn{3}{l}{risk of disconnect} \\ \cline{2-3} or no signal & \(<=-100\) dBmW & \(<=-10\) dB & \(<-15\) dBmW \\ \hline \hline \end{tabular}
\end{table}
Table 4. LTE assessment criteria, based on [38].  
Figure 5. Highway under analysis. Test drives were performed in both directions as indicated by the arrows, based on [37].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **(a)** & **(b)** & **(c)** & **(d)** & **(e)** \\  & & **A** & **A** & **A** & **B** & **B** \\ \hline (a) & A & 1 & 0.84 & 0.82 & 0.76 & 0.59 \\ (b) & A & 0.84 & 1 & 0.86 & 0.75 & 0.60 \\ (c) & A & 0.82 & 0.86 & 1 & 0.78 & 0.67 \\ (d) & B & 0.76 & 0.75 & 0.78 & 1 & 0.85 \\ (e) & B & 0.59 & 0.60 & 0.67 & 0.85 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 5. Spatial correlation of RSRP. A and B indicate the respective providers under investigation.  
The average of the RSRP for each position was calculated for each provider. The results are shown in Figure 7. Furthermore, the confidence interval for a confidence of 0.8 was calculated and included. When comparing Figure 7a, based on three measurements, to Figure 7b, based on two measurements, the reduction of the width of the confidence interval due to the higher number of measurements is obvious.  
The width of the confidence intervals has been included in a histogram in Figure 8 to allow further analysis. Though the distributions are different in their overall characteristic, the mean values of the widths of the confidence intervals are almost identical at 14 dBmW (Figure 8a) and 13 dBmW (Figure 8b), respectively. A significant variance across different measurements for identical positions is expected if the system is connected to different network cells while performing the measurement.  
Figure 6: RSRP as a function of distance based on five independent measurements (solid lines: raw data; dots: resampled, interpolated data). Gray, dotted horizontal lines indicate ranges according to Table 4.  
Figure 7: Mean values of RSRP as a function of distance including the limits of the confidence interval for a confidence of 0.8.  
The measurement shown in Figure 6 has been evaluated based on the criteria in Table 4 and the result is presented in Table 6. It indicates a significant number of measurements with RSRP \(<-100\) dBmW for both providers, which is assessed as \"risk of disconnect or no signal\" (Table 4). However, for provider A the coverage is better compared to provider B when comparing the range of \"risk of disconnect or no signal\" as indicated in Table 6. While for provider A the measurements show a \"risk of disconnect or no signal\" for distances between 361 m and 671 m, those for provider B indicate a range between 831 m and 949 m.