# 5G Positioning: An Analysis of Early Datasets
## 4 Results  
### SNR Analysis  
A preliminary analysis of the SNR values is performed. We, firstly, discuss the findings obtained from analyzing Take 01.  
We investigate which base station has the best mean SNR value and how the distance between the base station and the trolley can influence it. A graph illustrating the SNR values for all the outdoor stations is shown in Figure 6.  
The constant or almost constant values correspond to static or low straight dynamic intervals. Stations 7 and 8 provide the best SNR values. Statistics of the SNR values are computed for each station (Table 2). As an example, Figure 7 depicts the SNR of station 8 along the trajectory, while Figure 8 displays the mean SNR within each distance interval for all the stations.  
Figure 6: Take 01. SNR (dB) values plotted against time for each base station.  
Figure 7: Take 01, base station 8: SNR along the trajectory.  
For our data, no correlation exists between the SNR values and the distances between the stations and the receiver. This is due to the small range of distances and covered area. The objective of the preliminary SNR investigation is to search for a criterion to select the optimal reference station for the \(TDoA\). In the following, we assess the influence of the SNR of the reference station on the quality of the data. For each take, the following scenarios are considered for the \(TDoA\) computation:  
* one reference station for the whole trajectory (this choice is repeated for each one station);
* the pivot method, with the schema: \(BS7\)-\(BS8\), \(BS8\)-\(BS9\), \(BS9\)-\(BS10\), \(BS10\)-\(BS11\);
* at each epoch the reference station is the station with the best SNR.  
For all the above cases we compute the \(TDoA\) individual errors, as the differences between the observed TDoA and the true single differences of the distances between the stations and the receiver. Table 3 shows the statistics on the \(TDoA\) errors for each case. In the analysis of the errors, a few observations of some stations are clearly affected by isolated blunders of more than 100 m. These observations, less than ten, are excluded by the following analysis and least squares solutions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(\mathbf{BS}\) 7 & \(\mathbf{BS}\) 8 & \(\mathbf{BS}\) 9 & \(\mathbf{BS}\) 10 & \(\mathbf{BS}\) 11 \\ \hline Mean (dB) & 31 & 31 & 30 & 30 & 30 \\ St.dev. (dB) & 2 & 1 & 1 & 2 & 2 \\ Max. (dB) & 36 & 34 & 35 & 35 & 34 \\ Min. (dB) & 22 & 25 & 24 & 19 & 23 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Take 01: statistics of SNRs (dB) of the base stations.  
Figure 8: Take 01: mean SNR for each distance interval.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \(\mathbf{Ref.}\) & \(\mathbf{Ref.}\) & \(\mathbf{Ref.}\) & \(\mathbf{Ref.}\) & \(\mathbf{Ref.}\) & \(\mathbf{Ref.}\) & \(\mathbf{Pivot}\) & \(\mathbf{Best SNR}\) \\  & [7] & [8] & [9] & [10] & [11] & & \\ \hline Cum. err. (m) & 0.8 & 0.6 & 0.8 & 1.0 & 0.8 & 0.9 & 0.8 \\ Mean (m) & 0.1 & \(-\)0.1 & 0.0 & 0.5 & \(-\)0.2 & 0.0 & 0.2 \\ St. dev. (m) & 0.6 & 0.4 & 0.5 & 0.6 & 0.6 & 0.7 & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Take 01: errors (measured minus ground truth) in \(TDoA\) for different choices of reference station. Ref. i: base station i as reference for all the epochs; Pivot: pivot scheme; Best SNR: for each epoch the best SNR at each epoch. Mean: mean; St. dev.: standard deviation. Cum. err.: cumulative error, square root of the sum of the squares of the errors divided by the population.  
In our data, no correlation exists between the SNR of the reference station and the resulting \(TDoA\) errors; therefore, the SNR sorting is not an optimal criterion to select the best reference station in \(TDoA\) computation. The above conclusions, discussed in detail, are relevant to Take 01, but all the other takes provide similar results.