# Design and Implementation of an Indoor Localization System Based on RSSI in IEEE 802.11 ax
## 3 Results
\begin{table}
\begin{tabular}{c c c} \hline
**Distance (m)** & **Mean RSSI (dBm)** & **Standard Deviation** \\ \hline
2 & \(-36\) & \(1.6546\) \\
4 & \(-49\) & \(2.1884\) \\
5 & \(-50\) & \(2.2917\) \\
6 & \(-52\) & \(2.7710\) \\
7 & \(-54\) & \(2.9925\) \\ \(11\) & \(-68\) & \(3.5216\) \\ \hline \end{tabular}
\end{table} 
Table 1: Mean RSSI and its standard deviation as a function of distance. Figure 3: Proposed GPS circuit. \begin{table}
\begin{tabular}{c c} \hline
**Neo-6M Pin** & **ESP32 Pin** \\ \hline Vcc & \(3.3\)V \\ GND & GND \\ Tx & Rx \\ Rx & Tx \\ \hline \end{tabular}
\end{table} 
Table 2: Connections between the ESP32 and the Neo-6M GPS module. distances and times using the Physics Toolbox app to analyze the relationship between the RSSI and distance. The results were compared with the RSSI vs. distance data from reference [1]; as shown in Figure 4, the average RSSI decreases with distance, while the standard deviation increases at longer ranges, indicating greater variability, as shown in Table 3. This comparison reveals that the trend curve for the RSSI-distance relationship from reference [1] closely aligns with the curve derived from our measurements, demonstrating the strong consistency between the two datasets. Additionally, RSSI measurements were taken at different times of the day, considering the distance. Figure 5 shows how the RSSI varies with distance, consistently decreasing as the distance increases. The mean and standard deviation of these measurements are presented in Table 3. To visualize the correlation between RSSI and distance, scatter plots were created and are shown in Figure 6. The average RSSI values decrease as the distance increases. The corresponding standard deviations follow a similar trend, as shown in Table 3. The analysis of the relationship between RSSI and distance shows a decreasing linear trend, indicating an inverse correlation. This implies that as the distance between the transmitter and the receiver increases, the RSSI value decreases, aligning with signal loss theories as a function of distance. This linear relationship reinforces the hypothesis of a significant negative correlation between the two variables. Similarly, the variation in the RSSI over time was analyzed, considering the daily measurements from day 1 to day 31. The average values and standard deviations for each day were calculated, and the results are presented in Table 4. Based on these data and as observed in Figure 7, no clear correlation was identified between the RSSI and the measurement day. This suggests that the RSSI values were not significantly influenced by the date on which the measurements were taken. This reinforces the conclusion that the primary factors affecting the variability in the RSSI are distance and signal propagation. The analysis of the relationship between measurement time and RSSI is represented in a dispersion diagram. At a distance of 2 m, the average RSSI is \(-\)33.50 dBm, with a low standard deviation of 1.65 dBm, indicating a strong and stable signal. As the distance increases, the RSSI becomes more negative, with average values of \(-\)49.57 dBm at 4 m, \(-\)52.66 dBm at 5 m, \(-\)56.51 dBm at 6 m, \(-\)58.32 dBm at 7 m, and \(-\)64.53 dBm at 11 m, with standard deviations ranging from 2.19 dBm to 3.52 dBm. On the other hand, the analysis of the measurements taken at different times (10:00 a.m., 12:00 p.m., 2:00 p.m., 5:00 p.m., 8:00 p.m., and 10:00 p.m.) shows that the average RSSI remains stable within a range of \(-\)51.67 dBm to \(-\)53.83 dBm, with no clear trend linking the time of day to signal strength. This suggests that RSSI does not vary significantly throughout the day. The average values and standard deviations of RSSI are presented in Table 5, while Figure 8 shows a dispersion diagram for the relationship between the RSSI and measurement hours, illustrating the data distribution over time.