## 5 Experiments
### Propagation Models  
A key aspect in the proposed method is the selection of the most appropriate propagation model. It is used to estimate the distance from the measured power and to again estimate the power from the estimated distance. Specifically, in our experiments the power is measured in terms of RSSI (Received Signal Strength Indication). The indoor-radio channel differs from the outdoor channel because the indoor channel has shorter distances to cover, higher path-loss variability, and greater variance in the received signal power. Several models have been proposed in the literature to estimate the path loss in the indoor environment. In our experiments, we have used the one-slope and multi-wall models [38, 39, 46]. These are the most important and frequently employed path loss models for the estimation of the average received power levels in indoor propagation scenarios, since they provide a good trade-off between simplicity and precision. For the one-slope model, the path loss in dB is given by  
\[L_{dB}=L_{0,dB}+10n\log_{10}\left(r\right) \tag{16}\]  
\begin{table}
\begin{tabular}{c|c|c|c|c} \hline \hline
**ANCHOR** & **00-00** & **28-1F** & **95-4C** & **1E-57** \\ \hline \multicolumn{5}{c}{**Office room**} \\ \hline A1 & 24.10 & 7.63 & 34.00 & 24.35 \\ A2 & 25.62 & 42.00 & 12.50 & 33.36 \\ A3 & 29.21 & 6.20 & 39.98 & 20.31 \\ A4 & 29.27 & 14.54 & 38.00 & 25.21 \\ A5 & 23.01 & 30.00 & 20.55 & 36.45 \\ A6 & 13.60 & 30.00 & 10.85 & 43.07 \\ A7 & 27.09 & 23.03 & 21.96 & 29.59 \\ A8 & 41.96 & 15.30 & 19.63 & 21.87 \\ A9 & 33.81 & 26.26 & 21.44 & 21.96 \\ A10 & 9.60 & 34.49 & 23.53 & 28.02 \\ \hline \multicolumn{5}{c}{**Flat**} \\ \hline A1 & 13.17 & 5.01 & 23.00 & 20.28 \\ A2 & 21.98 & \(-\)0.54 & 18.00 & 25.00 \\ A3 & 16.00 & 16.92 & 36.00 & 16.00 \\ A4 & 28.10 & 12.00 & 4.73 & 9.29 \\ A5 & \(-\)8.48 & 29.08 & 22.51 & 9.97 \\ A6 & 4.91 & 6.86 & 22.00 & 35.02 \\ A7 & 7.57 & 18.98 & \(-\)0.  
where \(L_{0,dB}\) is the path loss at distance of 1 m, \(n\) is the attenuation coefficient and \(r\) is the distance. \(L_{0,dB}\) should be estimated in a free space and it is not affected by the environment. It only depends on physical properties of link (distance and frequency) and can be estimated _a priori_ by the following Friis free-space equation (in dB)  
\[L_{friis,dB}=20\log_{10}\left(f_{MHz}\right)+20\log_{10}\left(r\right)-28 \tag{17}\]  
For the 2.4 GHz and for the distance of 1 m the Equation (17) has a value of \(40.2 dB\). As for the coefficient \(n\), it is environment dependent and in literature there are several studies that provide an estimation of this value. In our experiments, we have selected the value of \(n=4.2\) in accordance with the study in [40, 41, 42]. This model has been used for the conference and office environment. For the flat scenario, due to the presence of walls we have used the multi-wall model given by the following expression  
\[L_{dB}=L_{0,dB}+10n\log_{10}\left(r\right)+\sum\limits_{i=1}^{N}k_{i}L_{wi} \tag{18}\]  
where the integer \(N\) is the number of wall types, \(k_{i}\) denotes the number of wall of type \(i\), and \(L_{wi}\) the signal loss for wall type \(i\). There are different \(L_{wi}\) values in relationship to the material and thickness of the walls, but in our work all walls have same characteristic. So the difference among the wall is only their position in the path. In our experiments, in accordance with the work in [43], we used the calibration method proposed in [44] to estimate the \(L_{wi}\) values for our flat environment. Whether the wall is the first or the second in the path changes the value of \(L_{wi}\). After the calibration, we obtained these values: \(L_{w1}=8.21\) and \(L_{w2}=7.12\). The described models are then used to extract the distance from the collected RSSI measures, but before this, a conversion is needed since these measures do not represent exactly the received power, which is instead given by the following expression  
\[P_{RX,dB}=RSSI+Offset \tag{19}\]  
For the used CC2530 chipset, _Offset_\(=-73\).