# A Novel Bitrate Adaptation Method for Heterogeneous Wireless Body Area Networks
## 4 Heterogeneous WBAN Simulator
### The Results of Measurements Used in the Simulator
#### 4.2.3 Accuracy of Radio Distance Measurements  
It is known that the RDMs contain some measurement error [31,45]. Based on the results presented in [45], it was necessary to determine the RDM error function, which will compensate the mean error,  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Model Parameters for 868 MHz Narrowband Channel**} \\ \hline  & \(\mathbf{n}\) & \(\overline{L_{S}(d_{0})}\) & \(\mu_{B[\text{dB}]}\) & \(\sigma_{B[\text{dB}]}\) & \(\mu_{F[\text{dB}]}\) & \(\sigma_{F[\text{dB}]}\) \\ \hline LOS & [0.16; 0.34] & [64.7; 75.9] & [\(-0.2\); 0.0] & [0.8; 2.0] & [\(-0.4\); \(-0.2\)] & [1.5; 2.1] \\ NLOS & [1.40; 3.80] & [65.9; 76.2] & [\(-0.4\); \(-0.2\)] & [1.5; 2.6] & \(-0.4\) & [1.8; 2.2] \\ \hline \multicolumn{4}{c}{**Model Parameters for 6489 MHz Ultra-Wide Band Channel**} \\ \hline  & \(\mathbf{n}\) & \(\overline{L_{S}(d_{0})}\) & \(\mu_{B[\text{dB}]}\) & \(\sigma_{B[\text{dB}]}\) & \(\mu_{F[\text{dB}]}\) & \(\sigma_{F[\text{dB}]}\) \\ \hline LOS & [0.13; 0.85] & [23.4; 28.9] & [\(-0.3\); \(-0.17\)] & [1.3; 2.2] & [\(-0.3\); \(-0 based on all the results obtained in the NLOS conditions. The slope, \(a_{RDM}~{}=~{}0.923\), as well as the intercept term, \(b_{RDM}~{}=~{}0.615\), of the linear RDM error function were determined empirically. It is also important to define the distribution of the estimated distance error due to the usage of the RDM results in the proposed AMASD method. According to the measurement accuracy of the SDS-TWR method with the DWM1000 modules [31], the distribution of errors around the average value for stationary scenarios can be modelled by a normal distribution. It was assumed that for the analyzed off-body communication, and for dynamic scenarios, the distribution of this error could also be described with the Gaussian distribution, while the parameters will be different for each scenario. The error was determined by subtracting the empirical values of the RDMs from the output values of the MAF, with the \(M~{}=~{}10\) length. In Figure 3, an example of an empirical error probability density function (PDF) around the average value with a fitted normal distribution for one of the measurement scenarios is presented. The values of standard deviations, \(\sigma\), of the fitted normal distributions to the empirical values of the distance estimation error for all measurement scenarios were determined and are presented in Table 2. The mean values for all analyzed cases are close to zero. However, the linear RDM error function (with \(a_{RDM}\) and \(b_{RDM}\) parameters mentioned earlier) should be considered during simulation of the distribution of the RDMs values in the NLOS conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**MN LOCATION** & **SCENARIO** & **LOS/NLOS Conditions** & \(\sigma~{}(m)\) \\ \hline \multirow{4}{*}{\(\mathrm{HE_{R}}\)} & \multirow{2}{*}{APR} & LOS & 0.18 \\  & & NLOS & 0.52 \\ \cline{2-4}  & & & LOS & 0.28 \\ \cline{2-4}  & & & NLOS & 0.56 \\ \hline \multirow{4}{*}{\(\mathrm{TO_{F}}\)} & \multirow{4}{*}{APR} & LOS & 0.09 \\  & & NLOS & 0.49 \\ \cline{2-4}  & & & LOS & 0.43 \\ \cline{2-4}  & & & NLOS & 0.66 \\ \hline \multirow{4}{*}{\(\mathrm{AB_{L}}\)} & \multirow{4}{*}{APR} & LOS & 0.26 \\  & & NLOS & 0.44 \\ \cline{1-1} \cline{2-4}  & & & LOS & 0.25 \\ \cline{1-1} \cline{2-4}  & & & NLOS & 0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of the standard deviation of a normal distribution of the distance estimation error fitted to the empirical values for all the measurement scenarios. Figure 3: An example of an empirical error probability density function (PDF) around the average value with a fitted normal distribution for one of the measurement scenarios. As expected, for all measurement scenarios, the RDMs error values are higher for the NLOS conditions. This is due to the very strong attenuation of the direct propagation component.