# Field-Based Optimal Placement of Antennas for Body-Worn Wireless Sensors
## 3 Simulations and Results
In this case the objective function was defined as the minimum value from among two parameters: \(S_{21}\) and \(S_{31}\) in the frequency range: 2.4-2.5 GHz. For the same starting point as previously, the initial value of objective function was \(-109\) dB. After 61 iterations it was improved to \(-80\) dB, which is a gain of 29 dB in the radio link budget. The improvement of the objective function in the optimization process _vs._ iteration number is presented in Figure 8.  
In Figure 9 we present the scattering matrix parameter values (\(S_{21}\) and \(S_{31}\)) before and after optimization for 2.4 GHz. The improvement of \(S_{31}\) is visible while \(S_{21}\) changed only slightly. Figure 8: Optimization process with the three-antenna scenario; the objective function is the minimum of \(S_{21}\) and \(S_{31}\). Figure 9: Scattering matrix parameter values _vs._ frequency before and after optimization for 2.4 GHz frequency band. The good performance of the optimization procedure that we observed at 2.4 GHz was then verified in the 5.8 GHz ISM band. For this purpose we used shorter dipoles (20 mm long) which were tuned for the frequency equal to 5.8 GHz. The optimization starting point and the objective function definition were the same as for 2.4 GHz. The results were obtained after 67 iterations. The initial value of the objective function (the lowest value of \(S_{21}\) and \(S_{31}\) within the frequency range from 5.7 GHZ to 5.9 GHz) was \(-124\) dB and it improved after 67 iterations to \(-96\) dB. Figure 10 presents the scattering matrix parameter values before and after optimization. The results of all the described optimization experiments are gathered in Table 1.  
We have assessed the validity of our simplified human body model using a much more detailed numerical anthropomorphic, heterogeneous body model (NMR Hershey) which is available in Remcom Xfdtd. We selected the model version comprising 5 mm voxels. The final antenna position obtained in the optimization process was applied to the model of the sensor network but this time with the heterogeneous numerical phantom. The simulations were performed at 2.4 GHz with three antennas/nodes. The results are presented in Figure 11. A good agreement between the values obtained with the simplified model and the heterogeneous model can be observed, which advocates for the usage of the simplified one. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Optimization Scenario**} \\ \hline
**2 Antennas, 2.4 GHz** & **2 Antennas, 2.4 GHz** & **3 Antennas, 2.4 GHz** & **3 Antennas, 5 GHz** \\
**Fixed Distance** & **Variable Distance** & **Variable Distance** & **Variable Distance** \\ \hline
**Final Value of Angle [rad]** & \(0.63\) & \(0.5\) & \(0.22\) & \(0.35\) \\ \hline
**Final Value of Vertical** & \(0.567\) & \(0.379\) & \(0.18\) & \(0.335\) \\
**Coordinate [m]** & & & & \\ \hline
**Final Value of Antenna** & \(0.001\) & \(0.007\) & \(0.007\) & \(0.0045\) \\
**Distance [m]** & & & & \\ \hline
**Initial Value of Objective** & \(-81\) & \(-81\) & \(-109\) & \(-124\) \\
**Function [dB]** & & & & \\ \hline
**Final Value of Objective** & \(-69\) & \(-64\) & \(-80\) & \(-96\) \\
**Function [dB]** & & & & \\ \hline
**Improvement of Objective** & \(12\) & \(17\) & \(29\) & \(28\) \\
**Function [dB]** & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimization with the evolution strategy algorithm. Figure 10: Scattering matrix parameter values _vs._ frequency before and after optimization for 5.8 GHz frequency band.