# Multi-Objective Optimization of a Wireless Body Area Network for Varying Body Positions
## 5 Simulation and Optimization Results  
The results presented and discussed in this section were obtained for a three-antenna system as described in Reference [20]. To make the results of our investigation more general, a very simple antenna was modeled in this study with the radiation pattern independent of rotation around the \(z\)-axis. The antennas are dipoles placed in a vertical position matched to operate at 2.45 GHz. The initial placement of the antennas was defined by the positions of the pockets on the firefighter's uniform, which were originally considered for the wireless sensors. The coordinates of the second antenna were \(\phi_{2}\) = 1.4 rad and \(z_{2}\) = 1.03 m. The coordinates of the third antenna were \(\phi_{3}\) = \(-\)2 rad and \(z_{3}\) = 0.23 m. Figure 10 shows the history of the optimization process in the objective function space. The initial values for the objective function components were \(\mathrm{S_{start}}\) = \(-\)105.8, \(\mathrm{G_{start}}\) = 0.034, where \(\mathrm{S_{start}}\) = \(\mathrm{inf}[\mathrm{S_{31}}\),\(\mathrm{S_{21}}\),\(\mathrm{S_{23}}]\), \(\mathrm{G_{start}}\) = \(\mathrm{G_{1+2}}\) before optimization. The final values were \(\mathrm{S_{stop}}\) = \(-\)89.8, \(\mathrm{G_{stop}}\) = 0.27, where \(\mathrm{S_{stop}}\) = \(\mathrm{S_{21}}\), and \(\mathrm{G_{stop}}\) = \(\mathrm{G_{1+2}}\) after optimization. Both components were significantly increased (improved). This solution was achieved in 55 iterations which lasted approximately 24 h, most of which was taken up by the time-consuming computation of the objective function components G and S. Figures 11 and 12 present the initial positions of the antennas for the standing and sitting positions, respectively. These positions resulted in the scattering matrix values (as a function of frequency) shown in Figure 13 (for the standing and sitting positions) and the radiation patterns in Figure 14 (for the standing and sitting positions). The final coordinates of the antennas were \(\phi_{2}\) = 2.26 rad, \(z_{2}\) = 0.94 m, \(\phi_{3}\) = \(-\)0.94 rad,  
Figure 11: The initial placement of antennas on the standing model. Figure 12: The initial placement of the antennas on the sitting model. Figure 13: The initial S parameters. Figure 16: The final placement of the antennas on the sitting model. Figure 14: The initial radiation patterns. Figure 15: The final placement of the antennas on the standing model. An additional run of our multi-objective optimization process was performed from a different starting point. This time the initial placement of the antennas was intentionally configured in such a way that should result in relatively low path-loss in the on-body communication scenario. Antennas 2 and 3 were located relatively close to each other, on the same side of the body (on the front). The aim was to check whether our algorithm could improve the G component without significantly deteriorating the S component. The initial coordinates of the antennas were \(\phi_{2}=0\) rad, \(z_{2}=1.06\) m, \(\phi_{3}=0\) rad, and \(z_{3}=0.18\) m while the initial values of the objective components were S\({}_{\text{start}}=-94.2\), G\({}_{\text{start}}=0.00035\), where S\({}_{\text{start}}=\inf\)[S\({}_{31}\),S\({}_{21}\),S\({}_{23}\)], G\({}_{\text{start}}=\) G\({}_{1+2}\) before optimization. The final values were S\({}_{\text{stop}}=-93.58\), G\({}_{\text{stop}}=0.337\), where S\({}_{\text{start}}=\inf\)[S\({}_{31}\),S\({}_{21}\),S\({}_{23}\)], G\({}_{\text{start}}=\) G\({}_{1+2}\). The final coordinates were \(\phi_{2}=1.97\) rad, \(z_{2}=0.92\) m \(\phi_{3}=-1.53\) rad and \(z_{3}=0.23\) m. Once again, both components were improved. The increase in the G component was particularly substantial. This optimization loop lasted 54 iterations and 24 h. The history of the process is presented in Figure 19, along with the cloud of intermediate solution points.