# Field-Based Optimal Placement of Antennas for Body-Worn Wireless Sensors
## 3 Simulations and Results  
In the optimization process the chest antenna location constraints were defined as a region by the three following ranges of design variable values: Rotation angle 0.2 rad \(<\varphi_{p}<\) 1.55 rad, antenna vertical position 0 m \(<z<\) 0.6 m and antenna distance to the body 0 \(<d<\) 0.01 m. These values follow from the application of our research to the firefighters system under development, in which the defined region corresponds to the possible predetermined localization of the jacket pocket for the node. Due to the presence of other firefighter equipment, it was only possible to place the pocket for the chest node in the left-front part of the jacket (two other sensors have a fixed location on the right arm and the left side of the head). We assumed that the distance between the antenna and the body could be adjusted slightly by placing the pocket on the inner or the outer side of the jacket or by using styrofoam spacers. We also assumed that the optimization process will start from the location of the chest antenna defined by the \(\varphi_{p}=\) 1 rad \(Z_{p}=\) 0.4 m and \(d=\) 0.001 m (antenna azimuthal position or rotation angle, antenna vertical position, antenna distance to the body surface according to Figure 5). It is the location of an already existing jacket pocket, which we intended to use for the chest module. During the first stage of the optimization experiment a sub-problem of Equation (2) was considered, defined by Equation (3), where we are considering only two antennas operating in the ISM 2.4 GHz band: the head antenna with a fixed position and the chest antenna with a variable position. \[\text{Find}\,\inf_{x\in\text{ft}}\,\sup_{f\in B}\,S_{21}\left(x,f\right)\,,\,x =\left(z_{p},\varphi_{p}\right)\,,\,\Omega\subset\Re^{3}\,,\,\text{B}=\left[ f_{L},f_{H}\right] \tag{3}\]  
with \(f_{L}=\) 2.4 GHz and \(f_{H}=\) 2.5 GHz. Therefore in Equation (3) only S\({}_{21}\) is present. The objective function (to be maximized) was chosen as the minimum value of S\({}_{21}\) in the 2.4-2.5 GHz frequency band. Consequently, a two-variable optimization was considered first. The third design variable--Antenna distance--Was fixed at \(d=\) 0.001 m. The results obtained after 51 iterations are presented in Figure 7 (blue line). The initial value of \(S_{21}\) objective function was \(-81\) dB and the final was \(-69\) dB. We may observe that the radio link quality has improved because the signal received in the optimized case has 12 dB (\(-81\) dB \(vs.\)\(-69\) dB) greater amplitude. Subsequently, the full problem defined by Equation (2) was considered, _i.e._, optimization experiments with two antennas operating at 2.4 GHz was repeated, but this time all three variables of  
Figure 7: Optimization process for the two-antenna scenario; the objective function is \(S_{21}\). the chest antenna position were identified (antenna rotation angle, antenna vertical position, antenna distance to the surface of the body). The results obtained after 49 iterations are presented in Figure 7 (red line). The initial value of \(S_{21}\) objective function was \(-81\) dB, and the final was \(-64\) dB. This means that also in this case the link quality has improved because the signal received in the optimized setup has 17 dB greater amplitude. It can be concluded that the three-variable optimization may provide a greater improvement of the objective function. This result may seem trivial considering that a better solution should exist in the three-parameter optimization space compared to the two-parameter optimization space. However, the problem is that this solution may not be found a particular optimization algorithm. The improvement achieved in our experiments suggests that ESTra algorithm is suitable for the class of problems under consideration. We used the three-variable approach to optimize the three-antenna scenario operating at 2.4 GHz.