# Multi-Objective Optimization of a Wireless Body Area Network for Varying Body Positions
## 2 Wireless Body Area Sensor Network
two, G\({}_{2}\) or G\({}_{3}\), over the angles in the horizontal plane, meaning that the receiver will always select the strongest available signal to detect. Therefore, it should be noted that G\({}_{23}\) is not the sum of G\({}_{2}\) and G\({}_{3}\). This two-antenna switched-pattern approach presented also in [20], can give a better system performance than a two antenna array operating with a single transceiver, a power splitter, and two waveguides. The wearable two-antenna array would suffer from a radiation pattern with deep interference minima which could cause a signal drop, particularly in outdoor environments [21]. The time-diversity in off-body transmission from the two antennas located on the opposite sides of a body reduces the minima in the resultant horizontal pattern gain. Our solution can improve the link reliability in outdoor systems, depending on the particular position of the antennas with respect to the body [20]. To obtain a stable and reliable off-body link irrespective of the free movement of the user, the wearable antennas should have a quasi-omnidirectional pattern. In two-antenna systems, this can be achieved by the complementarity of the radiation patterns for antennas 2 and 3. Randomly selecting the locations of the antennas can lead to a poor off-body link, as may be observed in Figure 3, where for angles 210-315\({}^{\circ}\), the gain of both antennas is below \(-20\) dB. Because the antennas are close to the human body, which influences their radiation properties, they have to be positioned appropriately. This was our motivation for applying an automated optimization procedure to the placement of the antennas. In the optimization process, the geometrical coordinates of nodes 2 and 3 on the trunk surface are the design variables. They have an influence on both the path loss in the on-body link and the radiation pattern in the off-body link. However, while the locations of the antennas on opposite sides of the body result in a desirable quasi-omnidirectional diversity pattern, at the same time, the on-body transmission suffers from high signal attenuation, introduced by the human tissues. The goal was, therefore, to optimize the performance of the off-body link while maintaining good performance in the on-body transmission channel. The on-body performance of the network was evaluated by scattering matrix parameters defined for a 3-port network, where each port refers to an antenna port, as presented in Figure 4. The scattering matrix is defined by Equation (1). \[[\mathrm{B}]\ =\ [\mathrm{S}]\cdot[\mathrm{A}] \tag{1}\]  
where:  
B: the vector of output signals  
S: the scattering matrix  
Figure 2: The off-body communication scenario: (**a**) transmission for antenna 2 with gain G\({}_{2}\); (**b**) transmission for antenna 3 with gain G\({}_{3}\); (**c**) transmission for both antennas 2 and 3 with the resultant gain G\({}_{23}\). It should be noted that in any given direction, G\({}_{23}\) is not the arithmetic sum of G\({}_{2}\) and G\({}_{3}\) but the greater of the two, because the two transceivers operate at the same frequency but in different time slots. In that sense, this is not a two-element antenna array with the superposition of radiation patterns but a switched pattern antenna. A: the vector of input signals. In the case of a network that consists of three antennas, the scattering matrix S is given by Equation (2). \[\left[ \begin{array}{c}\text{b}_{1}\\ \text{b}_{2}\\ \text{b}_{3}\end{array} \right]\ =\ \left[ \begin{array}{ccc}S_{11}&S_{12}&S_{13} \\ S_{21}&S_{22}&S_{23}\\ S_{31}&S_{32}&S_{33}\end{array} \right].\left[ \begin{array}{c}\text{a}_{1}\\ \text{a}_{2}\\ \text{a}_{3}\end{array} \right] \tag{2}\]  
In the case of the network considered in this paper, the matrix is diagonally symmetrical. To characterize the attenuation of the signal between the antennas, only three parameters are needed. In what follows, only the parameters \(S_{21},S_{31},S_{23}\) are considered. Figure 4: The scattering parameters defined with reference to the on-body antenna signals.