# Field-Based Optimal Placement of Antennas for Body-Worn Wireless Sensors
## 2 Methods
### Optimization Algorithm
* The last step rules the size of the search region that will be used for the successive iteration: when a design point that is better than the current one is found, the radius of the search region is increased around the new point to search for further improvements; if no improvement is found, the radius of the search region is gradually decreased, up to convergence. In contrast to gradient-based methods of numerical optimization, EStra is suitable for non-convex, non-smooth and discontinuous functions; in particular, it is able to approximate the global minimum of the objective function, regardless of the starting point. The implementation of lowest-order EStra originated a cost-effective algorithm of numerical optimization, with respect to a multi-member implementation, where at each iteration a set of parent individuals recombines to generate a set of offspring individuals; this feature is particularly important when the solution of the direct problem relies on a time-consuming field analysis. In fact, successful applications of ESTra to the design of low-frequency electromagnetic setups can be found in [26], while its combination with a FDTD solver for body-worn wireless sensor network optimization is an original concept presented in this paper. The subject is an emerging one. In fact, in [36] a flow optimization model for designing WBAN is provided; attention is focused on network installation cost and energy consumption of antennas, which are both design criteria to minimize. In [9] a robust optimization model and a new algorithm for designing WBAN in terms of topology and routing, taking into account data generation uncertainty, is presented. Also nature-mimicking algorithms are successfully exploited in WBAN design: for instance, [7] presents a fast evolutionary algorithm inspired by an ant colony; the case study is the optimal design of the body sensor network defined in [8]. As far as the implementation of the optimization procedure proposed in this paper is concerned, the following remarks can be put forward:  
The XFdtd package provides users with a scripting language based on ECMAScript, in which one can prepare an antenna geometry model, as well as meshing and simulation procedures. In contrast, ESTra optimization algorithm was originally coded in Mathworks Matlab and for further work Octave [37] environment was applied because it is freeware and compatible with original Matlab scripts. The Octave and XFdtd scripts are combined and operate in turns to generate a new antenna position and calculate the objective function. Synchronization and data exchange between XFdtd and Octave have been solved by file exchange (Figure 6). The position of the antenna towards the chest was controlled using a cylindrical coordinate system: \(Z_{p}\)--Antenna vertical position, \(\varphi_{p}\)--Antenna azimuthal position and \(d\)--Antenna distance to the body surface, presented in Figure 5. Due to the utilization of the simplified cylindrical body model it was easy to use three design variables for creating the antenna location constraints region which was equidistant to the cylindrical body surface. The numerical model of the network under optimization consists of a human body model (1.8 m tall) and the dipole antennas of 1 mm diameter and the length equal to 53 mm for the 2.4 GHz case and 20 mm for the 5.8 GHz case. In order to decrease the computation time, we chose an adaptive meshing in XFdtd. For the simulations in 2.4 GHz band the voxel within the body model has an edge length equal to 10 mm, and 5 mm for 5.8 GHz. In the regions where antennas were located the voxel size was reduced to 0.5 mm. The model for 2.4 GHz consists of 8,276,136 voxels. With a computer equipped with two Nvidia Tesla C2075 processors the simulation time was ca 30 s. In the case of simulations for 5.8 GHz band, 13,306,865 voxels were used and the simulation time was ca 60 s.  
As already clarified, we focus on the effect of the human body impact on the path loss assuming free-space environment in which the person is located.