# Optimal Design of Switchable Wearable Antenna Array for Wireless Sensor Networks
## 5 Conclusions  
In our study, we considered a wearable four-antenna phased array synthesizing a switchable directivity pattern intended to improve the signal to interference ratio in off-body links. We applied an evolutionary algorithm to optimize the spatial placement and feed phasing of the elementary on-body antennas. To simplify the future implementations, we assumed only two possible values of phase (0 or \(\alpha_{const}\)) in the antenna feeding network. At this stage of our research, for simplicity, we considered an array consisting of half-wave dipoles with vertical orientation on the body. Consequently, we optimized five variables: four angular positions of the elementary antennas on the body and a single value of the phase shift \(\alpha_{const}\). In each iteration of the optimization loop, we calculated the signal-to-interference ratio for 3720 combinations of signal and interference angles of arrival and feed phasing vectors. This number of full-wave electromagnetic simulations would be prohibitive. Therefore, to keep the computation time realistic, we applied a considerably simplified model of the wearable antenna array. We proposed and tested four diverse versions of the objective function, i.e., min-max, nadir point distance maximization, utopia point distance minimization, and full Pareto-like. Our experience justifies the assumption that for complex problems in electromagnetics, the capability of stochastic optimization methods for  
Figure 17: The radiation patterns of the antenna array for the worst combination of signal and interference angles: (**a**) before optimization, (**b**) after optimization. Figure 18: The radiation patterns of the optimized antenna array for the worst combination of signal and interference angles after optimization, obtained with the simplified model, cylindrical model, and heterogeneous model. an effective exploration and exploitation of the objective space depends strongly on the objective function formulation. The common denominator linking the diverse formulations was the same computational method, i.e., an algorithm of evolutionary computing in either its single-objective version (min-max, nadir point, utopia point formulations) or multi-objective version (full Pareto-like formulation). Out of the four versions, we obtained the best results using the min-max objective function with a single-objective evolutionary algorithm of the lowest order--Estra. The single-objective optimization performed with three other algorithms: Nelder-Mead, Powell and \"interior-point\" not only identified inferior solutions but also with significantly greater number of iterations; moreover, the solutions independently identified by ESTra and Powell are mutually non-dominated, but ESTra solution was found in a substantially shorter runtime. In fact, the fastest convergence was observed with Pareto-like optimization that required approximately half of the number of calls to the objective function compared to min-max algorithm, giving a solution that was similarly good. Our investigation indicates that evolutionary optimization algorithms can be successfully applied to significantly improve the design of wearable antenna arrays in wireless body area networks. The other way around, i.e., comparing various optimization algorithms belonging to either the deterministic class or the stochastic one, against a specific formulation of the inverse problem, would be surely meaningful. Nevertheless, the approach would imply a substantial number of experiments: in the basic case of only two algorithms against four formulations, \(2^{4}\) optimization runs would be in order; for the time being, this was out of the scope of our research. In our follow-up research, we will investigate simplified but more accurate analytical models of wearable antenna array radiation patterns taking into account the interaction with human arms as well as coupling between the antennas.