Stochastic Surrogate Models of Deformable Antennas Based on Vector Spherical Harmonics and Polynomial Chaos Expansions: Application to Textile Antennas

Abstract

A methodology for modeling the Far field (FF) radiated by antennas subject to random variabilities with surrogate models of high efficiency is presented herein. The FF is expanded onto vector spherical harmonics, then the stochastic variability of their coefficients is quantitatively modeled with the polynomial chaos expansion. The accuracy of the surrogate model is guaranteed by a robust and efficient adaptive procedure; “extreme parsimony” of the model is achieved thanks to various “compression” techniques; moreover, the characterization of the antenna’s frequency behavior over a band of interest has been taken into account in the modeling for the first time. The methodology is applied to a practical wearable textile patch antenna designed to cover the 2.4–2.5 GHz band and which is subject to five geometric and material random parameters. Specifically, the “Weierstrass” curves crumpling effect is modeled for the first time. Comparison to the full-wave simulations shows that the derived surrogate model predicts the FF with a good accuracy and with a speed up factor of $10^{5}$ . Such type of surrogate models could be beneficial not only for antenna design and optimization purpose, but also, e.g., for joint antenna-channel stochastic analyses.