Adaptive Polynomial Chaos Expansion for Uncertainty Quantification and Optimization of Horn Antennas at SubTHz Frequencies

TL;DR

This work tackles uncertainty in subTHz horn antenna performance caused by CNC milling tolerances by introducing an adaptive polynomial chaos expansion (PCE) surrogate. The method builds a sparse surrogate using an anisotropic hyperbolic index set with Legendre polynomials for uniformly distributed inputs and estimates coefficients via Weighted OMP, guided by leave-one-out validation and a complexity-corrected error measure. The adaptive PCE enables fast QoI sampling, PDF and moment calculations, and calculation of Sobol total indices, while also serving as a cheap generator of samples for particle swarm optimization (PSO) to maximize horn gain at 95 GHz. Empirical results show close agreement with MC for mean and variance with far fewer full-wave EM solves, and the PSO-PCE combination achieves near-optimal designs with substantial computational savings, underscoring the practical impact for uncertainty quantification and design optimization of subTHz antennas.

Abstract

Sub-terahertz (subTHz) antennas will play an important role in the next generations of wireless communication systems. However, when comes to the subTHz frequency spectrum, the antenna fabrication tolerance needs to be accurately considered during the design stage. The classic approach to studying the average performance of an antenna design considering fabrication tolerances is through the use of the Monte-Carlo (MC) method. In this paper, we propose an adaptive polynomial chaos expansion (PCE) method for the uncertainty quantification analysis of subTHz horn antennas with flat-top radiation patterns. The proposed method builds a surrogate model of the antenna's response to electromagnetic (EM) excitation and estimates its statistical moments with accuracy close to the reference MC method, but with a much smaller computational complexity of roughly two orders of magnitude. Moreover, the surrogate model based on PCE can substitute full-wave EM solvers in producing samples for electromagnetic quantities of interest, resulting in significant computational efficiency gains during optimization tasks. To this end, we successfully combined PCE with the particle swarm optimization method to design the free parameters of a horn antenna at $95$ GHz for a flat-top gain.

Figures (12)

• Figure 1: Geometry and design parameters of the horn antenna in wang2019 operating at $95$ GHz, which is realized as a cascade of multiple linear circular waveguide sections.
• Figure 2: The EM-simulated flat-top radiation pattern of the subTHz horn antenna shown in Fig. \ref{['HA']} with the parameters $a_{0}=1.2$, $a_{1}=1.5$, $w_{1}=1.5$, $a_{2}=2.3$, $w_{2}=1.8$, $a_{3}=4.55$, $w_{3}=1.6$, $w_{4}=1.35$, and $a_{4}=6.85$ (all in mm) operating at $95$ GHz.
• Figure 3: The parameter $\mu_G$ versus the angle of radiation for the PCE method with $p_{\rm max}=4$ and $M=25$. Respective results via the MC method are also included.
• Figure 4: The parameter $\sigma_G$ versus the angle of radiation for the PCE method with $p_{\rm max}=4$ and $M=25$. Respective results via the MC method are also included.
• Figure 5: The parameter $\sigma_G$ versus the angle of radiation for the PCE method with $p_{\rm max}=5$ and $M=50$. Respective results via the MC method are also included.