A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

Seppe Van Brandt; Jo Verhaevert; Tanja Van Hecke; Hendrik Rogier

doi:10.3390/s22145229

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

Sensors (Basel). 2022 Jul 13;22(14):5229. doi: 10.3390/s22145229.

Authors

Seppe Van Brandt¹, Jo Verhaevert¹, Tanja Van Hecke¹, Hendrik Rogier¹

Affiliation

¹ IDLab, Department of Information Technology, Faculty of Engineering and Architecture, Ghent University-imec, 9052 Gent, Belgium.

Abstract

The effects of random array deformations on Direction-of-Arrival (DOA) estimation with root-Multiple Signal Classification for uniform circular arrays (UCA root-MUSIC) are characterized by a conformally mapped generalized Polynomial Chaos (gPC) algorithm. The studied random deformations of the array are elliptical and are described by different Beta distributions. To successfully capture the erratic deviations in DOA estimates that occur at larger deformations, specifically at the edges of the distributions, a novel conformal map is introduced, based on the hyperbolic tangent function. The application of this new map is compared to regular gPC and Monte Carlo sampling as a reference. A significant increase in convergence rate is observed. The numerical experiments show that the UCA root-MUSIC algorithm is robust to the considered array deformations, since the resulting errors on the DOA estimates are limited to only 2 to 3 degrees in most cases.

Keywords: conformal map; deformation; direction-of-arrival; error propagation; polynomial chaos; root-MUSIC; uniform circular array.

Grants and funding

This work was supported by the Fonds Wetenschappelijk Onderzoek – Vlaanderen - FWO under Grants n° G0F4918N (EOS ID 30452698) and n° S001521N IoBaLeT: Sustainable Internet of Battery-Less Things.