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

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.

Improving the accuracy of a digital spectral correlation-interferometric method of direction finding with analytical signal reconstruction for processing an incomplete spectrum of the signal

“…In [10], using subspace methods, a joint range estimation method is applied based on the unitary advanced multiple signal classification (MUSIC) algorithm, also known as the root-MUSIC algorithm. And in [11] they struggle with random deformations of signal arrays. The ESPRIT and root-MUSIC methods are generally used in the presence of a priori information about the number of signals in the mixture and lose stability at low signal-to-noise ratios.…”