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

Area of Science:

• Signal Processing
• Array Signal Processing
• Statistical Signal Processing

Background:

• Direction-of-Arrival (DOA) estimation is crucial for applications like radar and sonar.
• Uniform Circular Arrays (UCAs) are commonly used for DOA estimation.
• Random array deformations can significantly impact DOA estimation accuracy.

Purpose of the Study:

• To characterize the effects of random array deformations on UCA root-MUSIC.
• To introduce a novel conformal mapping for improved DOA estimation under deformations.
• To assess the robustness and convergence of the proposed method.

Main Methods:

• Utilized a conformally mapped generalized Polynomial Chaos (gPC) algorithm.
• Modeled elliptical array deformations using Beta distributions.
• Introduced a novel conformal map based on the hyperbolic tangent function.
• Compared the new map against regular gPC and Monte Carlo sampling.

Main Results:

• The novel conformal map significantly increased the convergence rate.
• The UCA root-MUSIC algorithm demonstrated robustness to array deformations.
• DOA estimation errors were limited to 2-3 degrees in most cases, even with larger deformations.

Conclusions:

• The proposed conformally mapped gPC algorithm effectively characterizes DOA estimation under random array deformations.
• The hyperbolic tangent-based conformal map enhances robustness and convergence for UCA root-MUSIC.
• The UCA root-MUSIC algorithm is reliable in the presence of the studied array deformations.