Performance analysis of an improved MUSIC DoA estimator

TL;DR

This paper compares the performance of traditional MUSIC and improved G-MUSIC DoA estimators in large-sample regimes, showing G-MUSIC's advantages in resolving closely spaced sources.

Contribution

It demonstrates that G-MUSIC maintains source separation capabilities in closely spaced scenarios where traditional MUSIC fails, and provides asymptotic variance analysis.

Findings

G-MUSIC can consistently separate closely spaced sources.

Traditional MUSIC is consistent for widely spaced sources.

G-MUSIC has lower asymptotic variance in certain regimes.

Abstract

This paper adresses the statistical performance of subspace DoA estimation using a sensor array, in the asymptotic regime where the number of samples and sensors both converge to infinity at the same rate. Improved subspace DoA estimators were derived (termed as G-MUSIC) in previous works, and were shown to be consistent and asymptotically Gaussian distributed in the case where the number of sources and their DoA remain fixed. In this case, which models widely spaced DoA scenarios, it is proved in the present paper that the traditional MUSIC method also provides DoA consistent estimates having the same asymptotic variances as the G-MUSIC estimates. The case of DoA that are spaced of the order of a beamwidth, which models closely spaced sources, is also considered. It is shown that G-MUSIC estimates are still able to consistently separate the sources, while it is no longer the case for the MUSIC ones. The asymptotic variances of G-MUSIC estimates are also evaluated.