Probability of Resolution of MUSIC and g-MUSIC: An Asymptotic Approach

TL;DR

This paper uses Random Matrix Theory to analyze the asymptotic behavior and resolution limits of MUSIC and g-MUSIC DoA estimation methods, providing a theoretical foundation for their performance prediction.

Contribution

It derives a general CLT for eigenvector-based cost functions, enabling accurate asymptotic analysis of MUSIC and g-MUSIC resolution capabilities.

Findings

Asymptotic joint Gaussian distribution of cost functions established

Accurate prediction of resolution limits achieved

Theoretical framework for eigenvector-based DoA estimation performance

Abstract

In this article, the outlier production mechanism of the conventional Multiple Signal Classification (MUSIC) and the g-MUSIC Direction-of-Arrival (DoA) estimation technique is investigated using tools from Random Matrix Theory (RMT). A general Central Limit Theorem (CLT) is derived that allows to analyze the asymptotic stochastic behavior of eigenvector-based cost functions in the asymptotic regime where the number of snapshots and the number of antennas increase without bound at the same rate. Furthermore, this CLT is used to provide an accurate prediction of the resolution capabilities of the MUSIC and the g-MUSIC DoA estimation method. The finite dimensional distribution of the MUSIC and the g-MUSIC cost function is shown to be asymptotically jointly Gaussian distributed in the asymptotic regime.