How to Determine an Optimal Noise Subspace?

TL;DR

This paper investigates how selecting a partial noise subspace, rather than all small eigenvalue eigenvectors, can improve the accuracy of DOA estimation using the MUSIC algorithm.

Contribution

It reveals that using a partial noise subspace yields more accurate DOA estimates and proposes a method to select the optimal eigenvectors for the noise subspace.

Findings

Partial noise subspace improves DOA estimation accuracy

Optimal eigenvector selection enhances MUSIC performance

Traditional full noise subspace is not always optimal

Abstract

The Multiple Signal Classification (MUSIC) algorithm based on the orthogonality between the signal subspace and noise subspace is one of the most frequently used method in the estimation of Direction Of Arrival (DOA), and its performance of DOA estimation mainly depends on the accuracy of the noise subspace. In the most existing researches, the noise subspace is formed by (defined as) the eigenvectors corresponding to all small eigenvalues of the array output covariance matrix. However, we found that the estimation of DOA through the noise subspace in the traditional formation is not optimal in almost all cases, and using a partial noise subspace can always obtain optimal estimation results. In other words, the subspace spanned by the eigenvectors corresponding to a part of the small eigenvalues is more representative of the noise subspace. We demonstrate this conclusion through a number of experiments. Thus, it seems that which and how many eigenvectors should be selected to form the partial noise subspace would be an interesting issue. In addition, this research poses a much general problem: how to select eigenvectors to determine an optimal noise subspace?