A Large-Dimensional Analysis of ESPRIT DoA Estimation: Inconsistency and a Correction via RMT

TL;DR

This paper analyzes the limitations of classical ESPRIT DoA estimation in large arrays and proposes a new consistent method based on random matrix theory, supported by theoretical proofs and simulations.

Contribution

It identifies the inconsistency of classical ESPRIT in large-dimensional regimes and introduces a novel, consistent G-ESPRIT method leveraging random matrix theory.

Findings

Classical ESPRIT produces inconsistent DoA estimates as array size and snapshots grow large.

The proposed G-ESPRIT method is proven to be consistent in large-dimensional settings.

Numerical simulations confirm the theoretical advantages of G-ESPRIT over classical ESPRIT.

Abstract

In this paper, we perform asymptotic analyses of the widely used ESPRIT direction-of-arrival (DoA) estimator for large arrays, where the array size $N$ and the number of snapshots $T$ grow to infinity at the same pace. In this large-dimensional regime, the sample covariance matrix (SCM) is known to be a poor eigenspectral estimator of the population covariance. We show that the classical ESPRIT algorithm, that relies on the SCM, and as a consequence of the large-dimensional inconsistency of the SCM, produces inconsistent DoA estimates as $N,T \to \infty$ with $N/T \to c \in (0,\infty)$, for both widely-~and~closely-spaced DoAs. Leveraging tools from random matrix theory (RMT), we propose an improved G-ESPRIT method and prove its consistency in the same large-dimensional setting. From a technical perspective, we derive a novel bound on the eigenvalue differences between two potentially non-Hermitian matrices, which may be of independent interest. Numerical simulations are provided to corroborate our theoretical findings.