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arXiv · 2501.02746

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

Zhengyu Wang·Wei Yang·Xiaoyi Mai·Zenan Ling·Zhenyu Liao·Robert C. Qiu
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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.

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Zhengyu Wang, Wei Yang, Xiaoyi Mai, Zenan Ling, Zhenyu Liao, Robert C. Qiu. 2026-04-15. A Large-Dimensional Analysis of ESPRIT DoA Estimation: Inconsistency and a Correction via RMT. https://doi.org/10.1109/tsp.2026.3683673

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