Papers › A Large-dimensional Analysis of ESPRIT DoA Estimation: Inconsistency and a Correction via RMT
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
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 →∞ with N/T →c ∈(0,∞), 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 random matrices, which may be of independent interest. Numerical simulations are provided to corroborate our theoretical findings.
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