Multidimensional ESPRIT for Damped and Undamped Signals: Algorithm, Computations, and Perturbation Analysis

Abstract

In this paper, we present and analyze the performance of multidimensional ESPRIT ( $N$ -D ESPRIT) method for estimating parameters of $N$ -D superimposed damped and/or undamped exponentials. $N$ -D ESPRIT algorithm is based on low-rank decomposition of multilevel Hankel matrices formed by the $N$ -D data. In order to reduce the computational complexity for large signals, we propose a fast $N$ -D ESPRIT using truncated singular value decomposition (SVD). Then, through a first-order perturbation analysis, we derive simple expressions of the variance of the estimates in $N$ -D multiple-tones case. These expressions do not involve the factors of the SVD. We also derive closed-form expressions of the variances of the complex modes, frequencies, and damping factors estimates in the $N$ -D single-tone case. Computer results are presented to show effectiveness of the fast version of $N$ -D ESPRIT and verify theoretical expressions.