Analytical Performance Assessment of 2-D Tensor ESPRIT in Terms of Physical Parameters

Abstract

In this paper, we present an analytical performance assessment of 2-D Tensor ESPRIT in terms of physical parameters. We show that the error in the $r$-mode depends only on two components, irrespective of the dimensionality of the problem. We obtain analytical expressions in closed form for the mean squared error (MSE) in each dimension as a function of the signal-to-noise (SNR) ratio, the array steering matrices, the number of antennas, the number of snapshots, the selection matrices, and the signal correlation. The derived expressions allow a better understanding of the difference in performance between the tensor and the matrix versions of the ESPRIT algorithm. The simulation results confirm the coincidence between the presented analytical expression and the curves obtained via Monte Carlo trials. We analyze the behavior of each of the two error components in different scenarios.

Keywords

• 2-D Tensor ESPRIT
• harmonic retrieval
• performance assessment
• first-order perturbation analysis