Analytical performance assessment for multi-dimensional Tensor-ESPRIT-type parameter estimation algorithms

Subspace-based high-resolution parameter algorithms such as ESPRIT, MUSIC, or RARE are known as efficient and versatile tools in various signal processing applications including radar, sonar, medical imaging, or the analysis of MIMO channel sounder measurements. Since these techniques are based on the singular value decomposition (SVD), their performance can be analyzed with the help of SVD-based perturbation theory. Recently we have demonstrated that in the R-dimensional case (R ≥ 2), the estimation accuracy of these schemes can be improved by replacing the measurement matrix by a measurement tensor and the SVD by the Higher-Order SVD (HOSVD). In case of ESPRIT, this gives rise to the family of Tensor-ESPRIT algorithms, e.g., standard Tensor-ESPRIT and Unitary Tensor-ESPRIT. In this paper we derive the analytical performance for Tensor-ESPRIT-type algorithms via a recently introduced perturbation theory for the HOSVD-based signal subspace estimate. All expressions are asymptotic in the SNR, but not in the sample size. We first present the explicit equations as a function of the current noise realization, where no assumption on the statistics of symbols or noise are required. Next, we show the result of performing statistical expectation over white Gaussian noise. To demonstrate the usefulness of the results we also present a compact expression for the asymptotic efficiency in the case of a single source, which is only a function of the array size.