Analytical performance evaluation of multi-dimensional Tensor-ESPRIT-based algorithms for strictly non-circular sources

Abstract

Exploiting inherent signal structure is a common approach towards improving the performance of conventional parameter estimation algorithms. It has recently been shown that the multi-dimensional (RD) nature of the signals and their statistical properties, i.e., their second-order (SO) strictly non-circular (NC) structure, can be exploited simultaneously by R-D NC Tensor-ESPRIT-type algorithms. In this contribution, we develop an analytical first-order performance evaluation of R-D NC Standard Tensor-ESPRIT and R-D NC Unitary Tensor-ESPRIT. The derived expressions are asymptotic in the effective signal-to-noise ratio (SNR), i.e., they become exact for high SNRs or a large sample size. Moreover, apart from a zero mean and finite SO moments, no assumptions on the noise statistics are required. We show that as in the corresponding NC matrix case, the performance of R-D NC Standard Tensor-ESPRIT and R-D NC Unitary Tensor-ESPRIT is asymptotically identical. Simulations verify the derived expressions.