The Fractional Lower Order Moments Based ESPRIT Algorithm for Noncircular Signals in Impulsive Noise Environments

Abstract

By applying the covariation statistics, this paper generalizes the non-circularity to the scenario of complex isotropic symmetric alpha-stable (\( S\alpha S \)) signals. The matrices based on fractional lower order moments for the extended sensor array outputs, which have been shown to have similar forms to the covariance matrix for the Gaussian distributed signals and noise, are formulated for the case of complex \( S\alpha S \) signals and noise. Therefore, the similarity transformation based estimating signal parameter via rotational invariance techniques can be applied to these matrices resulting to the improved direction of arrival estimates for noncircular signals in the presence of impulsive noise environments. The robustness of our proposed algorithm, especially for low generalized signal to noise ratio situations, and for quite highly impulsive noise environments is demonstrated by Monte-Carlo simulations.