Performance analysis of ESPRIT-type algorithms for strictly non-circular sources using structured least squares

Abstract

This paper presents a first-order analytical performance assessment of the 1-D non-circular (NC) Standard ESPRIT and the 1-D NC Unitary ESPRIT algorithms both using structured least squares (SLS) to solve the set of augmented shift invariance equations. These high-resolution parameter estimation algorithms were designed for strictly second-order (SO) non-circular sources and provide a reduced estimation error as well as an increased identifiability of twice as many sources. Our results are based on a first-order approximation of the estimation error that is explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the approximation becomes exact for either high SNRs or a large sample size. We also find mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required. Simulations show that the asymptotic performance of both algorithms is asymptotically identical in the high effective SNR.