OPERATOR APPROACH TO PERFORMANCE ANALYSIS OF ROOT-MUSIC AND ROOT-MIN-NORM

We carry out a performance analysis of two eigenstructure-based direction-of-arrival (DOA) estimation algorithms, using a series expansion of projection operators (or projectors) on the signal and noise subspaces. In the interest of algebraic simplicity, an operator formalism is utilized rather than a more conventional direct use of eigenvectors and eigenvalues of the array covariance matrix. A perturbation analysis is performed on the projectors, the result of which is used to determine the effect on the estimated parameters. Our approach affords us the possibility to carry out the analysis to any chosen order of expansion of the projectors. This is made possible by using an original recurrence formula developed for the higher order terms in the series expansion of the projectors. We apply this method to study the root-MUSIC and the root-Min-Norm algorithms and establish the superiority of root-MUSIC in all cases. Our analysis has also resulted in new insightful asymptotic expressions that describe the statistical behavior of the estimated angles and radii of the signal zeros. Simulations which verify the analytical derivations are provided.