Operator approach to performance analysis of root-MUSIC and root-min-norm

The authors carry out a performance analysis of two eigenstructure-based direction-of-arrival 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. A perturbation analysis is performed on the projectors, the results of which are used to determine the effect on the estimated parameters. The approach makes it possible to carry out the analysis to any chosen order of expansion of the projectors by using an original recurrence formula developed for the higher-order terms in the series expansion of the projectors. This method is used to study the root-MUSIC and root-min-norm algorithms and establish the superiority of root-MUSIC in all cases. The analysis has also resulted in insightful asymptotic expressions that describe the statistical behavior of the estimated angles and radii of the signal zeros