Performance analysis of Root-Music

The authors analyze the performance of Root-Music, a variation of the MUSIC algorithm, for estimating the direction of arrival (DOA) of plane waves in white noise in the case of a linear equispaced sensor array. The performance of the method is analyzed by examining the perturbation in the roots of the polynomial formed in the intermediate step of Root-Music. In particular, asymptotic results for the mean squared error in the estimates of the direction of arrival are derived. Simplified expressions are presented for the one- and two-source case and compared to those obtained for least-squares ESPRIT. Computer simulations are also presented, and they are in close agreement with the theory. An important outcome of this analysis is the fact that the error in the signal zeros has a largely radial component. This provides an explanation as to why the Root-Music is superior to the spectral MUSIC algorithm.>