The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise

This paper presents an asymptotic statistical analysis of the null-spectra of two eigen-assisted methods, MUSIC [1] and Minimum-Norm [2], for resolving independent closely spaced plane waves in noise. Particular attention is paid to the average deviation of the null-spectra from zero at the true angles of arrival for the plane waves. These deviations are expressed as functions of signal-to-noise ratios, number of array elements, angular separation of emitters, and the number of snapshots. In the case of MUSIC. an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise. This result is validated by Monte Carlo simulations.