Comparison of resolving power of array processing methods by using an analytical criterion

Resolving power is very important when comparing localization methods in underwater passive listening. The authors introduce a simple criterion that is based on a second-order analysis of different localization functions usually available in array processing: conventional and adaptive beamforming and the MUSIC method. A general procedure is presented in both finite- and infinite-time observation cases, providing a system of equations. Its solutions are shown to describe areas as functions of the spectral levels and bearings of the two sources to be resolved. Explicit analytical formula are given in the asymptotic case. The angular resolving powers of the three methods have been derived by approximations and compared with an ultimate resolution bound. It is found that the resolving power of the classical approach depends only on array geometry, whereas that of the adaptive beamforming and MUSIC methods is varies as the fourth root of the input-signal-to-noise ratio