Estimating the number of signals using the eigenvalues of the correlation matrix

A central problem in certain high-resolution parameter estimation algorithms is estimating the number of emitters that are present. For example, Schmidt´s (1981, 1986) MUSIC algorithm, the ESPRIT algorithm of Roy and Kailath, and Cadzow´s variation of Schmidt´s algorithm all require an accurate estimate of the number of emitters to yield maximum performance. These algorithms are all based upon the eigenvalue decomposition of a vector space formed by the action of an antenna element manifold on a set of signal vectors. A number of different tests have been formulated for predicting the number of emitters present. These tests fall into two categories: those in which a sequence of hypothesis tests are formed using likelihood ratio tests and those in which a convex function is minimized. In the present work the authors report the results of a comparison of these tests and advance some reasons why some of the tests perform poorly. It is shown that both of Schmidt´s tests appear to be reliable, as does Wax´s (1985) MDL (minimum descriptive length). The other tests perform poorly