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.<
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