Statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing

The performances of the Akaike (1974) information criterion and the minimum descriptive length criterion methods are examined. The events which lead to erroneous decisions are considered, and, on the basis of these events, the probabilities of error for the two criteria are derived. The probabilities of the first two events are derived based on the asymptotic distribution of the sample eigenvalues of an estimated Hermitian matrix. It is further shown that the probabilities of missing and false alarm for these two criteria can be evaluated to a close approximation. Although the derivation of the probabilities of error is based on an asymptotic analysis, the results are confirmed to be in very close agreement with computer simulation results