Asymptotic performance analysis of information-theoretic criteria for determining the number of signals in spatially correlated noise

A new information-theoretic criterion for the determination of the number of signals in unknown correlated noise was derived in Zhang and Wong (1993) supported with computer simulations. In the present correspondence, the theoretic performance of the criterion is presented. The authors establish a simple expression, in a closed form, for the probability of correct estimation by the criterion. Then on this basis, they analyze its consistency properties, showing that the criterion is consistent if the penalty coefficient α=(1/2)logN and inconsistent if α=1