Statistical Characteristics of the AIC and MDL Criteria in the Problem of Estimating the Number of Sources of Multivariate Signals in the Case of a Short Sample

At present, there are many methods for estimating the number of signal sources detected by an antenna array. The most well-known methods are based on the AIC (Akaike Information Criterion) and MDL (Minimum Description Length) criteria. The statistical characteristics of these methods have been analyzed in a large number of papers. However, the results obtained in these papers are valid for an unknown internal-noise intensity, and the found theoretical estimates are asymptotic. In the case of short samples, the characteristics of these methods are usually analyzed on the basis of numerical simulations. In this paper, we find the AIC and MDL statistical characteristics in the case of a known internal-noise intensity of the antenna array. It is shown that within the framework of such a formulation of the problem, the characteristics of the estimate of the number of multivariate-signal sources obtained by these methods can be calculated analytically on the basis of the formulas derived by the authors of this paper for the distribution of the maximum noise eigenvalue of the sample correlation matrix of Gaussian input signals. Analytical expressions for the probability of overvaluation of the number of signal sources are obtained for any size of the sample.