Generalized Bayesian Information Criterion for Source Enumeration in Array Processing

We investigate the problem of enumerating source signals impinging on an array of sensors in an information theoretic framework. The conventional Bayesian information criterion (BIC) does not yield satisfactory performance for this problem because it only considers the density of the observations. In order to remedy the limitations of the BIC, we propose a generalized Bayesian information criterion (GBIC) rule by incorporating the density of the sample eigenvalues or corresponding statistics. Such a density contains extra information and complements the density of the observations in constructing the GBIC. As a result, two different expressions for the GBIC are suggested. Simulation results validate the superiority of the proposed GBIC over the conventional BIC in terms of correctly determining the number of sources while their computational costs are comparable.