On detection of the number of signals in presence of white noise

In this paper, the authors propose procedures for detection of the number of signals in presence of Gaussian white noise under an additive model. This problem is related to the problem of finding the multiplicity of the smallest eigenvalue of the covariance matrix of the observation vector. The methods used in this paper fall within the framework of the model selection procedures using information theoretic criteria. The strong consistency of the estimates of the number of signals, under different situations, is established. Extensions of the results are also discussed when the noise is not necessarily Gaussian. Also, certain information-theoretic criteria are investigated for determination of the multiplicities of various eigenvalues.