Comparison of algorithms for detection of the number of signal sources

Some procedures for detection of the number of signal sources in presence of noise are compared. Two kinds of noise are considered. First, signals in the presence of Gaussian white noise under an additive model are examined. In this case, the problem is just to find the multiplicity of the smallest eigenvalue of the covariance matrix of the observation vector. Second, signals in presence of noise with arbitrary covariance matrix are investigated. In this case, the problem is to find the multiplicity of the smallest eigenvalue of the multiplicity of the covariance matrix of the observation vector and the inverse of the covariance matrix of the noise vector. For both cases methods based on information theoretic criteria are used. Specifically, the AIC method introduced by Akaike (1972), Schwartz's (1978) method, Rissanen's (1978) MDL, and Zhao, Krishnaih and Bai's (1986) method are used.