An eigenvalue residuum-based criterion for detection of the number of sinusoids in white Gaussian noise

In this paper, based on the fact that the small eigenvalues of a covariance matrix, which derives from data of multiple sinusoidal signals in white Gaussian noise, are asymptotic Gaussian random processes with zero mean. An eigenvalue residuum-based criterion for the detection of the number of sinusoids in white Gaussian noise is introduced. We first consider the eigenvalues of a covariance matrix as a set of measured data, and then gradually rule out the small eigenvalues based on the proposed criterion until the final estimate is obtained. Simulation results show that the proposed method gives superior performance over the Akaike information criterion and the minimum description length principle, especially with a low signal-to-noise ratio (SNR), short data records, and a high number of sinusoids. In addition, the implementation of the new criterion is simpler and faster.