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

Abstract

It is understood that the eigenvalues of a covariance matrix, deriving from the data of multiple sinusoidal signals in white Gaussian noise, can be divided into two groups when the dimensions of the covariance matrix are larger than the number of sinusoidal signals. One is composed of the sinusoidal signals plus the noise. Another is called ‘small eigenvalues’ which is produced by the noise only. It is also known that the small eigenvalues are an asymptotic Gaussian random process. Based on these facts, an eigenvalue-based residuum criterion for the detection of the number of sinusoids in white Gaussian noise is presented in this paper. Using this criterion, the small eigenvalues of the covariance matrix can gradually be ruled out. While the eigenvalues which belong to the signal and noise are separated, the number of sinusoids is detected successfully. Simulation results exhibit that the proposed method gives a superior performance over the Akaike information criterion (AIC) and the minimum description length principle (MDL), especially for situations where the analyzed signals exhibit 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.