Source Enumeration Utilizing Adaptive Diagonal Loading and Linear Shrinkage Coefficients

Source enumeration is typically studied under the assumption of white noise, which may not be suitable for real-world applications. In this article, a source enumeration algorithm robust against both white and colored noises is presented, where the adaptive diagonal loading (ADL) technique combined with linear shrinkage (LS) coefficients are employed. First, a proper loading level is adaptively determined under the presumed number of sources v, which is then applied to mitigate correlated and heterogeneous noise, and simultaneously yields an encouraging result that the loaded eigenvalues match the asymptotic ratio behavior of the eigenvalues obtained under white noise. Then, by analyzing the characteristics of the loaded LS coefficients in various situations, source enumeration is successfully achieved by performing the second-order difference (SOD) operation on the loaded LS coefficients. The proposed algorithm does not require iteration or assume any prior information on noise, and therefore achieves high efficiency and robust enumeration results.