Source enumeration method by combining diagonal loading and constructing second-order statistics

A source enumeration method based on diagonal loading of eigenvalues and constructing second-order statistics is proposed, for the case that the antenna array observed signals are overlapped with spatial colored noise, and the number of antennas compared with the number of snapshots meet the requirement of general asymptotic regime. Firstly, the sample covariance matrix of the observed signals is obtained, the eigenvalues of the sample covariance matrix can be acquired by eigenvalue decomposition, and the eigenvalues are diagonally loaded, and a new formula for calculating the diagonal loading is presented. Based on the diagonal loaded eigenvalues, the difference values are calculated for the adjacent eigenvalues after diagonal loading, and the statistical variance of the difference values is calculated. On this basis, the second-order statistics of the difference values are constructed, and when the second-order statistics are minimized, the corresponding number of sources is estimated. The proposed method has wide applicability, which is suitable for both general asymptotic regime and classical asymptotic system, and is suitable for both white Gaussian noise environment and colored noise environment. The method makes up for the lack of source enumeration methods in the case of general asymptotic system and colored noise.