Accurate Estimation of Number of Signal Sources by Eigenvalue Quadratic Diagonal Loading

Abstract

To solve the problem of estimating the number of sources when an antenna array is used for signal reception, an eigenvalue quadratic diagonal loading technique is proposed. The proposed method is applicable under the condition of the proportional relationship between the number of antenna elements and that of snapshots, and whether the received signals are mixed with white Gaussian or colored noise is unknown. The method we proposed belongs to an important area of antenna array signal processing in the field of sensor technology. Firstly, the covariance matrix of received signals is eigenvalue-decomposed. Secondly, eigenvalues are loaded diagonally. The first diagonal loading value is taken as the arithmetic average of all eigenvalues, and the original eigenvalues and diagonal loading value are added to replace the original eigenvalues. The quadratic diagonal loading formula is devised to carry out the quadratic diagonal loading on the eigenvalues immediately after the first diagonal loading. Finally, the information theoretic criterion and random matrix theory methods are chosen to combine with the proposed method to estimate the number of sources. The method is validated by simulation experiments. By combining the proposed method with the existing information theoretic criterion methods, the proposed method can be suitable for the general asymptotic regime with the same number of antenna elements and snapshots in a white Gaussian or colored noise environment. The application range of the random matrix theory methods is extended by the proposed method, so that it can be applied to the colored noise environment.