A Novel Source Number Estimator With Improved Degrees of Freedom

This paper proposes a new source number estimator with improved degrees of freedom for blind source separation, where the mixing matrix does not have the parameterized structure. In order to enhance the degrees of freedom, we exploit the sample dependence of each source and construct a new matrix by vectorizing some delayed covariance matrices based on Khatri-Rao product. Then, an improved Gerschgorin disk estimator for source number is presented based on the new matrix. This estimator can detect the number of sources up to 2M - 1 using only M sensors, while the traditional source number estimators can merely estimate the number of sources less than M employing the same number of sensors. Simulation results verify the superiority of the proposed method by comparing with the existing source enumeration methods in scenario of spatially non-uniform noise when the sensor number is more than the source number and validate the reliability of the proposed method in the case with fewer sensors than sources.