Analysis on blind decorrelation of isotropic noise correlation matrices based on symmetric decomposition

Recently, a technique named `blind decorrelation´ was proposed by which we can blindly diagonalize correlation matrices of isotropic noises observed by particular crystal-shape sensor arrays. This technique enables us to estimate the power of unknown target signals, which may improve the performance of inverse filters such as the Wiener filter. It was clarified that several classes of crystal-shape arrays achieve the blind decorrelation; and some necessary conditions imposed on a sensor array to realize the blind decorrelation were revealed. However, we do not have a necessary and sufficient condition for a sensor array to achieve the blind decorrelation. In this paper, we show a necessary and sufficient condition for a sensor array to achieve the blind decorrelation, using a novel matrix analysis scheme named `symmetric decomposition´.