Closed-form optimized composite-order estimator for blind separation of instantaneous linear mixtures

In the field of blind source separation, formulation of closed-form estimators constitutes an important framework. In this work, we present an optimal composition of third- and fourth-order cumulants leading to a closed-form ICA estimator for a pair-wise blind source separation. We introduce a free weight parameter in combining the cumulants and evaluated its optimal value such that the mean-square estimation of Givens rotation is minimized. We have shown that the optimal value of weight parameter depends on the statistical knowledge of the mixing signals and additive Gaussian noise. Computer simulations have been performed to illustrate the behavior of the proposed optimized closed-form estimator for the maximization of the weighted contrast.