Signal separation of nonlinear time-delayed mixture: Time domain approach

In this paper, a novel algorithm is proposed to solve blind signal separation of nonlinear time-delayed mixtures of statistically independent sources. Both mixing and nonlinear distortion are included in the proposed model. Maximum Likelihood (ML) approach is developed to estimate the parameters in the model and this is formulated within the framework of the generalized Expectation-Maximization (EM) algorithm. Adaptive polynomial basis expansion is used to estimate the nonlinearity of the mixing model. In the E-step, the sufficient statistics associated with the source signals are estimated while in the M-step, the parameters are optimized by using these statistics. Generally, the nonlinear distortion renders the statistics intractable and difficult to be formulated in a closed form. However, in this paper it is proved that with the use of Extended Kalman Smoother (EKS) around a linearized point, the M-step is made tractable and can be solved by linear equations.