Abstract
Blind source recovery (BSR) denotes recovery of original sources or signals without any explicit identification of the environments which may include convolution, temporal variation, and even nonlinearity. This chapter provides an overview of a generalized (i.e., nonlinear and time-varying) state-space BSR formulation by the application of stochastic optimization principles to the Kullback-Lieblar divergence as an information-theoretic performance functional. The multivariable optimization technique is used to derive update laws for nonlinear time-varying dynamical systems, which are subsequently specialized to time-invariant and linear systems. Furthermore, the various possible state-space demixing network structures have been exploited to develop learning rules, capable of handling most filtering paradigms-which are conveniently extendible to nonlinear models. Distinct linear state-space algorithms are presented for the minimum phase and nonminimum phase mixing environment models. Illustrative simulation examples are then presented to demonstrate the on-line adaptation capabilities of the developed algorithms.