Blind identification of nonlinear channels excited by discrete alphabet inputs

Hidden Markov Models (HMMs) are employed in this paper to describe digital communication channels, and their parameters are estimated in a blind fashion. General nonlinear channels can be accommodated which are not restricted to be of the Volterra type. Contrary to standard HMM parameter estimation techniques, which resort to nonlinear optimization of the likelihood function, the proposed method is based on a graph theoretic approach. We exploit the De-Bruijn property of the channel's state transition graph, and develop computationally efficient blind estimation procedures involving shortest path searches. We show identifiability of the associated graph problem and discuss convergence issues. Finally, some illustrative simulations are presented.