Blind Equalization of a Nonlinear Satellite System Using MCMC Simulation Methods

This paper proposes the use of Markov Chain Monte-Carlo (MCMC) simulation methods for equalizing a satellite communication system. The main difficulties encountered are the nonlinear distorsions caused by the amplifier stage in the satellite. Several processing methods manage to take into account the nonlinearity of the system but they require the knowledge of a training/learning input sequence for updating the parameters of the equalizer. Blind equalization methods also exist but they require a Volterra modelization of the system. The aim of the paper is also to blindly restore the emitted message. To reach the goal, we adopt a Bayesian point of view. We jointly use the prior knowledge on the emitted symbols, and the information available from the received signal. This is done by considering the posterior distribution of the input sequence and the parameters of the model. Such a distribution is very difficult to study and thus motivates the implementation of MCMC methods. The presentation of the method is cut into two parts. The first part solves the problem for a simplified model; the second part deals with the complete model, and a part of the solution uses the algorithm developed for the simplified model. The algorithms are illustrated and their performance is evaluated using bit error rate versus signal-to-noise ratio curves.