Blind Equalization of a Nonlinear Satellite System Using MCMC Simulation Methods
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lind Equalization of a Nonlinear Satellite System Using MCMC Simulation Methods Stéphane Sénécal Groupe Non-Linéaire, Laboratoire des Images et des Signaux CNRS UMR 5083, LIS-ENSIEG, BP 46, 38402 Saint Martin d’Hères Cedex, France Email: [email protected]
Pierre-Olivier Amblard Groupe Non-Linéaire, Laboratoire des Images et des Signaux CNRS UMR 5083, LIS-ENSIEG, BP 46, 38402 Saint Martin d’Hères Cedex, France Email: [email protected] Received 31 July 2001 and in revised form 12 October 2001 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. Keywords and phrases: traveling wave tube amplifier, Bayesian inference, Markov chain Monte-Carlo simulation methods, Gibbs sampling, Hastings-Metropolis algorithm.
1. INTRODUCTION The importance of telecommunication since the last decade leads to use satellites for transmitting the information. The main drawback of this transmission method is the attenuation of the signal due to its trip through the atmosphere. Therefore, one of the aims of the satellite is to “re-amplify” the signal before sending it back to Earth. The lack of space and energy available on the satellite leads to use TWT (Traveling Wave Tube) amplifiers for realising this stage of transmission [1]. Unfortunately, these kinds of amplifiers are intrinsically nonlinear and thus imply complex processing methods for realizing the equalization. Neural networks inspired methods for modeling and equalizing these communication systems have been successfully implemented [2, 3, 4]. A Volterra identification coupled with a Viterbi receiver has also been studied in [5]. However, these methods need a learning (or training) input sequence for setting the parameters of the equalization al-
gorithm. Some of the recently proposed methods perf
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