# Séparation aveugle de mélanges convolutifs de sources cyclostationnaires

Abstract : This thesis addresses the problem of blind separation of convolutive mixtures of cyclostationnary, linearly modulated signals. We mainly focus on signals issued from digital communications systems. Our work involves separating methods based on the minimisation of a criterion (like the constant modulus) combined with a deflation approach. In the first part of the manuscript we considered convolutive mixtures of non second order circular signals such as BPSK and $1/2$ index CPM modulations. We have proven that if the transmission sources all have different baud rates and offset frequencies, minimizing the constant modulus criterion and using a deflation approach successfully achieves the extraction of the original signals from the mixture without prior knowledge of the signal cyclic and non conjugate cyclic frequencies. This result is no longer obtained if all the transmission sources have the same baud rate and frequency offset. We have proven that in this case the CMA criterion has non separating local minima and that the minimisation algorithm very often converges to these spurious points. This means that in a non-negligible number of cases separation is not achieved for this type of mixtures. We therefore propose a new criterion based on the CMA which combined with a deflation approach ensures the extraction of source signals from this particular type of mixtures. This new criterion does not need prior knowledge of the cyclic frequencies but does need information on the most significant non conjugate cyclic frequencies of the signals. We also propose an estimation method for these frequencies and we show that our new algorithm works correctly with the estimated non conjugate cyclic frequencies and that it is capable to extract all the source signals from those types of mixtures for which the CMA fails.The second part of this manuscript focuses on a class of Maximum Likelihood derived separators. We are only considering second order circularly modulated signals. We first studied the case of instantaneous mixtures and then extended our results to convolutive mixtures. For the instantaneous mixtures, we have developed Maximum Likelihood based estimators and presented an implementation method for them. We have then studied their asymptotic properties and we have shown that, in the absence of noise, these estimators improve the performance of the CMA algorithm. Under the same assumptions we have shown that the Maximum Likelihood based estimators allow, in some cases, to extract the signal with the largest bandwidth with a lower error than the one obtained when using other well known separating methods. This results however are no longer true in more realistic contexts such as the presence of noise. We have extended this study to the convolutive mixtures of signals but in this case we have not seen an important improvement on the performances achieved by the CMA algorithm, not even in the absence of noise. Even though this study does not have practical applications, it has nevertheless a certain theoretical significance
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• HAL Id : tel-00607229, version 1

### Citation

Elena Florian. Séparation aveugle de mélanges convolutifs de sources cyclostationnaires. Autre [cs.OH]. Université Paris-Est, 2010. Français. ⟨NNT : 2010PEST1023⟩. ⟨tel-00607229⟩

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