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In this paper an original Bayesian approach for blind detection for code division multiple access (CDMA) systems in presence of spatial diversity at the receiver is developed. In the noiseless context, the blind detection/identification problem relies on the canonical decomposition (also referred as parallel factor analysis [Sidiropoulos, IEEE SP'00], PARAFAC). The author in [Bro,INCINC'96] proposes a suboptimal solution in least-squares sense. However, poor performances are obtained in presence of high noise level. The recently emerged Markov chain Monte Carlo (MCMC) signal processing method provides a novel paradigm for tackling this problem. Simulation results are presented to demonstrate the effectiveness of this method.