We consider blind equalization for block transmissions over the frequency selective Rayleigh fading channel. In the absence of pilot symbols, the receiver must be able to perform joint equalization and blind channel identification. Relying on a mixed discrete-continuous state-space representation of the communication system, we introduce a blind Bayesian equalization algorithm based on a Gaussian mixture parameterization of the a posteriori probability density function (pdf) of the transmitted data and the channel. The performances of the proposed algorithm are compared with existing blind equalization techniques using numerical simulations.