In this paper, a completely blind equalizer based on probability density function (pdf) fitting is proposed. It doesn't require any prior information about the transmission channel or the emitted constellation. We also investigate Automatic Modulation Classification (AMC) for Quadrature Amplitude Modulation (QAM) based on the pdf of the equalized signal. We propose three new approaches for AMC. The first employs maximum likelihood functions (ML) of the modulus of real and imaginary parts of the equalized signal. The second is based on the lowest quadratic or Bhattacharyya distance between the estimated pdf of the real and imaginary parts of the equalizer output and the theoretical pdfs of M-QAM modulations. The third approach is based on theoretical pdf dictionnary learning. The performance of the identification scheme is investigated through simulations.