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This paper investigates the problem of blindly and semi-blindly acquiring the channel gains for an underdetermined synchronous multiuser multicarrier system. The special case of a multiple-input single-output (MISO) channel is considered where the different users transmit at the same time and in the same bandwidth. In order to separate the different users blindly, techniques exploiting the finite alphabet are used. For such techniques, and for a general underdetermined MIMO system, we study conditions under which the channel and the data for each user are blindly and semi-blindly identifiable. We consider the stochastic maximum likelihood (SML) criterion in which the unknown input symbols are modeled as discrete random variables. We apply the expectation-maximization (EM) algorithm in the frequency domain to get blind and semi-blind channel estimates for each user in the MISO case. We also present a recursive EM solution that updates the channel and noise estimates at each time instant. Simulations show that users can be separated, even at low SNR. Furthermore, semi-blind estimation allows for a more robust estimation solution since a possible singularity problem is avoided.