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Traditional designs of mobile communication receivers commonly rely on a (colored or white) Gaussian model of the signal disturbance. Such a model does not accurately reflect the statistics of co-channel interference, a dominant source of signal disturbance that limits the capacity of most cellular networks. Consequently, the performance of receivers designed based on the Gaussian model is often far from optimum in a heavily loaded network. In this paper, we explore the potential of suppressing interference in channel estimation by using a non-Gaussian noise model of the signal disturbance. An EM-based, iterative algorithm is derived for jointly estimating the channel response and the parameters that characterize the non-Gaussian noise model. As an example, we also consider a special case where the non-Gaussian model has a constant envelope characteristic. Using the GSM/EDGE air interface, we demonstrate that significant performance gains can be obtained with the proposed channel estimation algorithm when a dominant GMSK-modulated interference exists. The proposed algorithm can also be used in combination with equalizers designed for non-Gaussian noise models to provide further performance gains.