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We present a maximum likelihood (ML) approach for deconvolving a multi-input-multi-output (MIMO) non-dispersive system and recovering its inputs, from observation of its outputs. We apply this approach to the specific problem of separating several narrowband digital communication signals that share the same frequency band. A computationally efficient adaptive algorithm for solving this problem is presented, and is shown to be insensitive to lack of precise knowledge of the signals carrier frequencies and phases. Thus, the proposed algorithm can be applied at the front-end of a multi-channel digital communication receiver, whose outputs are then fed into conventional single-channel receivers. Some examples are provided to demonstrate the usefulness of the proposed approach.