In recent years many sparse estimation methods, also known as compressed sensing, have been developed for channel identification problems in digital communications. However, all these methods presume the transmitted sequence of symbols to be known at the receiver, i.e. in form of a training sequence. We consider blind identification of the channel based on maximum likelihood (ML) estimation via the EM algorithm incorporating a sparsity constraint in the maximization step. We apply this algorithm to a linear modulation scheme on a doubly-selective channel model.