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Blind estimation of a class of single-input multiple-output (SIMO) time-varying channels is considered using only the second-order statistics of the data. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). The multistep linear predictors-based method for blind identification of time-invariant channels is extended to time-varying channels represented by a CE-BEM. Sufficient conditions for channel identifiability are investigated. The proposed method requires the knowledge of the active basis functions in the CE-BEM. It is not as sensitive to overestimation of the channel length as some of the existing methods. Computer simulation examples are presented to illustrate the approach and to compare it with three existing approaches.