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A multistep linear prediction (MSLP) approach is presented for blind channel estimation for short-code DS-CDMA (direct sequence code division multiple access) signals in time-varying multipath channels. The time-varying channel is assumed to be described by a complex exponential basis expansion model (CE-BEM). We first extend a recently proposed MSLP approach to blind channel estimation for time-varying SIMO (single-input multiple-output) systems, to time-varying MIMO systems in order to define a "signal" subspace. Then, the knowledge of the spreading code of a desired user is exploited in conjunction with the signal subspace to estimate the time-varying channel of the desired user. Sufficient conditions for channel identifiability are investigated. An illustrative simulation example is provided.