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A new semiblind channel estimation technique is proposed for space-time coded wideband CDMA systems using aperiodic and possibly multirate spreading codes. Using a decorrelating matched filter, the received signal is projected onto subspaces from which channel parameters and data symbols can be estimated jointly. Exploiting the subspace structure of the WCDMA signaling and the orthogonality of the space-time code, the proposed algorithm provides the least squares channel estimate in closed form. A new identifiability condition is established. The mean square error of the estimated channel is compared with the Cramer-Rao bound, and a bit error rate (BER) expression for the proposed algorithm is compared with differential schemes.