A new semi-blind channel estimation technique is proposed for space-time coded wideband CDMA systems using aperiodic and possibly multirate spreading codes. Exploiting the subspace structure of the WCDMA signaling and the orthogonality of the spacetime code, the proposed algorithm provides the least squares channel estimate in closed form. Using a decorrelating matched filter, the proposed method projects the received signal into subspaces from which channel parameters and data symbols can be estimated jointly. A new blind identifiability condition is established. The mean square error of the estimated channel is compared with the Cramér-Rao bound, and bit error rate (BER) is assessed through Monte Carlo simulation.