A new blind channel estimation technique is proposed for space-time coded wideband CDMA systems using aperiodic and possibly multirate spreading codes. Using a decorrelating front end, the received signal is projected onto a subspace from which channel parameters can be estimated up to a rotational ambiguity. Exploiting the subspace structure of the WCDMA signaling and the orthogonality of the unitary space-time codes, the proposed algorithm provides a blind channel estimate via least squares. A new identifiability condition is established under the assumption that the system is not heavily loaded. The mean square error of the estimated channel is compared with the Cramér-Rao bound, and the bit error rate (BER) performance of the proposed algorithm is compared with that of differential schemes.