This paper addresses the problem of blindly estimating the carrier offset and channel response in the uplink of multiuser CDMA systems having large variation in carrier offset. Two blind subspace-based estimation methods, namely exact determinant minimization method (EDMM) and approximate determinant minimization method (ADMM) are proposed, which exploit the orthogonality between the signal and noise subspaces. The performance of the proposed methods is compared with the available solution using generalized eigenvalue problem method (GEVPM). Simulation results are given to show that the proposed methods give better performance than the GEVPM and have a wider acquisition range for the carrier offset