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This paper addresses the problem on blindly estimating the channel impulse response (CIR) and the carrier frequency offset (CFO) in the uplink transmissions of multiuser code division multiple access system. Two blind subspace-based CIR and CFO estimation methods, namely, the exact determinant minimization method and the approximate determinant minimization method, are proposed. The performance of the proposed methods is compared with the available solution based on the generalized eigenvalue problem method (GEVPM). The computational complexity of the proposed methods is compared with that of GEVPM and the estimator proposed by Li and Liu. Simulation results are given to show that the proposed methods give better performance than the GEVPM and have a wide CFO acquisition range.