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This paper addresses the problem of joint estimation of carrier frequency offset (CFO) and channel impulse response (CIR) in the uplink transmission of multicarrier code-division multiple-access (MC-CDMA) systems. A subspace-based blind estimator is proposed, which only uses the received signal and the desired user's spreading code to estimate the CFO and CIR. The CFO is estimated using a one-dimensional linear search where the objective of the search is to minimize the determinant of a low dimensional matrix and the CIR is estimated as the unit-norm eigenvector corresponding to the minimum eigenvalue of this matrix. The identifiability of the CFO and CIR estimates is investigated by imposing asymptotic constraints on the spreading codes. Although the cost function used by the proposed estimator is nonlinear and nonconvex, it is locally convex in the neighborhood of the true CFO value. This property is used to formulate a simple two-stage CFO estimator. In the first stage, a coarse search is performed to lock into the local convexity region. Then, an adaptive algorithm is used in the second stage to finetune the CFO estimate. The ldquolinearizedrdquo proposed estimator is shown to be unbiased. The simulation results show that the proposed estimator's performance is close to the Cramer-Rao lower bound (CRLB).