In this paper, a novel blind carrier frequency offset (CFO) estimation is proposed on the basis of the linearly constrained optimization for the uplink transmission of space–time block‐coded multicarrier code division multiple access systems. First, the full‐dimensional spatial‐and‐temporal data are formed to avoid violation of the second‐order statistics in the conventional receiver design. A set of weight vectors is then provided for acquiring each multipath signal from the desired user while the others get rejected. Finally, the estimated CFO is obtained in accordance with maximizing the well‐defined measurement function, which is formulated by collecting all the output powers of the receiver. A space–time averaging technique is also proposed to enhance the robustness to the finite sample effect. Simulation study confirms that with the proposed CFO estimator used in the preceding, the receiver can successfully achieve the same performance of the optimal receiver working in the absence of CFO. Copyright © 2014 John Wiley & Sons, Ltd.