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This paper addresses the estimation problem of carrier frequency offset (CFO) in the downlink transmission of space-time block-coded multicarrier code-division multiple-access (STBC MC-CDMA) systems over multipath fading. This study proposes a multiply constrained minimum output energy (MCMOE)-based blind CFO estimator, which is simply assisted by the presented correlation matrix approach to efficiently achieve the CFO estimate. We formulate a two-level CFO estimator by optimizing the receiver output power, as well as the data correlation matrix. At the first level, all possible CFO candidates are found by evaluating the well-defined estimated merit figure. Then, exploiting multiple constraints in the design of the MCMOE receiver, a criterion is used in level two to determine the exact CFO estimate. Numerical results are presented to verify that both precise CFO estimation and reliable error performance can be achieved, even when the channel is dominated by noise because the impact of CFO on the output signal-to-interference-plus-noise ratio (SINR) and bit error rate (BER) are effectively removed by the proposed CFO estimator.