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An accurate, closed-form expression for the bit error rate (BER) of the space-time block coding (STBC) multicarrier code-division multiple-access (MC-CDMA) system with imperfect channel estimation is derived by using moment generating functions (MGF), and the accuracy of which is verified by computer simulations. In this paper, the effect of errors in the channel estimation on the transmit diversity based on Alamouti's STBC for a downlink MC-CDMA is studied. Two transmitting antennas at the base station and one receiving antenna at mobile station are engaged, however, the extension to the more general cases with an arbitary number of antennas is straightforward. In the case of imperfect channel estimation, it is shown that the BER performance for the MIMO MC-CDMA system is significantly degraded by the interference, introduced by the receiver channel estimation errors.