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Transmit diversity techniques have received a lot of attention recently, and open-loop and closed-loop downlink transmit diversity modes for two transmit antennas have been included in 3GPP WCDMA release 4. System capacity can be increased from that of open-loop modes if the transmitter is equipped with additional side information of the downlink channel. In a frequency division duplex system, this means that the receiver has to provide the information through a feedback mechanism. We study the performance loss caused by feedback errors using the bit error probability as a performance measure. It is shown that the asymptotic diversity of closed-loop schemes is reduced to one in the presence of feedback errors, i.e., the performance is similar to a single transmit antenna system with some SNR gain. The proof is given in a very general manner and it is valid for a large variety of feedback schemes. Two example schemes, selection and cophasing algorithms, are discussed in more detail to verify the results.