Performance analysis of closed-loop transmit diversity in the presence of feedback errors

Transmit diversity techniques have received a lot of attention recently, and open-loop and closed-loop down-link transmit diversity modes for two transmit antennas have been included into 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. In this paper, 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 co-phasing algorithms, are discussed in more detail to verify the results.