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

In this paper, a bit-error-rate (BER) analysis for closed-loop transmit div ersity in a time-selective Rayleigh fading channel containing feedback dela y is presented. In the absence of feedback delay, closed-loop transmit dive rsity always outperforms open-loop transmit for a given transmitted signal energy. This is no longer true in the presence of feedback delay. We derive closed-form expressions of the average BER for this case assuming QPSK and BPSK signaling. The results of the analysis are instrumental for comparing closed-loop with open-loop schemes under given operating conditions. In pa rticular, we demonstrate that, for a given transmitted energy and number of transmit antennas, open-loop outperforms closed-loop at sufficiently fast channel fading. We also show that, for a given transmitted signal energy an d fading rate, closed-loop outperforms open-loop for sufficiently large num bers of transmit antennas while the total average transmitted signal energy is kept constant. For some special cases, closed-form expressions for the fading rate at which the performance of open-loop is equal to closed-loop a re obtained.