On the Performance of Closed-Loop Transmit Diversity with Noisy Channel Estimates

In this paper, closed-form expressions of the bit error probability of closed-loop transmit diversity (CLTD) schemes with two transmit antennas and noisy channel estimates in time-varying Rayleigh fading channels are derived. Two CLTD schemes considered are the phase-only CLTD (PO-CLTD), where the transmit antennas transmit with the same power, and the phase-amplitude CLTD (PA-CLTD), where the transmit antennas can transmit with different powers. The results have indicated that, with the same channel estimation accuracy, PA-CLTD generally performs slightly better than PO-CLTD. We have also compared the performance of PA-CLTD with the performance of a system without transmit diversity and the performance of a system with the Alamouti space-time code employing the linear-combining decoder. The results have illustrated that, PA-CLTD is outperformed by the other two systems when the pilot SNR is very small and the Doppler spread is large.